commit 11ff7b79b463e3e9e60155cb98414fc6a56d8a6a Author: NotBigGhost Date: Fri Aug 14 16:37:13 2026 +0300 Начальный коммит: Vulkan-редактор SimVulcan + исследование KBC-LBM Состояние на момент заведения репозитория. C++ приложение (src/, shaders/, tests/) — минимальный редактор 3D-моделей на Vulkan 1.3: орбитальная камера, три опорные сетки через начало координат, загрузка .obj с режимами отображения. Весь Vulkan изолирован в src/vk/. Исследование (docs/) — оригинальные статьи по KBC (docs/origins) и Python-решатель D2Q9 KBC-N1 с AMR 2x и SDF+Bouzidi (docs/theory). В решателе перед коммитом исправлены дефекты, найденные сверкой с первоисточниками: относительный порог знаменателя энтропийного стабилизатора (абсолютный вырождал KBC в LBGK на 77-99% узлов), заворот вход/выход в углах домена, диагностика средней плотности по фиктивным узлам тела, зашитый refine=2. Подробности — docs/theory/solver_2x_sdf/README.md. Co-Authored-By: Claude Opus 5 diff --git a/.gitattributes b/.gitattributes new file mode 100644 index 0000000..be9fe28 --- /dev/null +++ b/.gitattributes @@ -0,0 +1,24 @@ +# Детерминированные переводы строк. У пользователя core.autocrlf=true (дефолт Git for Windows), +# из-за чего git ругался на LF→CRLF почти на каждом файле. Проект собирается ещё под Linux и +# macOS (см. CMakePresets.json), поэтому в репозитории храним LF, а в рабочей копии Windows +# git сам развернёт CRLF там, где это нужно. +* text=auto eol=lf + +# .bat обязан быть CRLF — иначе cmd.exe спотыкается на многострочных конструкциях +*.bat text eol=crlf + +# Бинарные: не диффать, не трогать переводы строк +*.png binary +*.gif binary +*.pdf binary +*.npz binary +*.spv binary +*.bin binary +*.exe binary + +# Wavefront OBJ — текст (ASCII), но диффы бессмысленны +*.obj text diff=none + +# Ноутбуки: слияние по строкам всегда даёт мусор из-за outputs/метаданных — +# конфликт решается вручную, а не авто-мержем +*.ipynb -merge diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..95d5975 --- /dev/null +++ b/.gitignore @@ -0,0 +1,55 @@ +# --------------------------------------------------------------------------- +# Сборка +# --------------------------------------------------------------------------- +# Каталог пресетов CMake целиком: объектники, SPIR-V, скопированные assets, +# и _deps — клоны зависимостей через FetchContent (только они ~775 МБ). +/build/ +/out/ +CMakeUserPresets.json # локальные пресеты разработчика, не общие +compile_commands.json # генерится (CMAKE_EXPORT_COMPILE_COMMANDS), часто симлинк в корень + +# Зависимости, если их когда-нибудь начнут класть вручную (сейчас каталог пуст, +# всё тянет FetchContent). Убрать строку, если вендорить их в репозиторий. +/extern/* +!/extern/.gitkeep + +# --------------------------------------------------------------------------- +# Артефакты выполнения приложения +# --------------------------------------------------------------------------- +# SimVulcan пишет их в текущий каталог при запуске (обычно внутри build/, +# но при запуске из другого места окажутся здесь). +imgui.ini +pipeline_cache.bin + +# --------------------------------------------------------------------------- +# Python (docs/theory — исследовательский код) +# --------------------------------------------------------------------------- +__pycache__/ +*.py[cod] +.ipynb_checkpoints/ +.venv/ +venv/ +.pytest_cache/ + +# Числовые сводки демо-прогонов: генерятся скриптами demos_gpu/*.py на GPU-сервере +# (ноутбук цитирует их значения в markdown). Сами прогоны воспроизводимы. +docs/theory/demos_gpu/out/ +docs/theory/solver_2x_sdf/out/ + +# ВАЖНО: docs/theory/figures/ и docs/theory/anim/ НЕ игнорируются намеренно — +# ноутбук kbc_lbm.ipynb их встраивает, и без них он нечитаем на свежем клоне +# (перегенерация требует GPU-сервера). См. заметку о них в README ветки research. + +# --------------------------------------------------------------------------- +# Редакторы и ОС +# --------------------------------------------------------------------------- +.vs/ +.vscode/ +.idea/ +*.user +*.suo +*.swp +*~ +.DS_Store +Thumbs.db +desktop.ini diff --git a/CLAUDE.md b/CLAUDE.md new file mode 100644 index 0000000..ff1832b --- /dev/null +++ b/CLAUDE.md @@ -0,0 +1,202 @@ +# CLAUDE.md + +This file provides guidance to Claude Code (claude.ai/code) when working with code in this repository. + +## Project Overview + +**SimVulcan** is a minimal **Vulkan 1.3 / C++20** 3D model editor. It renders a +3D editor space — three reference grid planes (XY, XZ, YZ) through the origin plus +coloured X/Y/Z axes — viewed through an orbit camera, and loads/displays `.obj` +models with selectable display modes (solid, wireframe, solid + wireframe). + +The C++ side runs no simulation: it is a focused rendering skeleton with an ImGui +interface (a Viewport control panel and a Mesh load panel). The repository *also* +carries an unrelated Python research prototype under `docs/theory/` — see +[Research prototype](#research-prototype-docstheory) below; it is not part of the +CMake build. + +## Build + +Prerequisites: **Vulkan SDK 1.3.290+** (provides `glslangValidator` for offline +shader compilation), **CMake 3.26+**, **Ninja**, a C++20 compiler (MSVC 19.36+, +gcc 11+, clang 14+). On macOS, Vulkan is via MoltenVK (Apple Silicon only). + +```sh +cmake --preset windows-msvc-release +cmake --build --preset windows-msvc-release +``` + +Presets: `windows-msvc-debug`, `windows-msvc-release`, `linux-gcc-release`, +`linux-clang-release`, `macos-arm64-release` (all Ninja, one dir per preset under +`build//`). The first configure fetches dependencies via FetchContent +(GLFW, GLM, volk, vk-bootstrap, VulkanMemoryAllocator, Dear ImGui, spdlog, +tinyobjloader, Catch2) and needs network access. `VK_NO_PROTOTYPES` is set +project-wide; Vulkan entry points load through **volk**. + +Warnings come from `simv_set_warnings` (`/W4 /permissive-`, or +`-Wall -Wextra -Wpedantic -Wshadow -Wold-style-cast …`); they are **not** errors. +`cmake/Sanitizers.cmake` defines `simv_enable_sanitizers` (Debug-only ASan/UBSan) +but no target currently calls it — wire it in manually when chasing memory bugs. + +## Running + +The executable resolves SPIR-V relative to the working directory (`FindSpvPath` +probes `spirv/` and `current_path()/spirv/`). The `SimVulcan` POST_BUILD +step copies the compiled `spirv/` tree and `assets/` next to the executable, so +**run from the executable's own directory** (`build//src/app/`). `main.cpp` +also probes several `../` ancestors for `assets/meshes`. Meshes load at runtime +through the ImGui Mesh panel. + +Running writes two files into the CWD: `pipeline_cache.bin` (serialised +`VkPipelineCache`, reloaded on the next start) and ImGui's `imgui.ini`. Both are +disposable — delete them if pipeline creation or the panel layout misbehaves. + +`ContextOptions::enableValidation` / `enableDebugUtils` default to **true** in +every build config, so the Khronos validation layer is requested even in Release; +messages (error + warning severity) go through spdlog. + +`run.bat` at the repo root is **stale**: it launches +`build/vs2022/src/app/Release/SimVulcan.exe`, a path the Ninja presets never +produce. Do not point users at it without fixing the path first. + +## Tests + +Catch2 unit tests, pure CPU/math (mesh bounds + welding). No GPU required. + +```sh +cmake --build --preset windows-msvc-debug --target simv_tests +ctest --preset windows-msvc-debug +``` + +`windows-msvc-debug` is the only preset with a `testPreset` — for the other +configs, invoke `ctest` in `build//` directly. + +Single test / subset — either through CTest (each `TEST_CASE` is registered +individually by `catch_discover_tests`): + +```sh +ctest --preset windows-msvc-debug -R "WeldVertices" -V +``` + +or by running the binary with a Catch2 name or tag filter: + +```sh +./build/windows-msvc-debug/tests/simv_tests.exe "[decimator]" +./build/windows-msvc-debug/tests/simv_tests.exe --list-tests +``` + +## Architecture + +### Library / target map + +``` +SimVulcan (exe) → simv_core, simv_vk, simv_mesh, simv_editor +simv_core → simv_vk (App owns Window + vk::Renderer; no Vulkan calls) +simv_editor → simv_core, simv_mesh (Camera, input, ImGui panels; no Vulkan) +simv_mesh → simv_core (CPU mesh only; no Vulkan) +simv_vk → third-party (volk, vk-bootstrap, VMA, GLFW, GLM, spdlog, imgui) +simv_shaders → glslangValidator (GLSL → SPIR-V) +``` + +Namespaces follow directories: `simv::core`, `simv::vk`, `simv::mesh`, +`simv::editor`. Each library exports `src/` as its include root, so includes are +written module-qualified (`#include "mesh/Mesh.h"`, `#include "vk/Renderer.h"`). + +### Frame loop + +`main.cpp` creates `core::App`, which owns the `core::Window` and a +`vk::Renderer`, then runs the loop. Each frame `Renderer::DrawFrame` calls the UI +callback (between ImGui NewFrame/Render), then records the scene: grid + mesh into +one dynamic-rendering pass with a depth attachment, followed by ImGui, then +presents (2 frames in flight, sync2 submits). + +`main.cpp` wires the editor via the UI callback: it draws the panels, applies +mouse input to the `editor::Camera`, and pushes the resulting state into the +renderer (`SetViewProj`, `SetRenderMode`, `SetGridVisible`). Mesh loads go through +`MeshLoadPanel`'s callback → `Renderer::SetMeshCpu`. + +### Mesh load path + +`MeshLoadPanel` lists `*.obj` in the mesh directory and kicks off +`mesh::LoadObjAsync` (worker thread, `std::future`). The future is **drained on +the main thread** at the top of `MeshLoadPanel::Draw`, so the `OnLoaded` callback +— and therefore the GPU upload — always runs on the render thread. Loader +exceptions surface as the panel's status string. + +`main.cpp`'s `OnLoaded` welds the mesh (`WeldVertices`, tolerance `1e-4`), logs +the counts, uploads via `SetMeshCpu`, and reframes the camera to the bbox radius. +Despite the file name, `mesh/MeshDecimator.h` implements **only** spatial-hash +vertex welding (collapse near-duplicates, drop degenerate triangles, recompute +bounds) — there is no LOD/decimation. + +### Non-obvious invariants (read before editing) + +- **All Vulkan lives in `src/vk/`.** `core/`, `mesh/`, `editor/` and `app/` make no + Vulkan API calls. `vk::Renderer`'s public header is deliberately Vulkan-free + (pImpl + glm/`RenderMode` only) so `App` can own it without pulling in volk. Keep + it that way — do not leak `Vk*` types into the public interfaces of those modules. +- **Single render pass with depth.** Scene (grid + mesh) and ImGui draw into one + `vkCmdBeginRendering` pass that has both a colour and a `D32_SFLOAT` depth + attachment. The ImGui backend is initialised with `depthAttachmentFormat` set so + its pipeline matches the pass; the depth buffer is recreated with the swapchain. +- **Wireframe needs `fillModeNonSolid`.** `MeshRenderer` builds a fill pipeline and + a `VK_POLYGON_MODE_LINE` pipeline; the line pipeline uses a small depth bias so + the overlay sits on top of the fill. The device feature is requested in `Context`. + Culling is off (`VK_CULL_MODE_NONE`) — loaded models may have mixed winding. +- **Camera is fixed on the origin.** `editor::Camera` orbits (yaw/pitch/distance) + the world origin; loaded models are recentred there via a translate-only model + matrix. Projection uses Vulkan clip space (`GLM_FORCE_DEPTH_ZERO_TO_ONE` + Y flip, + isolated to `Camera.cpp`). +- **Buffers.** `vk::GpuMesh` owns the model's vertex/index buffers (staged upload on + the transfer queue). `GridRenderer` builds a static host-visible line buffer once. + Both scene renderers use only a push constant — no descriptor sets. +- **Push-constant layout is a cross-file contract.** `MeshRenderer.cpp`'s anonymous + `MeshPC { mat4 mvp; vec4 color; }` must stay byte-identical to the + `push_constant` block in `mesh.vert`/`mesh.frag`; `color.a` is a *flag*, not + alpha (1 = flat-shaded, 0 = constant colour for wireframe). `GridRenderer` pushes + a bare `mat4` (vertex stage only). Change either side and you must change both. +- **Swapchain recreation rebuilds sync objects.** `RecreateSwapDependent` recreates + the per-frame `imageAvailable` semaphores (a failed acquire can leave one + signalled) *and* the per-swapchain-image `renderFinished` semaphores (the image + count may change), then re-ensures both pipelines. Keep that ordering if you + touch resize handling. +- **Mesh upload stalls the device.** `SetMeshCpu`/`ClearMesh` call `WaitIdle` + before touching `GpuMesh` — acceptable because loads are rare; do not copy that + pattern into per-frame paths. + +### Shaders + +GLSL under `shaders/editor/` (`mesh.{vert,frag}`, `grid.{vert,frag}`). `simv_shaders` +compiles each to `build//spirv/editor/.spv` targeting `vulkan1.3`, +with `shaders/` as the `-I` root (so `#include "common/foo.glsl"` would resolve). +Adding a shader under that globbed dir is picked up automatically +(`CONFIGURE_DEPENDS`). `mesh.frag` reconstructs a flat normal from screen-space +derivatives, so the vertex stream carries only positions (tight `float3`, one +binding, one attribute). + +## Logging + +`simv::core::Logger` (spdlog-backed, singleton) with category-based throttling. +Log via `LogFmt(LogCategory, LogLevel, fmt, args...)`. Categories: `Core`, +`Vulkan`, `MeshIO`, `UI`, `Test`. Per-category level, throttle interval and +on/off are settable at runtime (`SetMinLevel` / `SetThrottle` / `SetEnabled`). +Some low-level Vulkan code still calls `spdlog::` directly. + +## Research prototype (`docs/theory/`) + +Separate from the C++ application and from the CMake build: a Python **Lattice +Boltzmann (D2Q9, KBC-N1)** research codebase — cylinder flow with a ×2 nested AMR +patch and SDF+Bouzidi boundaries. **GPU/CuPy only, no CPU fallback.** Its +documentation and the running experiment log are in Russian. + +- `docs/theory/solver_2x_sdf/` — the component-split solver (`run.py`, + `run_blockage.py`, `run_factors.py`); its `README.md` is the authoritative + status/experiment log and maps every file to the physics it owns. +- `docs/theory/demos_gpu/` — demo runs that produce the notebook's figures/GIFs; + they import physics from `solver_2x_sdf`, never duplicate it. +- `docs/theory/kbc_lbm.ipynb` — the write-up; it embeds pre-rendered artefacts and + does not execute the simulations. +- `docs/origins/` — source PDFs behind the theory. + +Do not fold this into the CMake build, and do not treat it as dead code — it is +active research with a documented experiment history. diff --git a/CMakeLists.txt b/CMakeLists.txt new file mode 100644 index 0000000..f622733 --- /dev/null +++ b/CMakeLists.txt @@ -0,0 +1,139 @@ +cmake_minimum_required(VERSION 3.26) + +project(SimVulcan + VERSION 0.1.0 + DESCRIPTION "Vulkan 3D editor: orbit camera, reference grid, OBJ model viewer" + LANGUAGES CXX C +) + +set(CMAKE_CXX_STANDARD 20) +set(CMAKE_CXX_STANDARD_REQUIRED ON) +set(CMAKE_CXX_EXTENSIONS OFF) +set(CMAKE_POSITION_INDEPENDENT_CODE ON) + +list(APPEND CMAKE_MODULE_PATH "${CMAKE_SOURCE_DIR}/cmake") + +include(CompilerWarnings) +include(Sanitizers) +include(VulkanSetup) +include(ShaderCompile) +include(FetchContent) + +# ---------------------------------------------------------------------------- +# External dependencies (FetchContent — pinned commits) +# ---------------------------------------------------------------------------- +set(FETCHCONTENT_QUIET OFF) +set(BUILD_SHARED_LIBS OFF CACHE BOOL "" FORCE) + +# GLFW +set(GLFW_BUILD_EXAMPLES OFF CACHE BOOL "" FORCE) +set(GLFW_BUILD_TESTS OFF CACHE BOOL "" FORCE) +set(GLFW_BUILD_DOCS OFF CACHE BOOL "" FORCE) +FetchContent_Declare(glfw + GIT_REPOSITORY https://github.com/glfw/glfw.git + GIT_TAG 3.4 +) + +# GLM +FetchContent_Declare(glm + GIT_REPOSITORY https://github.com/g-truc/glm.git + GIT_TAG 1.0.1 +) + +# volk (lazy Vulkan loader) +FetchContent_Declare(volk + GIT_REPOSITORY https://github.com/zeux/volk.git + GIT_TAG 1.3.295 +) + +# vk-bootstrap +FetchContent_Declare(vk-bootstrap + GIT_REPOSITORY https://github.com/charles-lunarg/vk-bootstrap.git + GIT_TAG v1.3.295 +) + +# Vulkan Memory Allocator +FetchContent_Declare(VulkanMemoryAllocator + GIT_REPOSITORY https://github.com/GPUOpen-LibrariesAndSDKs/VulkanMemoryAllocator.git + GIT_TAG v3.1.0 +) + +# Dear ImGui (we wrap it in a small CMake target ourselves below). +FetchContent_Declare(imgui + GIT_REPOSITORY https://github.com/ocornut/imgui.git + GIT_TAG v1.91.5-docking +) + +# spdlog +set(SPDLOG_BUILD_SHARED OFF CACHE BOOL "" FORCE) +set(SPDLOG_FMT_EXTERNAL OFF CACHE BOOL "" FORCE) +FetchContent_Declare(spdlog + GIT_REPOSITORY https://github.com/gabime/spdlog.git + GIT_TAG v1.14.1 +) + +# tinyobjloader (header-only) +FetchContent_Declare(tinyobjloader + GIT_REPOSITORY https://github.com/tinyobjloader/tinyobjloader.git + GIT_TAG v2.0.0rc13 +) + +# Catch2 +FetchContent_Declare(Catch2 + GIT_REPOSITORY https://github.com/catchorg/Catch2.git + GIT_TAG v3.7.1 +) + +FetchContent_MakeAvailable( + glfw glm volk vk-bootstrap VulkanMemoryAllocator + imgui spdlog tinyobjloader Catch2 +) + +# ---------------------------------------------------------------------------- +# ImGui static library (needs explicit target — official repo has none) +# ---------------------------------------------------------------------------- +add_library(imgui STATIC + ${imgui_SOURCE_DIR}/imgui.cpp + ${imgui_SOURCE_DIR}/imgui_demo.cpp + ${imgui_SOURCE_DIR}/imgui_draw.cpp + ${imgui_SOURCE_DIR}/imgui_tables.cpp + ${imgui_SOURCE_DIR}/imgui_widgets.cpp + ${imgui_SOURCE_DIR}/backends/imgui_impl_glfw.cpp + ${imgui_SOURCE_DIR}/backends/imgui_impl_vulkan.cpp +) +target_include_directories(imgui PUBLIC + ${imgui_SOURCE_DIR} + ${imgui_SOURCE_DIR}/backends +) +target_link_libraries(imgui PUBLIC glfw Vulkan::Headers volk) +# Have ImGui's Vulkan backend pick up function pointers from volk directly, +# instead of asking us to load them via ImGui_ImplVulkan_LoadFunctions. +target_compile_definitions(imgui PUBLIC + IMGUI_IMPL_VULKAN_NO_PROTOTYPES + IMGUI_IMPL_VULKAN_USE_VOLK + VK_NO_PROTOTYPES +) + +# Catch2 helpers (catch_discover_tests). +include(CTest) +include(${Catch2_SOURCE_DIR}/extras/Catch.cmake) + +# ---------------------------------------------------------------------------- +# Project targets +# ---------------------------------------------------------------------------- +add_subdirectory(shaders) # produces simv_shaders custom target +add_subdirectory(src/core) +add_subdirectory(src/vk) +add_subdirectory(src/mesh) +add_subdirectory(src/editor) +add_subdirectory(src/app) +enable_testing() +add_subdirectory(tests) + +message(STATUS "") +message(STATUS "SimVulcan ${PROJECT_VERSION} configured.") +message(STATUS " Build type: ${CMAKE_BUILD_TYPE}") +message(STATUS " C++ std: ${CMAKE_CXX_STANDARD}") +message(STATUS " Vulkan: ${Vulkan_VERSION}") +message(STATUS " Generator: ${CMAKE_GENERATOR}") +message(STATUS "") diff --git a/CMakePresets.json b/CMakePresets.json new file mode 100644 index 0000000..9e33712 --- /dev/null +++ b/CMakePresets.json @@ -0,0 +1,67 @@ +{ + "version": 6, + "cmakeMinimumRequired": { "major": 3, "minor": 26, "patch": 0 }, + "configurePresets": [ + { + "name": "base", + "hidden": true, + "generator": "Ninja", + "binaryDir": "${sourceDir}/build/${presetName}", + "cacheVariables": { + "CMAKE_EXPORT_COMPILE_COMMANDS": "ON" + } + }, + { + "name": "windows-msvc-debug", + "inherits": "base", + "cacheVariables": { "CMAKE_BUILD_TYPE": "Debug" }, + "condition": { "type": "equals", "lhs": "${hostSystemName}", "rhs": "Windows" } + }, + { + "name": "windows-msvc-release", + "inherits": "base", + "cacheVariables": { "CMAKE_BUILD_TYPE": "Release" }, + "condition": { "type": "equals", "lhs": "${hostSystemName}", "rhs": "Windows" } + }, + { + "name": "linux-gcc-release", + "inherits": "base", + "cacheVariables": { + "CMAKE_BUILD_TYPE": "Release", + "CMAKE_C_COMPILER": "gcc", + "CMAKE_CXX_COMPILER": "g++" + }, + "condition": { "type": "equals", "lhs": "${hostSystemName}", "rhs": "Linux" } + }, + { + "name": "linux-clang-release", + "inherits": "base", + "cacheVariables": { + "CMAKE_BUILD_TYPE": "Release", + "CMAKE_C_COMPILER": "clang", + "CMAKE_CXX_COMPILER": "clang++" + }, + "condition": { "type": "equals", "lhs": "${hostSystemName}", "rhs": "Linux" } + }, + { + "name": "macos-arm64-release", + "inherits": "base", + "cacheVariables": { + "CMAKE_BUILD_TYPE": "Release", + "CMAKE_OSX_ARCHITECTURES": "arm64" + }, + "condition": { "type": "equals", "lhs": "${hostSystemName}", "rhs": "Darwin" } + } + ], + "buildPresets": [ + { "name": "windows-msvc-debug", "configurePreset": "windows-msvc-debug" }, + { "name": "windows-msvc-release", "configurePreset": "windows-msvc-release" }, + { "name": "linux-gcc-release", "configurePreset": "linux-gcc-release" }, + { "name": "linux-clang-release", "configurePreset": "linux-clang-release" }, + { "name": "macos-arm64-release", "configurePreset": "macos-arm64-release" } + ], + "testPresets": [ + { "name": "windows-msvc-debug", "configurePreset": "windows-msvc-debug", + "output": { "outputOnFailure": true } } + ] +} diff --git a/README.md b/README.md new file mode 100644 index 0000000..e9ab7fd --- /dev/null +++ b/README.md @@ -0,0 +1,61 @@ +# SimVulcan + +A minimal Vulkan 1.3 / C++20 **3D model editor**: an orbit camera over three +reference grid planes through the origin, with `.obj` model loading and display. + +## Features + +* Orbit camera — drag to rotate around the centre, wheel to zoom, and Front / Top + / Side buttons to align the view to the principal planes. +* A 3D editor space: three grid planes (XY, XZ, YZ) and coloured X/Y/Z axes meeting + at the origin. +* `.obj` loading with three display modes — solid (flat-shaded), wireframe, and + solid + wireframe overlay. +* ImGui interface (Viewport controls + Mesh load panel). + +All Vulkan code is isolated in `src/vk/`; the rest of the app is Vulkan-free. + +## Targets + +* Windows x64 (MSVC / clang-cl) +* Linux x64 (gcc / clang) +* macOS arm64 (Apple Silicon, via MoltenVK) + +## Prerequisites + +* Vulkan SDK 1.3.290+ (`https://vulkan.lunarg.com/`) +* CMake 3.26+ +* Ninja +* C++20 compiler (MSVC 19.36+, gcc 11+, clang 14+) + +## Build + +```sh +cmake --preset windows-msvc-release +cmake --build --preset windows-msvc-release +``` + +Run from the executable's own directory (`build//src/app/`) so it finds +the `spirv/` and `assets/` trees copied next to it. + +## Tests + +```sh +cmake --build --preset windows-msvc-debug --target simv_tests +ctest --preset windows-msvc-debug +``` + +## Layout + +``` +src/ + core/ Logger, Window, App (orchestration, Vulkan-free) + vk/ All Vulkan: Context, Swapchain, Buffer, Image, Shader, GpuMesh, + Renderer (frame loop + depth + ImGui), MeshRenderer, GridRenderer + mesh/ CPU mesh: tinyobjloader + welding (no Vulkan) + editor/ Camera, mouse input, EditorUI + MeshLoadPanel (ImGui, no Vulkan) + app/ main.cpp +shaders/ + editor/ mesh + grid vertex/fragment shaders (GLSL → SPIR-V at build time) +tests/ Catch2 unit tests (mesh math) +``` diff --git a/assets/meshes/Cube.obj b/assets/meshes/Cube.obj new file mode 100644 index 0000000..1d5cd52 --- /dev/null +++ b/assets/meshes/Cube.obj @@ -0,0 +1,70 @@ +mtllib C:\Users\ivan\Downloads\Cube.mtl +o Solid_1 +v -0.50000000 0.50000000 1 +v -0.50000000 -0.50000000 1 +v 0.50000000 -0.50000000 1 +v 0.50000000 0.50000000 1 +v -0.50000000 -0.50000000 0 +v 0.50000000 -0.50000000 0 +v -0.50000000 0.50000000 0 +v 0.50000000 0.50000000 0 +vt 0 1 +vt 0 0 +vt 1 0 +vt 1 1 +vt 1 0 +vt 1 1 +vt 0 1 +vt 0 0 +vt 0 1 +vt 0 0 +vt 1 0 +vt 1 1 +vt 0 1 +vt 0 0 +vt 1 0 +vt 1 1 +vt 1 1 +vt 0 1 +vt 0 0 +vt 1 0 +vt 0 0 +vt 1 0 +vt 1 1 +vt 0 1 +vn 0 0 1 +vn 0 0 1 +vn 0 0 1 +vn 0 0 1 +vn 0 -1 0 +vn 0 -1 0 +vn 0 -1 0 +vn 0 -1 0 +vn -1 0 0 +vn -1 0 0 +vn -1 0 0 +vn -1 0 0 +vn 0 1 0 +vn 0 1 0 +vn 0 1 0 +vn 0 1 0 +vn 0 0 -1 +vn 0 0 -1 +vn 0 0 -1 +vn 0 0 -1 +vn 1 0 0 +vn 1 0 0 +vn 1 0 0 +vn 1 0 0 +f 1/1/1 2/2/2 3/3/3 +f 3/3/3 4/4/4 1/1/1 +f 5/5/5 6/6/6 3/7/7 +f 3/7/7 2/8/8 5/5/5 +f 7/9/9 5/10/10 2/11/11 +f 2/11/11 1/12/12 7/9/9 +f 8/13/13 7/14/14 1/15/15 +f 1/15/15 4/16/16 8/13/13 +f 7/17/17 8/18/18 6/19/19 +f 6/19/19 5/20/20 7/17/17 +f 3/21/21 6/22/22 8/23/23 +f 8/23/23 4/24/24 3/21/21 diff --git a/assets/meshes/Cube1.obj b/assets/meshes/Cube1.obj new file mode 100644 index 0000000..1d5cd52 --- /dev/null +++ b/assets/meshes/Cube1.obj @@ -0,0 +1,70 @@ +mtllib C:\Users\ivan\Downloads\Cube.mtl +o Solid_1 +v -0.50000000 0.50000000 1 +v -0.50000000 -0.50000000 1 +v 0.50000000 -0.50000000 1 +v 0.50000000 0.50000000 1 +v -0.50000000 -0.50000000 0 +v 0.50000000 -0.50000000 0 +v -0.50000000 0.50000000 0 +v 0.50000000 0.50000000 0 +vt 0 1 +vt 0 0 +vt 1 0 +vt 1 1 +vt 1 0 +vt 1 1 +vt 0 1 +vt 0 0 +vt 0 1 +vt 0 0 +vt 1 0 +vt 1 1 +vt 0 1 +vt 0 0 +vt 1 0 +vt 1 1 +vt 1 1 +vt 0 1 +vt 0 0 +vt 1 0 +vt 0 0 +vt 1 0 +vt 1 1 +vt 0 1 +vn 0 0 1 +vn 0 0 1 +vn 0 0 1 +vn 0 0 1 +vn 0 -1 0 +vn 0 -1 0 +vn 0 -1 0 +vn 0 -1 0 +vn -1 0 0 +vn -1 0 0 +vn -1 0 0 +vn -1 0 0 +vn 0 1 0 +vn 0 1 0 +vn 0 1 0 +vn 0 1 0 +vn 0 0 -1 +vn 0 0 -1 +vn 0 0 -1 +vn 0 0 -1 +vn 1 0 0 +vn 1 0 0 +vn 1 0 0 +vn 1 0 0 +f 1/1/1 2/2/2 3/3/3 +f 3/3/3 4/4/4 1/1/1 +f 5/5/5 6/6/6 3/7/7 +f 3/7/7 2/8/8 5/5/5 +f 7/9/9 5/10/10 2/11/11 +f 2/11/11 1/12/12 7/9/9 +f 8/13/13 7/14/14 1/15/15 +f 1/15/15 4/16/16 8/13/13 +f 7/17/17 8/18/18 6/19/19 +f 6/19/19 5/20/20 7/17/17 +f 3/21/21 6/22/22 8/23/23 +f 8/23/23 4/24/24 3/21/21 diff --git a/assets/meshes/cow.obj b/assets/meshes/cow.obj new file mode 100644 index 0000000..6f20d28 --- /dev/null +++ b/assets/meshes/cow.obj @@ -0,0 +1,19993 @@ +# XSI Wavefront OBJ Export v3.0 +# File Created: Mon Apr 20 17:43:17 2015 +# XSI Version: 13.0.114.0 +mtllib cow.mtl + +o tornado_cow +# Hierarchy (from self to top father) +g tornado_cow + +#begin 2451 vertices +v 1.366384 10.958115 9.840135 +v 1.294512 10.550116 10.011008 +v 1.360174 11.697365 10.242814 +v 0.000000 4.565749 -8.994914 +v 1.228112 11.724024 10.721053 +v 1.053948 12.299612 10.569302 +v 0.723875 12.106613 11.171085 +v 0.404268 12.394442 11.116978 +v 1.189143 10.428855 10.751476 +v 1.253514 10.539756 10.364076 +v 1.237481 10.292868 10.251351 +v 1.164335 10.108447 10.613352 +v 1.429508 11.728526 9.345811 +v -0.365580 4.819098 -9.010605 +v 1.416293 11.217343 9.511442 +v 1.442518 12.140046 9.156790 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+l 784 783 +l 782 783 +l 882 881 +l 880 881 +l 980 979 +l 978 979 +l 1078 1077 +l 1076 1077 +l 1176 1175 +l 1174 1175 +l 3582 4082 +l 9304 9305 +l 9306 9303 +l 6213 6215 +l 6016 6280 +l 9181 9178 +l 6086 6092 +l 9214 9217 +l 6098 6099 +l 6216 6218 +l 3197 10673 +l 6017 6279 +l 6018 6326 diff --git a/cmake/CompilerWarnings.cmake b/cmake/CompilerWarnings.cmake new file mode 100644 index 0000000..8327643 --- /dev/null +++ b/cmake/CompilerWarnings.cmake @@ -0,0 +1,20 @@ +function(simv_set_warnings TARGET) + if(MSVC) + target_compile_options(${TARGET} PRIVATE + /W4 /permissive- /Zc:preprocessor /Zc:__cplusplus + /wd4100 # unused parameter (interfaces have many) + ) + target_compile_definitions(${TARGET} PRIVATE + _CRT_SECURE_NO_WARNINGS + NOMINMAX + WIN32_LEAN_AND_MEAN + ) + else() + target_compile_options(${TARGET} PRIVATE + -Wall -Wextra -Wpedantic + -Wno-unused-parameter + -Wshadow -Wnon-virtual-dtor -Wold-style-cast + -Wcast-align -Wunused -Woverloaded-virtual + ) + endif() +endfunction() diff --git a/cmake/Sanitizers.cmake b/cmake/Sanitizers.cmake new file mode 100644 index 0000000..aca9a69 --- /dev/null +++ b/cmake/Sanitizers.cmake @@ -0,0 +1,11 @@ +function(simv_enable_sanitizers TARGET) + if(NOT CMAKE_BUILD_TYPE STREQUAL "Debug") + return() + endif() + if(MSVC) + target_compile_options(${TARGET} PRIVATE /fsanitize=address) + else() + target_compile_options(${TARGET} PRIVATE -fsanitize=address,undefined -fno-omit-frame-pointer) + target_link_options (${TARGET} PRIVATE -fsanitize=address,undefined) + endif() +endfunction() diff --git a/cmake/ShaderCompile.cmake b/cmake/ShaderCompile.cmake new file mode 100644 index 0000000..888f62f --- /dev/null +++ b/cmake/ShaderCompile.cmake @@ -0,0 +1,50 @@ +# Compile GLSL (.comp/.vert/.frag) into SPIR-V at build time. +# +# Usage: +# simv_compile_shaders(simv_shaders +# shaders/editor/mesh.vert +# shaders/editor/mesh.frag +# INCLUDES shaders +# ) +# +# Produces ${CMAKE_BINARY_DIR}/spirv//.spv as a custom target. + +function(simv_compile_shaders TARGET) + cmake_parse_arguments(SCS "" "" "INCLUDES" ${ARGN}) + + set(SOURCES ${SCS_UNPARSED_ARGUMENTS}) + set(SPIRV_OUT_DIR "${CMAKE_BINARY_DIR}/spirv") + file(MAKE_DIRECTORY "${SPIRV_OUT_DIR}") + + set(SPV_OUTPUTS "") + foreach(SRC IN LISTS SOURCES) + get_filename_component(SHADER_NAME "${SRC}" NAME) + file(RELATIVE_PATH REL_PATH "${CMAKE_CURRENT_SOURCE_DIR}" "${SRC}") + get_filename_component(REL_DIR "${REL_PATH}" DIRECTORY) + set(OUT_PATH "${SPIRV_OUT_DIR}/${REL_DIR}/${SHADER_NAME}.spv") + + get_filename_component(OUT_DIR "${OUT_PATH}" DIRECTORY) + file(MAKE_DIRECTORY "${OUT_DIR}") + + set(INCLUDE_FLAGS "") + foreach(INC IN LISTS SCS_INCLUDES) + # glslangValidator requires -I with NO whitespace. + list(APPEND INCLUDE_FLAGS "-I${INC}") + endforeach() + + add_custom_command( + OUTPUT "${OUT_PATH}" + COMMAND "${Vulkan_GLSLANG_VALIDATOR_EXECUTABLE}" -V --target-env vulkan1.3 + ${INCLUDE_FLAGS} -o "${OUT_PATH}" "${SRC}" + DEPENDS "${SRC}" + COMMENT "GLSL → SPIR-V: ${REL_PATH}" + VERBATIM + ) + list(APPEND SPV_OUTPUTS "${OUT_PATH}") + endforeach() + + add_custom_target(${TARGET} ALL DEPENDS ${SPV_OUTPUTS}) + set_target_properties(${TARGET} PROPERTIES + SIMV_SPIRV_DIR "${SPIRV_OUT_DIR}" + ) +endfunction() diff --git a/cmake/VulkanSetup.cmake b/cmake/VulkanSetup.cmake new file mode 100644 index 0000000..190888b --- /dev/null +++ b/cmake/VulkanSetup.cmake @@ -0,0 +1,17 @@ +# Locate Vulkan SDK + glslangValidator (needed for offline shader compilation). +# On macOS this expects MoltenVK to be present (provided by Vulkan SDK 1.3.290+). +find_package(Vulkan REQUIRED COMPONENTS glslangValidator) + +if(NOT Vulkan_glslangValidator_FOUND) + message(FATAL_ERROR "glslangValidator not found. Install Vulkan SDK from https://vulkan.lunarg.com/") +endif() + +message(STATUS "Vulkan version: ${Vulkan_VERSION}") +message(STATUS "Vulkan include dir: ${Vulkan_INCLUDE_DIRS}") +message(STATUS "glslangValidator: ${Vulkan_GLSLANG_VALIDATOR_EXECUTABLE}") + +if(APPLE) + # MoltenVK ships with the SDK; it's loaded as ICD at runtime, no link change needed, + # but we set MVK_CONFIG_USE_METAL_PRIVATE_API=0 in env when running. + message(STATUS "macOS detected — Vulkan via MoltenVK (Apple Silicon arm64 only)") +endif() diff --git a/docs/origins/Curved_geometries.pdf b/docs/origins/Curved_geometries.pdf new file mode 100644 index 0000000..cc7c42d Binary files /dev/null and b/docs/origins/Curved_geometries.pdf differ diff --git a/docs/origins/KBC_2d_realization.pdf b/docs/origins/KBC_2d_realization.pdf new file mode 100644 index 0000000..d3c92ba Binary files /dev/null and b/docs/origins/KBC_2d_realization.pdf differ diff --git a/docs/origins/KBC_3d_realization(2015).pdf b/docs/origins/KBC_3d_realization(2015).pdf new file mode 100644 index 0000000..9d77218 Binary files /dev/null and b/docs/origins/KBC_3d_realization(2015).pdf differ diff --git a/docs/origins/KBC_3d_realization(2024).pdf b/docs/origins/KBC_3d_realization(2024).pdf new file mode 100644 index 0000000..8861bd4 Binary files /dev/null and b/docs/origins/KBC_3d_realization(2024).pdf differ diff --git a/docs/origins/Moving_and_deforming_geometries.pdf b/docs/origins/Moving_and_deforming_geometries.pdf new file mode 100644 index 0000000..d285ab1 Binary files /dev/null and b/docs/origins/Moving_and_deforming_geometries.pdf differ diff --git a/docs/origins/Origin_principles.pdf b/docs/origins/Origin_principles.pdf new file mode 100644 index 0000000..8127a6e Binary files /dev/null and b/docs/origins/Origin_principles.pdf differ diff --git a/docs/theory/_amr_anims.py b/docs/theory/_amr_anims.py new file mode 100644 index 0000000..b1de8c0 --- /dev/null +++ b/docs/theory/_amr_anims.py @@ -0,0 +1,241 @@ +# AMR на цилиндре: полный домен 150x72, три версии (без AMR / 2x / вложенный 2x+4x). +# Встроенные зонды: сила на теле (обмен импульсом) -> Cd/Cl; u_y в следе -> Струхаль. +# Визуализация: inferno по |omega|, ТОЛЬКО рамки зон (без линий сетки), подписи осей. +# После прогона — анализ и сравнение трёх версий на реально собранных данных. +import sys, os, io as _io, numpy as np, matplotlib +matplotlib.use("Agg") +import matplotlib.pyplot as plt, matplotlib.patches as mpatches +from PIL import Image +try: sys.stdout.reconfigure(encoding="utf-8") +except Exception: pass +HERE = os.path.dirname(os.path.abspath(__file__)) +ANIM = os.path.join(HERE, "anim"); os.makedirs(ANIM, exist_ok=True) +FIGS = os.path.join(HERE, "figures"); os.makedirs(FIGS, exist_ok=True) + +C=np.array([[0,0],[1,0],[0,1],[-1,0],[0,-1],[1,1],[-1,1],[-1,-1],[1,-1]],float) +W=np.array([4/9,1/9,1/9,1/9,1/9,1/36,1/36,1/36,1/36]); CS2=1/3; Q=9 +CX,CY=C[:,0],C[:,1]; OPP=np.array([0,3,4,1,2,7,8,5,6]) +M=np.zeros((Q,Q)); M[0]=1;M[1]=CX;M[2]=CY;M[3]=3*(CX**2+CY**2)-2 +M[4]=CX**2-CY**2;M[5]=CX*CY;M[6]=CX**2*CY;M[7]=CX*CY**2;M[8]=CX**2*CY**2 +Dm=np.zeros((Q,Q)); Dm[4,4]=Dm[5,5]=1.0; Ps=np.linalg.inv(M)@Dm@M +def feq(rho,u): + ux=np.clip(u[0],-0.95,0.95); uy=np.clip(u[1],-0.95,0.95) + sx=np.sqrt(1+3*ux**2); sy=np.sqrt(1+3*uy**2); base=rho*(2-sx)*(2-sy) + Bx=((2*ux+sx)/(1-ux))[None]**CX[:,None,None]; By=((2*uy+sy)/(1-uy))[None]**CY[:,None,None] + return W[:,None,None]*base[None]*Bx*By +def macros(f): + r=f.sum(0); return r,np.stack([(CX[:,None,None]*f).sum(0)/r,(CY[:,None,None]*f).sum(0)/r]) +def collide(f,fe,beta): + dfn=f-fe; ds=np.einsum("ij,jab->iab",Ps,dfn); dh=dfn-ds; inv=1.0/fe + num=(ds*dh*inv).sum(0); den=(dh*dh*inv).sum(0) + with np.errstate(divide="ignore",invalid="ignore"): + g=np.where(den>1e-14,1/beta-(2-1/beta)*num/den,2.0) + return f-beta*(2*ds+g[None]*dh) +def stream(f): + fs=np.empty_like(f) + for i in range(Q): fs[i]=np.roll(f[i],(int(CY[i]),int(CX[i])),(0,1)) + return fs +def smoothstep(x): x=min(max(x,0.0),1.0); return x*x*(3-2*x) +def tauc(tp,r): return r*tp-(r-1)/2 +def vort(u): + return (np.roll(u[1],-1,1)-np.roll(u[1],1,1))*0.5-(np.roll(u[0],-1,0)-np.roll(u[0],1,0))*0.5 +def patch(pNx,pNy,ax,bx,ay,by,r): + Wx,Wy=bx-ax,by-ay; Nfx,Nfy=r*Wx+1,r*Wy+1 + FX,FY=np.meshgrid(ax+np.arange(Nfx)/r, ay+np.arange(Nfy)/r) + x0=np.floor(FX).astype(int); y0=np.floor(FY).astype(int) + x1=np.minimum(x0+1,pNx-1); y1=np.minimum(y0+1,pNy-1) + return dict(Nfx=Nfx,Nfy=Nfy,ax=ax,bx=bx,ay=ay,by=by,r=r,x0=x0,y0=y0,x1=x1,y1=y1, + tx=FX-x0,ty=FY-y0,slx=slice(r,r*Wx,r),sly=slice(r,r*Wy,r)) +def pint(fld,P): + return (fld[...,P["y0"],P["x0"]]*(1-P["tx"])*(1-P["ty"])+fld[...,P["y0"],P["x1"]]*P["tx"]*(1-P["ty"]) + +fld[...,P["y1"],P["x0"]]*(1-P["tx"])*P["ty"]+fld[...,P["y1"],P["x1"]]*P["tx"]*P["ty"]) +def ghost(pf,P,Rcf): + r,u=macros(pf); neq=pf-feq(r,u) + return feq(pint(r,P),np.stack([pint(u[0],P),pint(u[1],P)]))+Rcf*pint(neq,P) +def fill(cf,gh): + cf[:,0,:]=gh[:,0,:];cf[:,-1,:]=gh[:,-1,:];cf[:,:,0]=gh[:,:,0];cf[:,:,-1]=gh[:,:,-1]; return cf +def restrict(cf,pf,P,Rfc,fluid): + r,u=macros(cf); neq=cf-feq(r,u); slx,sly=P["slx"],P["sly"] + nv=feq(r[sly,slx],u[:,sly,slx])+Rfc*neq[:,sly,slx] + cur=pf[:,P["ay"]+1:P["by"],P["ax"]+1:P["bx"]] + pf[:,P["ay"]+1:P["by"],P["ax"]+1:P["bx"]]=np.where(fluid[None],nv,cur); return pf +def bb(pre,f,solid): + for i in range(Q): f[i,solid]=pre[OPP[i],solid] + return f +def cyl(NX,NY,ccx,ccy,rad,walls=True): + Y,X=np.mgrid[0:NY,0:NX]; m=(X-ccx)**2+(Y-ccy)**2<=rad*rad + if walls: m[0,:]=True; m[-1,:]=True + return m +def force_on(fpost,solid_body): + # обмен импульсом (Mei et al. 2002): по линкам жидкий-узел -> твёрдый сосед, + # F = sum c_i (f_i + f_ī)^post — корректная передача импульса на стенку. + fluid=~solid_body; Fx=0.0; Fy=0.0 + for i in range(1,Q): + nb=np.roll(solid_body,(-int(CY[i]),-int(CX[i])),(0,1)) # nb[x]=solid[x+c_i] + link=fluid & nb; s=(fpost[i]+fpost[OPP[i]])[link].sum() + Fx+=CX[i]*s; Fy+=CY[i]*s + return Fx,Fy + +# --- полный домен 150x72 (вся сетка в кадре, измельчение внутри) --- +Nx,Ny=150,72; D=16; cx,cy=40,36; U=0.07; Re=150.0; STEPS=8000; ramp=1000; FE=34 +D0=D; nu=U*D/Re; tau0=nu/CS2+0.5; b0=1/(2*tau0) +px,py=cx+3*D,cy # зонд в следе +solid0=cyl(Nx,Ny,cx,cy,D/2) # коарс: цилиндр + стенки +solid0_cyl=cyl(Nx,Ny,cx,cy,D/2,walls=False) +# уровень1 (2×, зелёный): тело+след +ax1,bx1,ay1,by1=16,118,8,64; P1=patch(Nx,Ny,ax1,bx1,ay1,by1,2) +t1=tauc(tau0,2); b1=1/(2*t1); R01=t1/(2*tau0); Rf01=1/R01 +solid1=cyl(P1["Nfx"],P1["Nfy"],(cx-ax1)*2,(cy-ay1)*2,D,walls=False) # D_L=32 +fl1=~solid0[ay1+1:by1,ax1+1:bx1] +# уровень2 (4×, оранжевый): у тела (в коарс-координатах [26:64]x[18:54]) +cx2a,cx2b,cy2a,cy2b=26,64,18,54 +P2=patch(P1["Nfx"],P1["Nfy"],(cx2a-ax1)*2,(cx2b-ax1)*2,(cy2a-ay1)*2,(cy2b-ay1)*2,2) +t2=tauc(t1,2); b2=1/(2*t2); R12=t2/(2*t1); Rf12=1/R12 +solid2=cyl(P2["Nfx"],P2["Nfy"],(cx-cx2a)*4,(cy-cy2a)*4,2*D,walls=False) # D_L=64 +fl2=np.ones((P2["by"]-P2["ay"]-1,P2["bx"]-P2["ax"]-1),bool) +onecol=np.ones((Ny,1)) +print(f"домен {Nx}x{Ny}; L1(2×) {P1['Nfx']}x{P1['Nfy']}; L2(4×) {P2['Nfx']}x{P2['Nfy']}; " + f"Re={Re} D0={D0} steps={STEPS}") + +def run(mode): # "none" | "amr2x" | "nested" + use1=mode in ("amr2x","nested"); use2=(mode=="nested") + DL={"none":D0,"amr2x":2*D0,"nested":4*D0}[mode] + f0=feq(np.ones((Ny,Nx)),np.zeros((2,Ny,Nx))) + f1=feq(np.ones((P1["Nfy"],P1["Nfx"])),np.zeros((2,P1["Nfy"],P1["Nfx"]))) if use1 else None + f2=feq(np.ones((P2["Nfy"],P2["Nfx"])),np.zeros((2,P2["Nfy"],P2["Nfx"]))) if use2 else None + Fx=np.zeros(STEPS+1); Fy=np.zeros(STEPS+1); uy=np.zeros(STEPS+1); frames=[] + for t in range(STEPS+1): + rho,u0=macros(f0) + if not np.all(np.isfinite(u0)): print("BLEW UP",mode,t); Fx=Fx[:t];Fy=Fy[:t];uy=uy[:t]; break + pre=f0.copy(); post0=collide(f0,feq(rho,u0),b0) + if mode=="none": Fx[t],Fy[t]=force_on(post0,solid0_cyl) + f0=stream(bb(pre,post0,solid0)) + uin=np.zeros((2,Ny,1)); uin[0,:,0]=U*smoothstep(t/ramp) + f0[:,1:-1,0]=feq(onecol,uin)[:,1:-1,0]; f0[:,1:-1,-1]=f0[:,1:-1,-2] + if use1: + g1o=ghost(pre,P1,R01); g1n=ghost(f0,P1,R01) + for s1 in range(2): + pre1=f1.copy(); r1,u1=macros(f1); post1=collide(f1,feq(r1,u1),b1) + if mode=="amr2x" and s1==1: Fx[t],Fy[t]=force_on(post1,solid1) + f1=stream(bb(pre1,post1,solid1)); f1=fill(f1,(1-(s1+1)/2)*g1o+((s1+1)/2)*g1n) + if use2: + g2o=ghost(pre1,P2,R12); g2n=ghost(f1,P2,R12) + for s2 in range(2): + pre2=f2.copy(); r2,u2=macros(f2); post2=collide(f2,feq(r2,u2),b2) + if s1==1 and s2==1: Fx[t],Fy[t]=force_on(post2,solid2) + f2=stream(bb(pre2,post2,solid2)); f2=fill(f2,(1-(s2+1)/2)*g2o+((s2+1)/2)*g2n) + f1=restrict(f2,f1,P2,Rf12,fl2) + f0=restrict(f1,f0,P1,Rf01,fl1) + uc=macros(f0)[1]; uy[t]=uc[1,py,px] + if use1 and t%FE==0: + frames.append((t,uc.copy(),macros(f1)[1].copy(),(macros(f2)[1].copy() if use2 else None))) + return dict(mode=mode,DL=DL,Fx=Fx,Fy=Fy,uy=uy,frames=frames) + +def save_gif(res,name,fps=24): + nested=(res["mode"]=="nested"); frames=res["frames"] + mid=frames[len(frames)//2][1] + vm=np.nanpercentile(np.abs(np.where(solid0,np.nan,vort(mid))),99.0) + cm=plt.get_cmap("inferno").copy(); cm.set_bad("white") + pil=[] + for (t,u0,u1,u2) in frames: + fig=plt.figure(figsize=(11.2,5.7),dpi=96); ax=fig.add_subplot(111) + ax.imshow(np.abs(np.where(solid0,np.nan,vort(u0))),origin="lower",cmap=cm,vmin=0,vmax=vm, + extent=(0,Nx,0,Ny),interpolation="nearest") + o1=np.abs(np.where(solid1,np.nan,vort(u1)))[1:-1,1:-1] + ax.imshow(o1,origin="lower",cmap=cm,vmin=0,vmax=vm, + extent=(ax1+0.5,bx1-0.5,ay1+0.5,by1-0.5),interpolation="nearest") + if nested and u2 is not None: + o2=np.abs(np.where(solid2,np.nan,vort(u2)))[1:-1,1:-1] + ax.imshow(o2,origin="lower",cmap=cm,vmin=0,vmax=vm, + extent=(cx2a+0.25,cx2b-0.25,cy2a+0.25,cy2b-0.25),interpolation="nearest") + # ТОЛЬКО рамки зон (без линий сетки) + ax.add_patch(mpatches.Rectangle((0.2,0.2),Nx-0.4,Ny-0.4,fill=False,edgecolor="#4fc3f7",lw=1.6)) + ax.text(1.5,Ny-4,"уровень 0: Δx (крупный)",color="#4fc3f7",fontsize=9,weight="bold") + ax.add_patch(mpatches.Rectangle((ax1,ay1),bx1-ax1,by1-ay1,fill=False,edgecolor="#aed581",lw=2.2)) + ax.text(ax1+1,by1-3.5,"уровень 1: Δx/2 (тело+след)",color="#aed581",fontsize=9,weight="bold") + if nested: + ax.add_patch(mpatches.Rectangle((cx2a,cy2a),cx2b-cx2a,cy2b-cy2a,fill=False,edgecolor="#ff8a65",lw=2.2)) + ax.text(cx2a+1,cy2b-3.5,"уровень 2: Δx/4 (у тела)",color="#ff8a65",fontsize=9,weight="bold") + ttl="Вложенный AMR на цилиндре: 2× (след) + 4× (у тела)" if nested else "AMR на цилиндре: одиночный блок 2×" + ax.set_title(f"{ttl} · поверх $|\\omega|$ · t={t}",fontsize=11) + ax.set_xlabel("x [lu]"); ax.set_ylabel("y [lu]") + ax.set_xlim(0,Nx); ax.set_ylim(0,Ny) + buf=_io.BytesIO(); fig.savefig(buf,format="png",bbox_inches="tight"); buf.seek(0); plt.close(fig) + pil.append(Image.open(buf).convert("RGB").convert("P",palette=Image.ADAPTIVE)) + path=os.path.join(ANIM,name) + pil[0].save(path,save_all=True,append_images=pil[1:],duration=int(1000/fps),loop=0,optimize=True) + print("saved",name,len(frames),"кадров") + +def analyze(res): + Fx,Fy,uy,DL=res["Fx"],res["Fy"],res["uy"],res["DL"] + n=len(uy); h=slice(n//2,n) # статистически установившаяся половина + Cd=2*Fx/(U**2*DL); Cl=2*Fy/(U**2*DL) + sig=uy[h]-uy[h].mean(); npad=8192 + freqs=np.fft.rfftfreq(npad,1.0); amp=np.abs(np.fft.rfft(sig,n=npad)) + fpk=freqs[1+int(np.argmax(amp[1:]))] if len(amp)>2 else 0.0 + St=fpk*D0/U + return dict(Cd=float(Cd[h].mean()),Clrms=float(Cl[h].std()),St=float(St), + uyrms=float(uy[h].std()),Cd_s=Cd,Cl_s=Cl,uy=uy,freqs=freqs,amp=amp,h0=n//2) + +# ===== прогон трёх версий ===== +print("=== none ==="); R0=run("none") +print("=== amr2x ==="); R1=run("amr2x") +print("=== nested ==="); R2=run("nested") +save_gif(R1,"amr2x_cyl.gif"); save_gif(R2,"amr_nested_cyl.gif") + +A0,A1,A2=analyze(R0),analyze(R1),analyze(R2) +LABELS=["без AMR (D=16)","AMR 2× (D=32)","AMR 2×+4× (D=64)"] +AS=[A0,A1,A2] +print("\n=== СРАВНЕНИЕ НА СОБРАННЫХ ДАННЫХ (установившийся режим) ===") +print(f"{'версия':22}{'D у тела':>9}{'St':>8}{'':>9}{'rms Cl':>9}{'rms u_y':>9}") +for lab,DL,a in zip(LABELS,[16,32,64],AS): + print(f"{lab:22}{DL:>9}{a['St']:>8.3f}{a['Cd']:>9.3f}{a['Clrms']:>9.4f}{a['uyrms']:>9.4f}") +print(f"{'литература Re≈150':22}{'—':>9}{0.183:>8.3f}{1.33:>9.3f}{'~0.3':>9}") +print("(лит.: St≈0.18, Cd≈1.3 для цилиндра при Re≈150; Williamson 1996, Henderson 1995)") + +# ===== фигура сравнения ===== +np.savez(os.path.join(HERE,"_amr_probe_data.npz"), + St=np.array([a['St'] for a in AS]), Cd=np.array([a['Cd'] for a in AS]), + Clrms=np.array([a['Clrms'] for a in AS]), uyrms=np.array([a['uyrms'] for a in AS]), + Cd0=A0['Cd_s'],Cd1=A1['Cd_s'],Cd2=A2['Cd_s'], + Cl0=A0['Cl_s'],Cl1=A1['Cl_s'],Cl2=A2['Cl_s'], + uy0=R0['uy'],uy1=R1['uy'],uy2=R2['uy']) +cols=["#9e9e9e","#1f6feb","#d1495b"] +fig=plt.figure(figsize=(13.5,8.2)) +gs=fig.add_gridspec(2,2,hspace=0.32,wspace=0.22) +# поле |omega| вложенного AMR +axA=fig.add_subplot(gs[0,0]) +mid=R2["frames"][len(R2["frames"])//2]; vmf=np.nanpercentile(np.abs(np.where(solid0,np.nan,vort(mid[1]))),99) +cmf=plt.get_cmap("inferno").copy(); cmf.set_bad("white") +axA.imshow(np.abs(np.where(solid0,np.nan,vort(mid[1]))),origin="lower",cmap=cmf,vmin=0,vmax=vmf, + extent=(0,Nx,0,Ny),interpolation="nearest") +axA.add_patch(mpatches.Rectangle((ax1,ay1),bx1-ax1,by1-ay1,fill=False,edgecolor="#aed581",lw=1.8)) +axA.add_patch(mpatches.Rectangle((cx2a,cy2a),cx2b-cx2a,cy2b-cy2a,fill=False,edgecolor="#ff8a65",lw=1.8)) +axA.set_title("Вложенный AMR: $|\\omega|$ + рамки зон 2×/4×"); axA.set_xlabel("x [lu]"); axA.set_ylabel("y [lu]") +# Cl(t) +axB=fig.add_subplot(gs[0,1]) +for a,lab,c in zip(AS,LABELS,cols): + axB.plot(a['Cl_s'][a['h0']:],lw=0.8,color=c,label=lab) +axB.set_title("Подъёмная сила $C_l(t)$ (зонд силы, обмен импульсом)") +axB.set_xlabel("шаг (установившийся режим)"); axB.set_ylabel("$C_l$"); axB.legend(fontsize=8); axB.grid(alpha=0.3) +# спектры u_y +axC=fig.add_subplot(gs[1,0]) +for a,lab,c in zip(AS,LABELS,cols): + sp=a['amp']/a['amp'][1:].max(); axC.plot(a['freqs']*D0/U,sp,lw=1.0,color=c,label=lab) +axC.axvline(0.183,color="k",ls="--",alpha=0.6,label="лит. St≈0.18") +axC.set_xlim(0,0.6); axC.set_title("Спектр $u_y$ в следе → число Струхаля") +axC.set_xlabel("St = f·D/U"); axC.set_ylabel("нормир. амплитуда"); axC.legend(fontsize=8); axC.grid(alpha=0.3) +# столбики St и Cd +axD=fig.add_subplot(gs[1,1]); x=np.arange(3); w=0.35 +axD.bar(x-w/2,[a['St'] for a in AS],w,color="#1f6feb",label="St") +axD.bar(x+w/2,[a['Cd'] for a in AS],w,color="#fb8c00",label="") +axD.axhline(0.183,color="#1f6feb",ls="--",alpha=0.6); axD.axhline(1.33,color="#fb8c00",ls="--",alpha=0.6) +axD.set_xticks(x); axD.set_xticklabels(["без AMR","2×","2×+4×"],fontsize=9) +axD.set_title("St и vs разрешение у тела (пунктир — лит.)"); axD.legend(fontsize=8); axD.grid(alpha=0.3,axis="y") +for i,a in enumerate(AS): + axD.text(i-w/2,a['St']+0.005,f"{a['St']:.3f}",ha="center",fontsize=7) + axD.text(i+w/2,a['Cd']+0.02,f"{a['Cd']:.2f}",ha="center",fontsize=7) +fig.suptitle("AMR на цилиндре: сравнение трёх версий на реально собранных данных зондов",fontweight="bold") +fig.savefig(os.path.join(FIGS,"11e_amr_probe_comparison.png"),dpi=110,bbox_inches="tight"); plt.close(fig) +print("saved figures/11e_amr_probe_comparison.png") +print("DONE") diff --git a/docs/theory/_amr_anims_sdf.py b/docs/theory/_amr_anims_sdf.py new file mode 100644 index 0000000..4188cf8 --- /dev/null +++ b/docs/theory/_amr_anims_sdf.py @@ -0,0 +1,244 @@ +# СЛЕДУЮЩАЯ ИТЕРАЦИЯ решателя: тот же AMR (без / 2× / вложенный 2×+4×), но граница тела +# задана ПОЛНОЦЕННЫМ SDF (знаковое поле расстояний) + интерполированное отражение Bouzidi +# (Bouzidi-Firdaouss-Lallemand 2001) — сглаживает ступенчатость криволинейной границы. +# Геометрия/Re/шаги ИДЕНТИЧНЫ _amr_anims.py — отличие ТОЛЬКО в граничном условии, поэтому +# результаты прямо сравнимы. В конце — сводное сравнение с версиями без SDF. +import sys, os, io as _io, numpy as np, matplotlib +matplotlib.use("Agg") +import matplotlib.pyplot as plt, matplotlib.patches as mpatches +from PIL import Image +try: sys.stdout.reconfigure(encoding="utf-8") +except Exception: pass +HERE = os.path.dirname(os.path.abspath(__file__)) +ANIM = os.path.join(HERE, "anim"); os.makedirs(ANIM, exist_ok=True) +FIGS = os.path.join(HERE, "figures"); os.makedirs(FIGS, exist_ok=True) + +# ===== проверенное ядро D2Q9 KBC (идентично _amr_anims.py) ===== +C=np.array([[0,0],[1,0],[0,1],[-1,0],[0,-1],[1,1],[-1,1],[-1,-1],[1,-1]],float) +W=np.array([4/9,1/9,1/9,1/9,1/9,1/36,1/36,1/36,1/36]); CS2=1/3; Q=9 +CX,CY=C[:,0],C[:,1]; OPP=np.array([0,3,4,1,2,7,8,5,6]) +M=np.zeros((Q,Q)); M[0]=1;M[1]=CX;M[2]=CY;M[3]=3*(CX**2+CY**2)-2 +M[4]=CX**2-CY**2;M[5]=CX*CY;M[6]=CX**2*CY;M[7]=CX*CY**2;M[8]=CX**2*CY**2 +Dm=np.zeros((Q,Q)); Dm[4,4]=Dm[5,5]=1.0; Ps=np.linalg.inv(M)@Dm@M +def feq(rho,u): + ux=np.clip(u[0],-0.95,0.95); uy=np.clip(u[1],-0.95,0.95) + sx=np.sqrt(1+3*ux**2); sy=np.sqrt(1+3*uy**2); base=rho*(2-sx)*(2-sy) + Bx=((2*ux+sx)/(1-ux))[None]**CX[:,None,None]; By=((2*uy+sy)/(1-uy))[None]**CY[:,None,None] + return W[:,None,None]*base[None]*Bx*By +def macros(f): + r=f.sum(0); return r,np.stack([(CX[:,None,None]*f).sum(0)/r,(CY[:,None,None]*f).sum(0)/r]) +def collide(f,fe,beta): + dfn=f-fe; ds=np.einsum("ij,jab->iab",Ps,dfn); dh=dfn-ds; inv=1.0/fe + num=(ds*dh*inv).sum(0); den=(dh*dh*inv).sum(0) + with np.errstate(divide="ignore",invalid="ignore"): + g=np.where(den>1e-14,1/beta-(2-1/beta)*num/den,2.0) + return f-beta*(2*ds+g[None]*dh) +def stream(f): + fs=np.empty_like(f) + for i in range(Q): fs[i]=np.roll(f[i],(int(CY[i]),int(CX[i])),(0,1)) + return fs +def smoothstep(x): x=min(max(x,0.0),1.0); return x*x*(3-2*x) +def tauc(tp,r): return r*tp-(r-1)/2 +def vort(u): + return (np.roll(u[1],-1,1)-np.roll(u[1],1,1))*0.5-(np.roll(u[0],-1,0)-np.roll(u[0],1,0))*0.5 +def patch(pNx,pNy,ax,bx,ay,by,r): + Wx,Wy=bx-ax,by-ay; Nfx,Nfy=r*Wx+1,r*Wy+1 + FX,FY=np.meshgrid(ax+np.arange(Nfx)/r, ay+np.arange(Nfy)/r) + x0=np.floor(FX).astype(int); y0=np.floor(FY).astype(int) + x1=np.minimum(x0+1,pNx-1); y1=np.minimum(y0+1,pNy-1) + return dict(Nfx=Nfx,Nfy=Nfy,ax=ax,bx=bx,ay=ay,by=by,r=r,x0=x0,y0=y0,x1=x1,y1=y1, + tx=FX-x0,ty=FY-y0,slx=slice(r,r*Wx,r),sly=slice(r,r*Wy,r)) +def pint(fld,P): + return (fld[...,P["y0"],P["x0"]]*(1-P["tx"])*(1-P["ty"])+fld[...,P["y0"],P["x1"]]*P["tx"]*(1-P["ty"]) + +fld[...,P["y1"],P["x0"]]*(1-P["tx"])*P["ty"]+fld[...,P["y1"],P["x1"]]*P["tx"]*P["ty"]) +def ghost(pf,P,Rcf): + r,u=macros(pf); neq=pf-feq(r,u) + return feq(pint(r,P),np.stack([pint(u[0],P),pint(u[1],P)]))+Rcf*pint(neq,P) +def fill(cf,gh): + cf[:,0,:]=gh[:,0,:];cf[:,-1,:]=gh[:,-1,:];cf[:,:,0]=gh[:,:,0];cf[:,:,-1]=gh[:,:,-1]; return cf +def restrict(cf,pf,P,Rfc,fluid): + r,u=macros(cf); neq=cf-feq(r,u); slx,sly=P["slx"],P["sly"] + nv=feq(r[sly,slx],u[:,sly,slx])+Rfc*neq[:,sly,slx] + cur=pf[:,P["ay"]+1:P["by"],P["ax"]+1:P["bx"]] + pf[:,P["ay"]+1:P["by"],P["ax"]+1:P["bx"]]=np.where(fluid[None],nv,cur); return pf + +# ===== ПОЛНОЦЕННЫЙ SDF + интерполированное отражение Bouzidi ===== +def sdf_circle(NX,NY,ccx,ccy,R): + # знаковое расстояние до окружности: >0 жидкость, <0 внутри тела + Y,X=np.mgrid[0:NY,0:NX]; return np.sqrt((X-ccx)**2+(Y-ccy)**2)-R +def sdf_from_mask(mask): + # общий SDF из произвольной бинарной маски (для не-круглых тел), через EDT + from scipy import ndimage + din=ndimage.distance_transform_edt(mask); dout=ndimage.distance_transform_edt(~mask) + return dout-din-0.5 # >0 жидкость, <0 тело; -0.5 — поверхность между узлами +def add_walls(phi): + NY=phi.shape[0]; Y=np.arange(NY)[:,None]*np.ones((1,phi.shape[1])) + return np.minimum(phi, np.minimum(Y-0.5, (NY-1.5)-Y)) # стенки: поверхность на y=0.5 и Ny-1.5 +def build_bc(solid, phi, cyl_mask): + # для каждого направления: линки жидкий->твёрдый, доля стенки q (по SDF), + # есть ли второй жидкий узел (для интерполяции), и принадлежит ли сосед телу (для силы) + fluid=~solid; bc=[] + for i in range(1,Q): + cy_,cx_=int(CY[i]),int(CX[i]) + nb_solid=np.roll(solid,(-cy_,-cx_),(0,1)) # solid[x+c_i] + mask=fluid & nb_solid + cl=mask & np.roll(cyl_mask,(-cy_,-cx_),(0,1)) # сосед — тело (не стенка) + phinb=np.roll(phi,(-cy_,-cx_),(0,1)) + with np.errstate(divide="ignore",invalid="ignore"): + qq=phi/(phi-phinb) # доля линка до стенки (phi=0) + q=np.where(mask, np.clip(qq,0.02,0.98), 0.5) + xff=mask & (~np.roll(solid,(cy_,cx_),(0,1))) # x_f - c_i — жидкий? + bc.append((i,int(OPP[i]),mask,q,xff,cl)) + return bc +def apply_bc(f, fpost, bc): + # Bouzidi (линейный): пристеночный жидкий узел получает корректно отражённую популяцию + for (i,ib,mask,q,xff,cl) in bc: + cy_,cx_=int(CY[i]),int(CX[i]) + fi=fpost[i]; fib=fpost[ib]; fiback=np.roll(fpost[i],(cy_,cx_),(0,1)) # f_i в x_f-c_i + near=mask&(q<0.5)&xff; bad=mask&(q<0.5)&(~xff); far=mask&(q>=0.5) + qn=q[near]; f[ib][near]=2*qn*fi[near]+(1-2*qn)*fiback[near] + f[ib][bad]=fi[bad] # запас: нет второго узла -> halfway + qf=q[far]; f[ib][far]=(1/(2*qf))*fi[far]+(1-1/(2*qf))*fib[far] + return f +def force_bc(fpost, f, bc): + # обмен импульсом (Mei et al. 2002) для интерполированной границы: F=sum c_i (f_i^post + f_ī^bc) + Fx=0.0; Fy=0.0 + for (i,ib,mask,q,xff,cl) in bc: + s=(fpost[i]+f[ib])[cl].sum(); Fx+=CX[i]*s; Fy+=CY[i]*s + return Fx,Fy + +# ===== геометрия (идентична версии без SDF) ===== +Nx,Ny=150,72; D=16; cx,cy=40,36; U=0.07; Re=150.0; STEPS=8000; ramp=1000; FE=34 +D0=D; nu=U*D/Re; tau0=nu/CS2+0.5; b0=1/(2*tau0); px,py=cx+3*D,cy +# коарс: цилиндр (SDF) + стенки +phi0=add_walls(sdf_circle(Nx,Ny,cx,cy,D/2)); solid0=phi0<0 +cyl0=sdf_circle(Nx,Ny,cx,cy,D/2)<0 +bc0=build_bc(solid0,phi0,cyl0) +# уровень1 (2×): тело+след +ax1,bx1,ay1,by1=16,118,8,64; P1=patch(Nx,Ny,ax1,bx1,ay1,by1,2) +t1=tauc(tau0,2); b1=1/(2*t1); R01=t1/(2*tau0); Rf01=1/R01 +phi1=sdf_circle(P1["Nfx"],P1["Nfy"],(cx-ax1)*2,(cy-ay1)*2,D); solid1=phi1<0 +bc1=build_bc(solid1,phi1,solid1); fl1=~solid0[ay1+1:by1,ax1+1:bx1] +# уровень2 (4×): у тела +cx2a,cx2b,cy2a,cy2b=26,64,18,54 +P2=patch(P1["Nfx"],P1["Nfy"],(cx2a-ax1)*2,(cx2b-ax1)*2,(cy2a-ay1)*2,(cy2b-ay1)*2,2) +t2=tauc(t1,2); b2=1/(2*t2); R12=t2/(2*t1); Rf12=1/R12 +phi2=sdf_circle(P2["Nfx"],P2["Nfy"],(cx-cx2a)*4,(cy-cy2a)*4,2*D); solid2=phi2<0 +bc2=build_bc(solid2,phi2,solid2); fl2=np.ones((P2["by"]-P2["ay"]-1,P2["bx"]-P2["ax"]-1),bool) +onecol=np.ones((Ny,1)) +print(f"[SDF] домен {Nx}x{Ny}; L1(2×) {P1['Nfx']}x{P1['Nfy']}; L2(4×) {P2['Nfx']}x{P2['Nfy']}; " + f"Re={Re} D0={D0} steps={STEPS}") + +def run(mode): # "none" | "amr2x" | "nested" + use1=mode in ("amr2x","nested"); use2=(mode=="nested") + f0=feq(np.ones((Ny,Nx)),np.zeros((2,Ny,Nx))) + f1=feq(np.ones((P1["Nfy"],P1["Nfx"])),np.zeros((2,P1["Nfy"],P1["Nfx"]))) if use1 else None + f2=feq(np.ones((P2["Nfy"],P2["Nfx"])),np.zeros((2,P2["Nfy"],P2["Nfx"]))) if use2 else None + Fx=np.zeros(STEPS+1); Fy=np.zeros(STEPS+1); uy=np.zeros(STEPS+1); frames=[] + for t in range(STEPS+1): + rho,u0=macros(f0) + if not np.all(np.isfinite(u0)): print("BLEW UP",mode,t); Fx=Fx[:t];Fy=Fy[:t];uy=uy[:t]; break + pre=f0.copy(); post0=collide(f0,feq(rho,u0),b0); f0=stream(post0); f0=apply_bc(f0,post0,bc0) + if mode=="none": Fx[t],Fy[t]=force_bc(post0,f0,bc0) + uin=np.zeros((2,Ny,1)); uin[0,:,0]=U*smoothstep(t/ramp) + f0[:,1:-1,0]=feq(onecol,uin)[:,1:-1,0]; f0[:,1:-1,-1]=f0[:,1:-1,-2] + if use1: + g1o=ghost(pre,P1,R01); g1n=ghost(f0,P1,R01) + for s1 in range(2): + pre1=f1.copy(); r1,u1=macros(f1); post1=collide(f1,feq(r1,u1),b1) + f1=stream(post1); f1=apply_bc(f1,post1,bc1) + if mode=="amr2x" and s1==1: Fx[t],Fy[t]=force_bc(post1,f1,bc1) + f1=fill(f1,(1-(s1+1)/2)*g1o+((s1+1)/2)*g1n) + if use2: + g2o=ghost(pre1,P2,R12); g2n=ghost(f1,P2,R12) + for s2 in range(2): + pre2=f2.copy(); r2,u2=macros(f2); post2=collide(f2,feq(r2,u2),b2) + f2=stream(post2); f2=apply_bc(f2,post2,bc2) + if s1==1 and s2==1: Fx[t],Fy[t]=force_bc(post2,f2,bc2) + f2=fill(f2,(1-(s2+1)/2)*g2o+((s2+1)/2)*g2n) + f1=restrict(f2,f1,P2,Rf12,fl2) + f0=restrict(f1,f0,P1,Rf01,fl1) + uc=macros(f0)[1]; uy[t]=uc[1,py,px] + if use1 and t%FE==0: + frames.append((t,uc.copy(),macros(f1)[1].copy(),(macros(f2)[1].copy() if use2 else None))) + return dict(mode=mode,Fx=Fx,Fy=Fy,uy=uy,frames=frames,DL={"none":D0,"amr2x":2*D0,"nested":4*D0}[mode]) + +def save_gif(res,name,fps=24): + nested=(res["mode"]=="nested"); frames=res["frames"] + vm=np.nanpercentile(np.abs(np.where(solid0,np.nan,vort(frames[len(frames)//2][1]))),99.0) + cm=plt.get_cmap("inferno").copy(); cm.set_bad("white") + pil=[] + for (t,u0,u1,u2) in frames: + fig=plt.figure(figsize=(11.2,5.7),dpi=96); ax=fig.add_subplot(111) + ax.imshow(np.abs(np.where(solid0,np.nan,vort(u0))),origin="lower",cmap=cm,vmin=0,vmax=vm, + extent=(0,Nx,0,Ny),interpolation="nearest") + ax.imshow(np.abs(np.where(solid1,np.nan,vort(u1)))[1:-1,1:-1],origin="lower",cmap=cm,vmin=0,vmax=vm, + extent=(ax1+0.5,bx1-0.5,ay1+0.5,by1-0.5),interpolation="nearest") + if nested and u2 is not None: + ax.imshow(np.abs(np.where(solid2,np.nan,vort(u2)))[1:-1,1:-1],origin="lower",cmap=cm,vmin=0,vmax=vm, + extent=(cx2a+0.25,cx2b-0.25,cy2a+0.25,cy2b-0.25),interpolation="nearest") + ax.add_patch(mpatches.Rectangle((0.2,0.2),Nx-0.4,Ny-0.4,fill=False,edgecolor="#4fc3f7",lw=1.6)) + ax.text(1.5,Ny-4,"уровень 0: Δx (крупный)",color="#4fc3f7",fontsize=9,weight="bold") + ax.add_patch(mpatches.Rectangle((ax1,ay1),bx1-ax1,by1-ay1,fill=False,edgecolor="#aed581",lw=2.2)) + ax.text(ax1+1,by1-3.5,"уровень 1: Δx/2 (тело+след)",color="#aed581",fontsize=9,weight="bold") + if nested: + ax.add_patch(mpatches.Rectangle((cx2a,cy2a),cx2b-cx2a,cy2b-cy2a,fill=False,edgecolor="#ff8a65",lw=2.2)) + ax.text(cx2a+1,cy2b-3.5,"уровень 2: Δx/4 (у тела)",color="#ff8a65",fontsize=9,weight="bold") + ttl="Вложенный AMR + SDF: 2×(след)+4×(тело)" if nested else "AMR + SDF: одиночный блок 2×" + ax.set_title(f"{ttl} · граница тела по SDF (Bouzidi) · поверх $|\\omega|$ · t={t}",fontsize=11) + ax.set_xlabel("x [lu]"); ax.set_ylabel("y [lu]"); ax.set_xlim(0,Nx); ax.set_ylim(0,Ny) + buf=_io.BytesIO(); fig.savefig(buf,format="png",bbox_inches="tight"); buf.seek(0); plt.close(fig) + pil.append(Image.open(buf).convert("RGB").convert("P",palette=Image.ADAPTIVE)) + pil[0].save(os.path.join(ANIM,name),save_all=True,append_images=pil[1:],duration=int(1000/fps),loop=0,optimize=True) + print("saved",name,len(frames),"кадров") + +def analyze(res): + Fx,Fy,uy,DL=res["Fx"],res["Fy"],res["uy"],res["DL"] + n=len(uy); h=slice(n//2,n); Cd=2*Fx/(U**2*DL); Cl=2*Fy/(U**2*DL) + sig=uy[h]-uy[h].mean(); npad=8192 + freqs=np.fft.rfftfreq(npad,1.0); amp=np.abs(np.fft.rfft(sig,n=npad)) + St=(freqs[1+int(np.argmax(amp[1:]))] if len(amp)>2 else 0.0)*D0/U + return dict(Cd=float(Cd[h].mean()),Clrms=float(Cl[h].std()),St=float(St),uyrms=float(uy[h].std()), + Cl_s=Cl,uy=uy,freqs=freqs,amp=amp,h0=n//2) + +print("=== SDF none ==="); R0=run("none") +print("=== SDF amr2x ==="); R1=run("amr2x") +print("=== SDF nested ==="); R2=run("nested") +save_gif(R1,"amr2x_cyl_sdf.gif"); save_gif(R2,"amr_nested_cyl_sdf.gif") +AS=[analyze(R0),analyze(R1),analyze(R2)]; LAB=["без AMR (D=16)","AMR 2× (D=32)","AMR 2×+4× (D=64)"] +print("\n=== SDF: СРАВНЕНИЕ НА СОБРАННЫХ ДАННЫХ ===") +print(f"{'версия':22}{'D у тела':>9}{'St':>8}{'':>9}{'rms Cl':>9}{'rms u_y':>9}") +for lab,DL,a in zip(LAB,[16,32,64],AS): + print(f"{lab:22}{DL:>9}{a['St']:>8.3f}{a['Cd']:>9.3f}{a['Clrms']:>9.4f}{a['uyrms']:>9.4f}") +np.savez(os.path.join(HERE,"_amr_probe_data_sdf.npz"), + St=np.array([a['St'] for a in AS]),Cd=np.array([a['Cd'] for a in AS]), + Clrms=np.array([a['Clrms'] for a in AS]),uyrms=np.array([a['uyrms'] for a in AS])) + +# ===== сводное сравнение SDF vs без SDF (если есть данные без SDF) ===== +nosdf_path=os.path.join(HERE,"_amr_probe_data.npz") +if os.path.exists(nosdf_path) and ("St" in np.load(nosdf_path).files): + N=np.load(nosdf_path); St_n,Cd_n,Cl_n=N["St"],N["Cd"],N["Clrms"] + St_s=np.array([a['St'] for a in AS]); Cd_s=np.array([a['Cd'] for a in AS]); Cl_s=np.array([a['Clrms'] for a in AS]) + print("\n=== СВОДНО: SDF vs без SDF ===") + print(f"{'версия':14}{'St(noSDF)':>11}{'St(SDF)':>9}{'Cd(noSDF)':>11}{'Cd(SDF)':>9}") + for k,lab in enumerate(["без AMR","2×","2×+4×"]): + print(f"{lab:14}{St_n[k]:>11.3f}{St_s[k]:>9.3f}{Cd_n[k]:>11.3f}{Cd_s[k]:>9.3f}") + print(f"{'лит. Re≈150':14}{0.183:>11.3f}{0.183:>9.3f}{1.330:>11.3f}{1.330:>9.3f}") + x=np.arange(3); w=0.38 + fig,axs=plt.subplots(1,2,figsize=(13.5,4.6)) + axs[0].bar(x-w/2,Cd_n,w,color="#9e9e9e",label="без SDF (ступенч.)") + axs[0].bar(x+w/2,Cd_s,w,color="#1f6feb",label="с SDF (Bouzidi)") + axs[0].axhline(1.33,color="k",ls="--",alpha=0.6,label="лит. Cd≈1.33") + axs[0].set_xticks(x); axs[0].set_xticklabels(["без AMR","2×","2×+4×"]); axs[0].set_ylabel("") + axs[0].set_title("Сопротивление: SDF убирает завышение от ступенчатой границы"); axs[0].legend(fontsize=8); axs[0].grid(alpha=0.3,axis="y") + axs[1].bar(x-w/2,St_n,w,color="#9e9e9e",label="без SDF") + axs[1].bar(x+w/2,St_s,w,color="#1f6feb",label="с SDF") + axs[1].axhline(0.183,color="k",ls="--",alpha=0.6,label="лит. St≈0.18") + axs[1].set_xticks(x); axs[1].set_xticklabels(["без AMR","2×","2×+4×"]); axs[1].set_ylabel("St") + axs[1].set_title("Число Струхаля"); axs[1].legend(fontsize=8); axs[1].grid(alpha=0.3,axis="y") + fig.suptitle("Цилиндр: SDF (Bouzidi) против ступенчатого bounce-back, на реально собранных данных",fontweight="bold") + fig.savefig(os.path.join(FIGS,"11f_sdf_vs_nosdf.png"),dpi=110,bbox_inches="tight"); plt.close(fig) + print("saved figures/11f_sdf_vs_nosdf.png") +else: + print("\n(нет свежего _amr_probe_data.npz со скалярами — сначала запусти _amr_anims.py)") +print("DONE") diff --git a/docs/theory/_amr_probe_data.npz b/docs/theory/_amr_probe_data.npz new file mode 100644 index 0000000..18ac278 Binary files /dev/null and b/docs/theory/_amr_probe_data.npz differ diff --git a/docs/theory/_amr_probe_data_sdf.npz b/docs/theory/_amr_probe_data_sdf.npz new file mode 100644 index 0000000..b2c6f29 Binary files /dev/null and b/docs/theory/_amr_probe_data_sdf.npz differ diff --git a/docs/theory/_legacy/kbc_lbm.ipynb b/docs/theory/_legacy/kbc_lbm.ipynb new file mode 100644 index 0000000..38b90fc --- /dev/null +++ b/docs/theory/_legacy/kbc_lbm.ipynb @@ -0,0 +1,2611 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "a5bd74f5", + "metadata": {}, + "source": [ + "# Метод KBC (энтропийный Lattice Boltzmann): математика, физика и рабочий разбор\n", + "\n", + "**Karlin–Bösch–Chikatamarla (KBC)** — энтропийная multi-relaxation-time (MRT)\n", + "формулировка решёточного метода Больцмана (Lattice Boltzmann Method, **LBM**),\n", + "которая обеспечивает **безусловную нелинейную устойчивость** при больших числах\n", + "Рейнольдса без явной модели подсеточной турбулентности (она работает как\n", + "*implicit LES*).\n", + "\n", + "Этот ноутбук — подготовка к реализации: мы разбираем метод «на бумаге»,\n", + "**выводим** ключевые формулы, **численно их самопроверяем** и строим рабочий\n", + "2D-солвер (решётка D2Q9) с валидацией. В конце — перенос на целевую решётку\n", + "D3Q27 и сравнение с подходом «полиномиальное равновесие + TRT + α-лимитер +\n", + "Smagorinsky», который применялся ранее (это и есть «что менять для перехода к\n", + "настоящему KBC»).\n", + "\n", + "> **О источниках.** Формулы по возможности взяты из оригинальных статей\n", + "> (Karlin, Bösch, Chikatamarla, *Phys. Rev. E* **90**, 031302(R), 2014;\n", + "> Bösch, Chikatamarla, Karlin, *Phys. Rev. E* **92**, 043309, 2015; Guo et al.,\n", + "> *Phys. Rev. E* **65**, 046308, 2002). Где доступ был только к вторичным\n", + "> источникам, формула помечена **⚠ сверить с оригиналом**, а в конце собран\n", + "> список таких мест. Главный страж корректности здесь — **численная\n", + "> самопроверка** каждой формулы." + ] + }, + { + "cell_type": "markdown", + "id": "cffa5789", + "metadata": {}, + "source": [ + "## Сводная таблица обозначений\n", + "\n", + "Везде используются **решёточные единицы** (lattice units): шаг сетки\n", + "$\\Delta x = 1$ (lu — *lattice unit*) и шаг по времени $\\Delta t = 1$ (ts — *time\n", + "step*). Переход к СИ описан в разделе «Единицы и обезразмеривание».\n", + "\n", + "| Символ | Название | Физический смысл | Единицы (lu/ts) | Единицы (СИ) | Диапазон |\n", + "|---|---|---|---|---|---|\n", + "| $f_i$ | популяция | плотность частиц со скоростью $\\mathbf c_i$ | $f_i$ безразм. (доля $\\rho$) | кг·с³/м⁶ | $f_i>0$ |\n", + "| $\\mathbf c_i$ | дискретная скорость | направление переноса $i$ | lu/ts | м/с | компоненты $\\in\\{-1,0,1\\}$ |\n", + "| $w_i$ | вес квадратуры | вес направления, $\\sum_i w_i=1$ | безразм. | безразм. | $\\{4/9,1/9,1/36\\}$ (D2Q9) |\n", + "| $c_s$ | скорость звука решётки | $c_s^2=1/3$ для D2Q9/D3Q27 | lu/ts | м/с | $c_s=1/\\sqrt3$ |\n", + "| $\\rho$ | плотность | $\\rho=\\sum_i f_i$ | безразм. (опорная 1) | кг/м³ | $\\approx 1$ |\n", + "| $\\mathbf u$ | скорость | $\\rho\\mathbf u=\\sum_i \\mathbf c_i f_i$ | lu/ts | м/с | $\\lvert\\mathbf u\\rvert\\ll c_s$ |\n", + "| $\\mathbf j$ | импульс | $\\mathbf j=\\rho\\mathbf u$ | — | — | — |\n", + "| $\\tau$ | время релаксации | задаёт вязкость | ts | с | $\\tau>1/2$ |\n", + "| $\\nu$ | кинематич. вязкость | $\\nu=c_s^2(\\tau-\\tfrac12)$ | lu²/ts | м²/с | $>0$ |\n", + "| $\\beta$ | параметр сдвиговой релаксации | $\\beta=1/(2\\tau)$ | безразм. | — | $0<\\beta<1$ |\n", + "| $\\gamma$ | **энтропийный стабилизатор** | релаксация высших мод | безразм. | — | $\\approx 2$ |\n", + "| $f_i^{\\mathrm{eq}}$ | равновесие | максимум энтропии при связях $\\rho,\\mathbf u$ | как $f_i$ | — | $>0$ |\n", + "| $k_i,s_i,h_i$ | части разложения | кинематич./сдвиг/высшие моды | как $f_i$ | — | — |\n", + "| $\\Delta s_i,\\Delta h_i$ | неравновесные части | $s_i-s_i^{eq}$, $h_i-h_i^{eq}$ | как $f_i$ | — | малы |\n", + "| $H$ | H-функция (энтропия) | $H=\\sum_i f_i\\ln(f_i/w_i)$ | безразм. | — | убывает |\n", + "| $\\langle X|Y\\rangle$ | энтропийное скал. произв. | $\\sum_i X_iY_i/f_i^{eq}$ | — | — | — |\n", + "| $\\mathrm{Ma}$ | число Маха | $\\mathrm{Ma}=\\lvert\\mathbf u\\rvert/c_s$ | безразм. | — | $\\lesssim 0.3$ |\n", + "| $\\mathrm{Re}$ | число Рейнольдса | $\\mathrm{Re}=UL/\\nu$ | безразм. | — | задача |\n", + "| $S_{\\alpha\\beta}$ | тензор скоростей деформации | $\\tfrac12(\\partial_\\alpha u_\\beta+\\partial_\\beta u_\\alpha)$ | 1/ts | 1/с | — |\n", + "| $\\nu_t$ | вихревая вязкость (LES) | $\\nu_t=(C_s\\Delta)^2\\lvert S\\rvert$ | lu²/ts | м²/с | $\\ge 0$ |\n", + "| $C_s$ | константа Смагоринского | — | безразм. | — | $0.1$–$0.17$ |\n", + "| $q$ | доля стенки | положение стенки между узлами | безразм. | — | $[0,1]$ |" + ] + }, + { + "cell_type": "markdown", + "id": "deb46243", + "metadata": {}, + "source": [ + "## 0. Стиль графиков и общие настройки\n", + "\n", + "Подключаем библиотеки и задаём единый «симпатичный» стиль matplotlib. Код\n", + "написан так, чтобы файл работал **и как ноутбук** (графики встраиваются), **и\n", + "как обычный скрипт** `python kbc_lbm.py` (графики сохраняются в `figures/` для\n", + "валидации физики)." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "24926b08", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-06T17:33:54.702809Z", + "iopub.status.busy": "2026-06-06T17:33:54.702509Z", + "iopub.status.idle": "2026-06-06T17:33:55.151554Z", + "shell.execute_reply": "2026-06-06T17:33:55.150855Z" + }, + "lines_to_next_cell": 2 + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "matplotlib 3.10.8 | numpy 2.4.3 | notebook: True\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "import matplotlib\n", + "\n", + "# Определяем, выполняемся ли мы внутри Jupyter. В скрипте используем неинтерактивный\n", + "# бэкенд Agg и сохраняем PNG; в ноутбуке полагаемся на inline-вывод nbconvert.\n", + "try:\n", + " get_ipython() # есть только в IPython/Jupyter\n", + " IN_NOTEBOOK = True\n", + "except NameError:\n", + " IN_NOTEBOOK = False\n", + "if not IN_NOTEBOOK:\n", + " matplotlib.use(\"Agg\")\n", + " # Консоль Windows может быть в cp1251 — выводим в UTF-8, чтобы кириллица и\n", + " # греческие символы в print() не роняли скрипт (в ноутбуке это не нужно).\n", + " import sys\n", + " try:\n", + " sys.stdout.reconfigure(encoding=\"utf-8\")\n", + " except Exception:\n", + " pass\n", + "\n", + "import os\n", + "import matplotlib.pyplot as plt\n", + "\n", + "FIGDIR = os.path.join(os.path.dirname(os.path.abspath(__file__)) if \"__file__\" in globals() else \".\", \"figures\")\n", + "os.makedirs(FIGDIR, exist_ok=True)\n", + "\n", + "plt.rcParams.update({\n", + " \"figure.dpi\": 110,\n", + " \"savefig.dpi\": 120,\n", + " \"font.size\": 11,\n", + " \"axes.titlesize\": 13,\n", + " \"axes.titleweight\": \"bold\",\n", + " \"axes.grid\": True,\n", + " \"grid.alpha\": 0.25,\n", + " \"axes.axisbelow\": True,\n", + " \"figure.facecolor\": \"white\",\n", + " \"axes.facecolor\": \"#fbfbfd\",\n", + "})\n", + "\n", + "def _finish(fig, name):\n", + " \"\"\"Сохранить фигуру в figures/ (для скрипта) и показать (в ноутбуке).\"\"\"\n", + " fig.savefig(os.path.join(FIGDIR, name), bbox_inches=\"tight\")\n", + " if IN_NOTEBOOK:\n", + " plt.show() # гарантированный inline-вывод при nbconvert\n", + " else:\n", + " plt.close(fig)\n", + "\n", + "print(\"matplotlib\", matplotlib.__version__, \"| numpy\", np.__version__, \"| notebook:\", IN_NOTEBOOK)" + ] + }, + { + "cell_type": "markdown", + "id": "f0833c9b", + "metadata": {}, + "source": [ + "## 1. Основы LBM и решётка D2Q9\n", + "\n", + "Решёточный метод Больцмана отслеживает **популяции** $f_i(\\mathbf x, t)$ —\n", + "плотность фиктивных частиц, движущихся в узле $\\mathbf x$ со скоростью\n", + "$\\mathbf c_i$. Динамика — чередование **переноса** (streaming) и **столкновения**\n", + "(collision):\n", + "$$ f_i(\\mathbf x + \\mathbf c_i\\,\\Delta t,\\; t+\\Delta t) = f_i(\\mathbf x,t) + \\Omega_i, $$\n", + "где $\\Omega_i$ — оператор столкновения.\n", + "\n", + "**Решётка D2Q9** (2D, 9 скоростей): покоящаяся частица, 4 «осевые» и 4\n", + "«диагональные». Скорость звука $c_s^2 = 1/3$. Веса $w_i$ выбраны так, чтобы\n", + "квадратура точно интегрировала моменты максвеллиана до нужного порядка\n", + "(изотропия 4-го порядка): $w_0=4/9$, осевые $1/9$, диагональные $1/36$,\n", + "$\\sum_i w_i = 1$.\n", + "\n", + "**Макроскопические моменты:**\n", + "$$ \\rho=\\sum_i f_i,\\qquad \\rho\\mathbf u=\\sum_i \\mathbf c_i f_i. $$" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "c6c5f84c", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-06T17:33:55.153999Z", + "iopub.status.busy": "2026-06-06T17:33:55.153749Z", + "iopub.status.idle": "2026-06-06T17:33:55.160031Z", + "shell.execute_reply": "2026-06-06T17:33:55.159233Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Решётка D2Q9: тождества весов и изотропии 2-го порядка — OK\n" + ] + } + ], + "source": [ + "# --- Решётка D2Q9 -----------------------------------------------------------\n", + "# Порядок направлений: 0 — покой; 1..4 — оси (+x,+y,-x,-y); 5..8 — диагонали.\n", + "C = np.array([[0, 0], [1, 0], [0, 1], [-1, 0], [0, -1],\n", + " [1, 1], [-1, 1], [-1, -1], [1, -1]], dtype=float) # c_i = (c_ix, c_iy)\n", + "W = np.array([4/9, 1/9, 1/9, 1/9, 1/9, 1/36, 1/36, 1/36, 1/36]) # веса w_i\n", + "CS2 = 1.0 / 3.0 # c_s^2\n", + "Q = 9\n", + "CX, CY = C[:, 0], C[:, 1]\n", + "OPP = np.array([0, 3, 4, 1, 2, 7, 8, 5, 6]) # индекс противоположного c_i\n", + "\n", + "# Самопроверка решёточных тождеств (нужны для корректной гидродинамики):\n", + "assert np.isclose(W.sum(), 1.0) # сумма весов = 1\n", + "assert np.allclose((W[:, None] * C).sum(0), 0.0) # sum_i w_i c_i = 0\n", + "assert np.allclose((W[:, None, None] * C[:, :, None] * C[:, None, :]).sum(0),\n", + " CS2 * np.eye(2)) # sum_i w_i c_ia c_ib = c_s^2 δ_ab\n", + "assert np.all(C[OPP] == -C) # c_{opp(i)} = -c_i\n", + "print(\"Решётка D2Q9: тождества весов и изотропии 2-го порядка — OK\")" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "4d09bb67", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-06T17:33:55.162182Z", + "iopub.status.busy": "2026-06-06T17:33:55.162008Z", + "iopub.status.idle": "2026-06-06T17:33:55.165873Z", + "shell.execute_reply": "2026-06-06T17:33:55.165125Z" + } + }, + "outputs": [], + "source": [ + "def make_grid(field_shape):\n", + " \"\"\"Удобный конструктор массива популяций формы (9, Ny, Nx).\"\"\"\n", + " return np.zeros((Q,) + field_shape)\n", + "\n", + "\n", + "def macros(f):\n", + " \"\"\"Плотность rho (Ny,Nx) и скорость u (2,Ny,Nx) из популяций f (9,Ny,Nx).\"\"\"\n", + " rho = f.sum(axis=0)\n", + " jx = (CX[:, None, None] * f).sum(axis=0)\n", + " jy = (CY[:, None, None] * f).sum(axis=0)\n", + " u = np.stack([jx / rho, jy / rho])\n", + " return rho, u" + ] + }, + { + "cell_type": "markdown", + "id": "b9c09d2f", + "metadata": {}, + "source": [ + "### Рисунок: стенсиль D2Q9\n", + "\n", + "Стрелки — направления $\\mathbf c_i$, цвет/толщина — вес $w_i$ (центральный узел\n", + "имеет наибольший вес $4/9$, диагонали — наименьший $1/36$)." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "2e96e518", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-06T17:33:55.168091Z", + "iopub.status.busy": "2026-06-06T17:33:55.167910Z", + "iopub.status.idle": "2026-06-06T17:33:55.651832Z", + "shell.execute_reply": "2026-06-06T17:33:55.650962Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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J6S8iZ3OwdvfpJaHef//9fI+vFxrXFipns/nAgQNzugT1+S655BJzBqX+mtcJVN98800zgarS1/n666+7dBnqc2qX5TXXXGPeI2192rp1q/lFoy0ZqlSpUvlav3ylE/7qGZa5L4Gkv850nyln3cpbFws7I0db8PQ1f/755wWuo2cK6T5V+rq09c55tpDWgWXLlpnHGDt2rE91qyBafu1GuPzyy83ZbFo/nPr06WOa9v352bWCdi9qC6tehmr16tVFdp87+fs1WvGeaivGbbfdZv6tZXROkKz1V88ydNJLuelnsbj1wNfnK+6+8JYnn7nCeFtendBZ912wypuX87ikLV7aSpq7y7E49X2kF/slUN9n+rr0jNkpU6aY8tapUyfnPv3u0dZxLbt+j+mxOy+f3ytHmLZ4qVGjRnk0qM/XQbeF3fLO2eNLWfz1Cz733Dya/J2/EvRsQndlqFKlipkPzdtfCN6cCHH99de7vWSQN/s/bwuQ/uIYNmxYkftZW69mzpyZ77lPnTpV6Hb6y2Xp0qVuX7svLV7ezCHkro7k3Vf6C0znklFF/ZrV+XEKu7SSJ3M+FVa33G2nZ/y4ey6duDbv5InB/Lx40+JVUD3RgbhFzeNVnNfojhXvad558PLeSpcunXNmuT/qgS/P5+2+yK2odYrzmfPXe6etSjp5rCcCUV5PPgM6iajzeYpT35/2Yr/4+/ssbwuezuuVm8475vw+SUtLK3B7T9+rsBlcXxSdA0bn+dIErUlVfxnp4DgdlKl9wDqvSN75mSKxLP/85z9z5i/S5K+/GvQXhP6ifPXVV81lebQsOrhcx3boOAB/DR7XMSLaSqSPp3Nv6cBE3Q/6y8jXsUwF0V8c+lr1F5VeCkgvsq2/WHKPPYqPjzevT/vq89J9oL+ydF/p+6KtbfqrRi+2/eSTT5rLHmlrWKjSC5B7OuZpxIgRsn79eunXr5/5Bam/TnXfVKtWTXr06GFaHYtTt9zReW50HJSWUZ9L33+ds+zrr7/OGawaip9dT2jrqO5HfQ90v1avXr3Ibfz9Gq14T5966in58ssvTUuDvkb9jOjnW09G0VYnLa+7sZW+1gNfn89f+8Kfn7nCeFNebUXROdCCWV53tKVSj/M6h+LKlSvzPY8v9X2EF/slEN9nzt6utm3bmpNmcnPWVZ3/Tgfhu+Pze+V1VANCjI4Z6dGjR84vF+2T1xn0g83Z4uVJK27uVphw4c2cV4hc1AP/0XGy2mq0fv16Pz4qQu29CusWL8D5S0wvkO38daRjcbp165Yz3gsAwoGeAa0t+zpGCpH7XoXt4HogN22e1gH6ejkSHQztDGBFXeYmkPTkAD0duVmzZkWuq10/f/vb3ywpF4DQ/TLXblY9niFy36sobfYKSKkARDSdyyr3WDpf5h1C+KMeAN4heAEAAFiEMV4AAAAWIXgBAABYhOAFAABgEc5qtJheXkcvQaCTvzkvnQEAQLjTM8r1clGXXXaZmUAV7vHNbzENXXlnyAUAIFJ8++23Hk2jY1cEL4tpS5datWq1uWCzJ7KysiQt7ZgkJia5vVCnHbFP2CfUEz47HEtC6/h64MABad26Zc73HNwjeFnM2b2ooatq1aoefwhSUxMkOTmF4MU+oZ54gc8O+4Q6Yv3nhmE0hWNwPQAAgEUIXgAAABahqxEAYKnjx4+bMUTZ2VlB3/PZ2Q45c+aMpKenS3R0VLCLExIK2idRUdESFxcn5513Pt2JxUCLFwDA0tB14MB+ycjIkFC4UnBUVJTExcWa/6PwfXJu7Feq7N69U06ePMHu8hEtXgAAy2hLlw6+rlGjZkicLORwOCQr66zExJQgfHmwT3Quyn379pgAVrp0QjDesrBnixYvbS4dM2aMdOnSxZzmqhVp4sSJHm07e/Zss76728GDBwNedgCIJNq9qMErFEIXvKcTo8bGxplgBt/YosXr8OHDMn78eDN9Q+PGjWXp0qVeP8bYsWOlTp06LsuSk5P9WEoAsAd69cIb71/x2CJ46ZxZ+/btk8qVK8uuXbukVq1aXj9G586dpWXLlgEpHwAAsAdbdDXGx8eb0FVcaWlpZnAhAACAL2wRvPyhU6dOkpSUJKVLl5Zu3brJTz/9FOwiAQDCmA5Qv/XW3pKSkiTVq1eVyZMnezR0pmLFCnLlla0Ddn+lShdIu3btvHw18JQtuhqLQ4NWnz59pGPHjpKYmCjr16+XSZMmSevWrWXDhg1So0aNIlvJ9Jb7WlZKW848bT3TwajZ2dkhMedNqGCfsE+oJ+H52dE5ovTkJD1zLhRoObQowSjP4MGD5PTpDNm161fZvXu3XHfdtVKvXl257rrrC9xm+PDH5OKLLzbzbLkrs7/uz8hwf79y7q+832H0CHmG4FWEXr16mZtTjx49zHgv/TUwYcIEmTFjRqHba0gbN26c21Oq9VpYnsjKypb09OOmssfE0EjJPqGeeIrPTujtE/3C1zminGfFHXzxdcnYs9+y54+vVlkqDu6b87fuB2cIzT1ovGrVKrJixedSt25d+eCDD+SWW3rL559/IS1atJBly5bKqFGjZPXqNT6X48SJE/LOOwtl1apvJCGhtFxyycVyzz33yKxZs0wPiztfffWlbNv2s2kMmDHj9XxnFvrr/rvv7iOvvz7DBCl3A+kdjmw5cyZTUlOP5vteQ9EIXj5o06bN/z58y4pcd+jQodKvXz+XFq/mzZubq77rBUg9oQcFrfx6FmV0NKdgs0+oJ57isxN6+0Sn99EWL50jSp3Ze0Aytu+y7PlzP7dyturo9Ba556xKSUmRU6dOmXWnTHlRLrqovum90L9ffvkVGTRosMvj9OjxV1m5cqXb56xWrbps2LDRZdn27TtMy+PllzfMWdao0RXywQcfujxu7sD6yCNDZfbsObJp03fmPcy9nj/v/+47LWtUvn2Sdwb7vN9h6elMquoJgpePqlWrJlu2bClyPe2e1FteWqG9mccmOjraHCSZ+4Z9Qj3xDp+d0NonzkvQBHOm+LzPrX8652d0SkpKNiFx3bp1kpl51rRC6ZgsPTN+48YNsmDB2y7rf/DBIq/KoDO/67hh17Cnz3nc7b555pl/ytVXXy2NGjUywUmDUe71/H9//n2Sd3/lrT98P3mG4OWjHTt2mMlYAQCRR0OQXt5o+vRXZciQIeaH9tGjqfLKKy9Lv373mbPliyMhoYzL+F917NgxKVu2bL51f/nlF5k7d46sW7fB7WMF+n74F8ErF+0G1IqvE6XGxsaaZYcOHcoXsBYvXmwG2T/44IN+fjsAwF50zFUoPp92xf7444+ydu1amT17ruzdu9dcY/LNN/8ta9euz7d+t25d5Ouvv3b7WHoS1qZNm12W1atXz7QaaaC79NJLzbJNmzbl/Du3lSu/NldKueSS+uZv7QLVW9WqleWHH7YG7P5q1aqY+9312sB3tgleU6dONc3EelMrVqyQs2fPDSwcNGiQafIdOXKkzJkzR3bu3Ck1a9Y09+nZizrbfdOmTc06eibjzJkzpUqVKmZwJQDAd1UeGRCSu0/HL02e/II8/PAj5hJH2hL1/POTpFOna+WCCy7It/5HHy326vETEhLkhhtulNGjR5lgp2c1zpz5uhn0nlevXr2lc+frcv5esGCBzJv3hnz44SJTLv/f/5a5X7tP3bXAoXhsE7yeffZZU7GdlixZYm7qjjvuMKHKnd69e8vHH39s1j158qSZBV8Hy48ePdr8GwAQeXRwvXY19u177uQo/Y7QVqHBg4f47TmmTJkq99/f37QsacAZNmx4zlQS2oLWpk1bGTFipJQqVcrcnJKSEk2vTMWKFc3f/r8/SUqUOHd/MMfiRaooR6hMpmIT2lytA/N37txtrh3pCT2lV0/b1V9gDF5kn1BPPMdnJ/T2yZ49534AV6tW+ByIVjk3H9VZc4YfIcOzfVLQe6jfb7Vq1ZA9e/Z4/P1mR0wKBQAAYBGCFwAAgEUIXgAAABYheAEAAFiE4AUAAGARghcAAIBFCF4AAAAWIXgBAABYhOAFAABgEYIXAABBoNcOvvXW3pKSkiTVq1eVyZMnF7juSy+9JC1aNJeEhFJy++23Bvj+2/zw6iB2v1YjAAChZPDgQZKRkSG7d+8x1xLu3LmTXHRRvZzrNeZWuXIlefzxx2X58uVy5MjhgN5/+HD+++E/tHgBAJBHxYoV5Oeffzb/fv/99yQ2NkZWr15t/l66dIk0bdqkWPvsxIkT8s47C2X8+L9LYmKiXHbZZeaC3LNnz3K7fs+eN0j37j2kXLlyQbkf/kOLFwAgaEa/P1Z2Ht5h2fPVKldbxvcYW+R6KSkpkp6ebv79wgsvSP369c3FxdVLL02VQYMGuazfvftfZOXKlW4fq1q16rJx43cuyzTUZWdnS4MGDXKWNWzY0IQ8RDaCFwAgaDR0/bD/x5B7B5KSkiU9/bisXbtWMjMz5ZprOsnRo0dl586dsmHDBnnrrbdd1v/gg0VePf6JE+mSlJTksiw5OVmOHz/ul/IjdNHVCABAHikp50LQ5MnPy5AhQ0x34NGjqfLKKy9Lv373SXx8fLH2WUJCGUlLS3NZduzYMSlbtizvRYQjeAEAkIe2Pv3444+mxeuGG240rVMHDuyXN9/8twwYcH++/dWtWxdJTk50e2vY8LJ869erV0+ioqJky5YtOcs2bdokl156Ke9FhKOrEQAQNDrmKhSfLzk5RSZPfkEefvgRKVGihGmJev75SdKp07VywQUX5Fv/o48We1WOhIQEE+hGjx4ls2fPNWc1zpz5usyY8brb9c+ePZtz07Fhp0+flpiYGImNjQ3Y/XFx8RIXF+fV60LRCF4AgKDxZKB7MOjgeu1q1DMNlbZ4HTx4UAYPHuK355gyZarcf39/qVatigl2w4YNz5lKQlvQ2rRpKyNGjDR/P/XUP2TChPE52y5cuFDuvPMumTlzVkDu1zMuc98P/4lyOBwOPz4eirB3716pVq2a7Ny5W6pWrerR/srKyjJn0+gvMP2FAvYJ9cQzfHZCb5/s2bPb/L9atRoSCvQrMCvrrMTElDBdfyh6nxT0Hur3W61aNWTPnj0ef7/ZEWO8AAAALELwAgAAsAjBCwAAwCIELwAAAIsQvAAAACxC8AIAALAIwQsAAMAiBC8AAACLELwAAAAsQvACACAIUlNT5dZbe0tKSpJUr15VJk+e7NO6GRkZ0r//fVK3bh1zv16UWy/mnVveC3eXLBknPXt2z7l/165d8te/dpMKFcpJlSqVpG/fe80lk+B/XKsRAIAgGDx4kAlNu3fvMRfJ7ty5k1x0Ub2c6zV6uq5e2Lpy5cry6adLpVatWrJy5Urp3v0vUrNmLWnVqpXZPjU1zeWyUbVr15Sbbro5Z9kDDwyQChUuMI9/6tQp6dXrJhk7doxMmvS8RXvDPmjxAgAgj4oVK8jPP/9s/v3+++9JbGyMrF692vy9dOkSadq0SbH22YkTJ8yFqMeP/7skJibKZZddZi7IPXv2LK/XTUhIkLFjx0nt2rXNtRXbtGkjrVu3ltWrv3H73J9++omkp6fLDTfc6NLidcstt0ipUqXMBcJ79Ogp//3vZupFANDiBQAImmFvpssvv2VZ9nwXXhAjz9xapsj1NHxoOFEvvPCC1K9f31xcXL300lQZNGiQy/rawqQtTe5Uq1ZdNm78zmWZhrrs7Gxp0KBBzrKGDRuakJeXN+s6g9r69etl0KDBbu+fM2e29OrV24Qsp0GDhsibb74pbdu2My1e7777jnTt2s3t9igeghcAIGg0dG3ea13w8lRSUrKkpx+XtWvXSmZmplxzTSc5evSo7Ny5UzZs2CBvvfW2y/offLDIq8c/cSJdkpKSXJYlJye7HVflzboa0Pr2vUeaNm0qnTpdm+/+w4cPy0cffSSfffa5y/L27dubQHb++SnmMa655hoZONA1XMI/6GoEACCPlJRzwWby5OdlyJAhpovv6NFUeeWVl6Vfv/skPj6+WPssIaGMpKX9Oe5KHTt2TMqWLevzug6HQx588AHZv/+A/Pvf8023Y17//ve/5cILL5QWLVq4jPnq1q2LdOnSRY4dOy6HD/9hxozdffddxXqNcI/gBQBAHtqi9OOPP5oWLx0LpS1OBw7sN2cLDhhwf779pcEl75mDzpueZZhXvXr1TDDasmVLzrJNmzbJpZde6tO6GroGDRpoln/00cdSpoz77lRt1br77j4uy7Qlb+/evfLQQwOlZMmSJmTed19/+eST/1AvAoCuRgBA0OiYq1B8vuTkFJk8+QV5+OFHpESJEqZ16fnnJ5nuuwsuuCDf+h99tNircuiAeA10o0ePktmz55ozFWfOfF1mzHjdp3X1rMc1a9bIkiVLTXByR7tIf/hhi9x++x0uy8uVK2cG5mtr3mOPDZczZ86Yx7/88su9ek3wDMELABA0ngx0DwYdXK9djXr2oNIWr4MHD8rgwUP89hxTpkyV++/vL9WqVTHBbtiw4TlTSWgLWps2bWXEiJFFrqtBTEOTdn/WqlUj5/F1W+f2ztYu7U50FxzffvsdefTRv8mLL042rWvNmzeXmTNn++214k9RDm2fhGW0ObdatWqyc+duqVq1qkfbaP+7nk2jv8BiYqz9dRiq2CfsE+pJeH529uzZbf5frdqfASGY9CswK+usxMSUcDsmyo6K2icFvYf6/abBb8+ePR5/v9kRY7wAAAAsQvACAACwCMELAADAIgQvAADgMUaGFw/BCwBgmaioaMnO5pyucJadnSXR0Zzo5SuCF0KeXrz1zjvvkEqVLpDExDLSvHkz+e67jcEuFmxU3zZupL75S1xcnJw5kyGnT5+WcJaRkSE7duyQTZu+M/Nj/fjjD3Ly5EmJdH/8ccTM81XcmfvtjHm8ENL0umhXXtlKrr76Gvnww4/MXDrLli1ze1kNgPoW+s4773w5fjxN9u3bI7GxcRLsGRy028zhyDYtcZ6WJSsrW44dS5XY2FhzLIqOjpIzZzLl998PRsSUP+72iS7Tli4NXWXKlJXzzy8X7GKGLYIXQtqDD94v7dq1kzfemOdy+Qydi2jjxg3y6KM3ytGjf5gD+Lp164NaVkRuffvpp5+kXbu2kpZ2zNS15557Ttq1ax/UsoYrnQW+UqXKkpqaauaKCoU5qzQ0aUucp/N4LVu21KzfsWPHnGWlSp0LXLNnzzaTryoNJ23aXCnhxt0+0f9p3XeGLuY88x3BCyFLm/G1dWvjxk1u73/44SHy7LOTpGXLlvL7779bXj7Yp77p9etee22GXHTRRbJ161bp2bO7/PjjT0EpZyQoXTrB3MJxQlmtJw888ICpJ+4mgX311Vdl7979Es6CPclupCN4IWTpOK7SpUtLgwYN8t23Zct/zYG7WbNm5u8KFSoEoYSwS32rUePPL1gNX2lpaaZVgF/99lNYPQE8weB6hCwdP6EDWN0Nwv3ll1+kVKmS0qNHd2nWrKm89NJLQSkj7FHfclu06ENp3LgxocumiqonR48eNSdktG/fTr744nPLy4fQR/BCyGrZspWUKVNGBg0aaLp3tmzZIlOnTpVff/3VNIWvWbNGXn75FVmx4nNz8ddNm9x3SQLFrW9OejHiESOGywsvvMhOtami6sm2bdvl22/XmmNTv3595dixY8EuMkIMwQshq3z58vLee+/LDz/8IC1aNJOrruogy5YtMd2KOjhXWx0qVapkDoJXX321bN78fbCLjAitb0q7F2+4oadMnvyiXHjhhcEuLkK0nlSuXNn8/5JLLpFLL71Utm3bxnsFF4zxQkhr27adrFy5Kt9yHdv122+/mS9DPZ171apV0rPnDUEpIyK/vmkL66239pb77rtPOnW6NihlQ+jXE+1m1PFfOsfV/v37TWtY7dq1g1JGhC6CF8L2lPRhw4ZJhw7tzFibG2+8SZo3bx7sYiFCffLJf+Szzz6Tgwd/k9dee80sW778M0lOTg520RBCfvzxRzMlic7qHh0dLc8++5ycd955wS4WQgzBC2Hr2ms7S69et3C6MwKua9ducupUBnsahWrdurV89x1DHlA4xngBAABYxBbBKz09XcaMGSNdunQxAyO1a2rixIkeb68zLA8YMMBsm5CQIB06dJB169YFtMwAACDy2CJ4HT58WMaPHy+bN282Z8J5Izs7W7p27Sr/+te/5KGHHpJnnnnGPJ5eKkJPJQYAAPCULcZ46ZQD+/btM6f57tq1S2rVquXxtgsXLjRnzM2fP1969+5tlt18883m+m2jR4+WBQsWBLDkAAAgktiixUtP7XXOreItDV7lypUzYctJuxx79eolixYtklOnTvmxpAAAIJLZosWrODZu3Gi6J/XU4Nx06oLp06eb7sbCui91nim9OR04cCBnXiC9eSI7O8t0eer/wT6hnniOzw77hDpi3efG0+80uyN4FUGDkp4i7K77UukkeYUFr0mTJsm4cePyLU9LOyapqQkevUlZWdmSnn5cHA6RmBhbNFIWiX3CPqGe8NnhWBJax1f9XkPRCF5F0K5E7arMq2TJkjn3F2bo0KHSr18/lyCnrWWJiUmSnJzi8a+PqCgxkzXqxHxgn1BPPMNnh31CHbHuc5OefsKHZ7MfglcRSpUqZa5En5fzyvR6f2ESExPNLa+YmBivJv7Urk79AHizTaRjn7BPqCd8djiWhM7xle8nz9BvVQTtUnSOy8rNuczXQfvwv637z8r0Fadk7xHGGQBwlZnlkPfWnZZ31p4245eAYKHFqwiNGjWSzz//3HxQcw+wX7NmjelurF+/fqDfI3hg6eYMeWDOuWbuf358ShpUjZEbmsbLdZfHSYVEfl8Adg1bq385K4s3ZciHG85Ixtlzy2d/lSGLhiYFu3iwKYJXnlasY8eOSZ06dSQ2NtYsu+mmm8yUEm+//XbOPF46gar+rROrFtXVCGvM/NK1O/i/e7Pkv3tPyoQPTkrTWiXk+svjCGGADZzVsLVdw9YZWbr5jBw96ci3zo/7s8ThcJirmABWs03wmjp1qrn0j97UihUr5OzZcz9/Bg0aJElJSTJy5EiZM2eO7Ny5U2rWrJkTvFq2bCl9+/Y1U0foHF7Tpk2TzMxMmTBhQlBfE/5Ur1KMrN35v5+zuehZOWt3nDU3DWG9W8TLk91LS3wsB1wg0qz8OVMefTNdDh3PH7Zyiy8hhC4EjW2C17PPPiu7d+/O+XvJkiXmpu644w4TvAoaLLh48WJ57LHHZMqUKXLy5Elp1qyZzJw5Uy6++GLLyo/CPXR1SfnXqvwnQeQNYfNXZ0irC0tI10b5z1QFEL60Beux+UWHLtWjSZwlZQLcsc3gF71UkH4w3d2crVuzZ892+dspJSVFXnvtNdPFqMHriy++MFNCIHRUSIqRZrU9+x2RkRnw4gCwWFa2yFkPx8zf0vLcdEBAMNimxQuRr0vDONOlWJiLK8dIt8b82o1kWdlZ8srnr8pb3y6QU5mnJEqi5NLKl8iTfx0ltcvXDnbxECAlYqLk0S6lZeSCwueSqnZetDn5BggW27R4IfJdd1mcmfSvIDoB89iepSWuBOO7Iln/OQNk5tez5MSZE5LtyJYsR5Z8v2+z9H7lVtl5aGewi4cAurFpnDSsVnio0hNtGFSPYCJ4IWKUT4w2ZzAW1hXx4Jx02XaQeb4i1YwvZ8h3eza5vU9DWN/Z95nhBIg82dkOefztE7JpT+Gf7+sb0uKN4CJ4IeK6GwtzJN0hd7ySRviKQBqs/rX6zULXOXbqmHz+0xeWlQnWhq6Fa88Uuh7djAgFBC9ElC6Xx0ly6SiXMV29WriGMcJXZFr+42eSdjqtyPWmrXiZVi8bhK6KSdHy4NWug+hvbRVPNyOCjsH1iCjnl42WV+4pI/NWZkjV86Llvg4lJbFUlJSMjZK5X2fkC1/z7k+UuhUZaBsJrV2vffGaR+vuOLRDvtm+Wlpf2Crg5ULwQte/HigrNcrFSOMaJWTBtxlyaZUS0q89ZzMi+AheiDhNa8WaW246aaoifEVua9f2Qzs8Xn/6F69Jqzotaf2I8NClOl4SZ25AqKCrEbagZzFp+LqrjevEqXQ72qu1y2nzvs2m1QuRHbqAUETwgm0QviKTt61duVu9OMMx/BC6EO4IXrAVwlfkmb/mLZ+201av/+7b4vfyIHAIXYgEBC/YDuErcqRnpMvmvZt93n7NjjV+LQ8Ch9CFSEHwgi0RviLDqTOnzcz0vvJk+gkEH6ELkYTgBdsifIW/cmXOl4T4BJ+3r1mupl/LA/8jdCHSELxga4Sv8H//7mp1p0/bXpBYQa5r0NnvZYL/ELoQiQhesD3CV3i7q/Wd0v6i9l5tk1I6RSb0GC+l487N74bQQ+hCpCJ4AbR8hbW4EnHyXK9n5Okb/yFlS5Ytcv3rG1wnb93/pjSp2cSS8sF7hC5EMoIX8D+0fIX3e3ftpddKxaSKRa77l0bd5Pwy51tSLniP0IVIR/ACciF8AcFD6IIdELyAPAhfgPUIXbALghfgBuELsA6hC3ZC8AIKQPgCAo/QBbsheAGFIHwBgUPogh0RvIAiEL4A/yN0wa4IXoAHCF+A/xC6YGcEL8BDhC+g+AhdsDuCF+AFwhfgO0IXQPACvEb4ArxH6ALOocUL8AHhC/AcoQv4E8EL8BHhCygaoQtwRfACioHwBRSM0AXkR/ACionwBeRH6ALcI3gBfkD4Av5E6AIKRvAC/ITwBRC6gKIQvAA/InzBzmjpAopG8AL8jPAFOyJ0AZ4heAEBQPiCnRC6AM8RvIAAIXzBDghdgHcIXkAAEb4QyQhdgPcIXkCAEb4QiQhdgG8IXoAFCF+IJIQuwHcEL8AihC9EAkIXUDwEL8BChC+EM0IXUHwEL8BihC+EI0IX4B8ELyAICF8IJ4QuwH8IXkCQEL4QDghdgH8RvIAgInwhlBG6AP8jeAFBRvhCKCJ0AYFB8AJCAOELoYTQBQQOwQsIEYQvhAJCFxBYBC8ghBC+EEyELiDwCF5AiCF8IRgIXYA1CF5ACCJ8wUqELsA6BC8gRBG+YAVCF2AtghcQwghfCCRCF2A9ghcQ4ghfCARCFxActgleGRkZMmLECKlSpYqUKlVKmjdvLp9++mmR282ePdt88bm7HTx40JKyA4Qv+FO2Q+SJd07JwrVnXJZXTIqWfz1QVmqUi2GHAwFSQmyiT58+snDhQhkyZIjUq1dP5syZI127dpXly5dL+/bti9x+7NixUqdOHZdlycnJASwx4D58qblfZ+QsP5LukDteSZO5/ROkXDx7DUW3dP1jcZR89H2my3JCF2ANWwSvb7/9VubPny8TJ06U4cOHm2V33XWXNGjQQIYNG2buL0rnzp2lZcuWFpQW8C183TX9hEy9VeQKfg+gkNClLV0ffR/lspzQBVjHFl2N2tIVHR0t/fv3z1lWsmRJ6du3r6xdu1Z27drl0eOkpaVJVlZWAEsKFK/b8cF/Rckvv1FHUfCYrnfX0dIFBJMtWrw2btxouglTUlJclus4L+f9NWvWLPQxOnXqJOnp6RIXF2f+/dxzz8lFF13kUVjTm9OBAwfM/zXAeRrisrOzJDs72/wf7BOnx7vFiyPbIW+s+nOcztGTUabla25/kQsvsN84HYfDUeQ6+lmy2w8oZ0tX/tAVJW8MKC1VU84dk+yI46v/9old65C3bBG8NOxUqlQp33Lnsv379xe4benSpc34sI4dO0piYqKsX79eJk2aJK1bt5YNGzZIjRo1Cn1uXXfcuHH5lqelHZPU1ASPyp+VlS3p6cdFv1NiYmzRSFkk9sk5D7XTE0eiZMH6qDxjvo7LtNsdUruc2Eq2Bwd+/QGVmnpU7DSQ/tyYLtfuxQplHfLSrdmSGJMmqaliWxxL/LdP9HsNRbNF8Dp16pTEx+cfdazdjc77C9KrVy9zc+rRo4cZ79WuXTuZMGGCzJgxo9DnHjp0qPTr188lBGpLW2JikiQnu7bAFUR/dURFnRvMHx1tv1YMd9gnfxp/s0Pi40/na/ka+Ga0GXBvp5av6JiiX2uZMmU8/uxFzpiuzHyh640BCVKzfKzYHccS/+2T9PQTfn1vIpUtgpdOH6HTSeR1+vTpnPu90aZNG2nRooUsW7asyHW1lUxvecXExJibp3SMmn4AvNkm0rFP/jS657nW09zhyzngft79iVK3Yoxtxr95Um/s8DnS0PXku+7GdEWZli4NXXbYD57gWOKffUJ98owt+q20S9E5tio357LKlSt7/ZjVqlWTP/74wy/lA/wROJ74a0np1cR1jJNzqoltBxl7YSeFTY6qLV06pgtAcNgieDVq1Ei2b98uR4+6jutYs2ZNzv3e2rFjh5QvX95vZQT8Eb6GdnLIna3jXJYTvuylqBnpq59PKxcQTLYIXjfddJM5Q2P69Ok5y7TrcdasWdKkSROpVatWTgvY1q1bJTPzz6b5Q4cO5Xu8xYsXm0H21113nUWvAPCM9rRpy5e7qSZo+Yp8XAYICH22GOOl47FuvvlmGTVqlBw+fFjq1q0rc+fOlZ07d8rSpUtz1hs5cqSZ0V6XO6eX0LMXGzduLE2bNpWkpCRzJuPMmTPNpYf08YBwm+HeTmO+7ITQBYQHWwQvpUFr9OjRMm/ePDM2S2etX7RokZkmojC9e/eWjz/+WJYsWSInT54048X0LEV9LHdTVAChgPBlL4QuIHxEOTyZcRB+s3fvXjMwf+fO3VK1alWPJ6XTeYf0FHjOGmGfeFNP9OM94YOTLi1f6vwyURHZ8nXLq7fJtt+2FbrOtDumSovaLcSuoYvjiSv2h//2iX6/1apVQ/bs2ePx95sd2WKMF2BXhV1eiDFf4Y+WLiD8ELyACEf4ikyELiA8EbwAGyB8RRZCFxC+CF6ATRC+IgOhCwhvBC/ARghf4Y3QBYQ/ghdgM4Sv8EToAiIDwQuwIcJXeCF0AZGD4AXYFOErPBC6gMhC8AJsjPAV2ghdQOQheAE2R/gKTYQuIDIRvAAQvkIMoQuIXAQvAAYtX6GB0AVENoIXgByEr+AidAGRj+AFwAXhKzgIXYA9ELwA5EP4shahC7APghcAtwhf1iB0AfZC8AJQIMJXYBG6APsheAEoFOErMAhdgD0RvAAUifDlX4QuwL4IXgA8QvjyD0IXYG8ELwAeI3wVD6ELAMELgFcIX74hdAFQBC8AXiN8EboA+IbgBcAnhC/P0NIFIDeCFwCfEb4KR+gCkBfBC0CxEL7cI3QBcKeEeOHbb7+V4rjkkkukTJkyxXoMAKEbvtTcrzNylh9Jd8gdr6TJvPsTpW7FGLELQhcAvwSvli1bmgOsr5YuXSpXXXWVz9sDCF2Er3MIXQD8FrxU//79TQDzxvHjx2XIkCHePhWAMGP38EXoAuD34NW2bVu57bbbvNrmyJEjMnjwYG+fCkAYsmv4InQB8Pvg+rffflvatWsn3kpMTDTbXn755V5vCyD82G3APaELQECC14033ihVq1YVb8XGxppty5Ur5/W2AMKTXcIXoQuAN5hOAkDARHr4InQBsDR4ff311/LSSy+5LJs/f75cdNFFcsEFF8jDDz8s2dnZxXkKAGEuUsMXoQuA5cHrySeflC+//DLn759//lnuvvtuiY6OliZNmsiUKVPkxRdfLM5TAIgAkRa+CF0AghK8tmzZIi1atMj5+4033pBSpUrJmjVrZPHixXLnnXfKzJkzi/MUACJEpIQvQheAoAWvtLQ0SUlJyfn7k08+kU6dOpmzGFWbNm1k586dxSoggMgR7uGL0AUgqMGrcuXK8sMPP5h/79+/XzZu3CjXXnutSzDTMxoBINzDF6ELQNCD1w033CBTp041k6P27NlTSpYsKd27d8+5f9OmTVKrVi1/lBNABAm38BXs0DVt2jS58MLaUqZMabnyytaydu1aj7d96KEHJTY2Jt+JUIFYB0CAg9e4cePkpptuknnz5snvv/8us2fPlgoVKuS0dr3zzjum6xEAwjV8BTt0LVjwlgwb9jcZNepJ+fbbdXLZZZdJ167Xy+HDh4vc9uOPP5LVq1eb3olArwPAguC1fv16mTRpkvzxxx9mLJeGMKcyZcqYZddcc01xngJABAvl8NWiRXOZNu3lAkPX6Kv2S4NaiXLo0KGAluOFF16Qfv3ukz597pFLLrnElElPYpo7d06h2/32228ycOBDMnv2nAKHfPhrHQAWBa+OHTvK0qVL3T9wdLR89tln0rlz5+I8BYAIF6rhKyk5RT4+0Dhf6LogMcq0dL3/rynSq1dvKV++vEePN3Hi05KcnFjo7ddff3XZ5syZM7Jhw3qXngM9tl511dWyevU3hT5fv373ysCBg0wLWaDXARDAi2Tn5nA4Cr1fDxp6kACAcLqwtnYvHqs1UI6cque6/MQBmdz3PEmJi5E33/y3fPbZ5zldcY89NsxMGP3oo8Okb99++R6zf/8BctNNNxf6vHm78rQ7MSsrSypUuMBluU5QvWrV9gIfR8dhnThxUh55ZGiB67z88rQi1/HkcQAEOHjp2K3U1NScv48cOZLvV5o6evSo/Pvf/5YqVap4+xSAi127dsmTT46SZcuWyokTJ6R+/Yvl5Zdflpo1a7KnIkiohC/nmK4jZa50WV6+TLYcWvqAlB70irzxxrvSsGEjady4sZw9e1aGD39Mli37TMqWLSstWzaXHj16yvnnn++y/XnnnWdugbZ161Z56qm/y8qV3xT4w3fbtm3y9NNPFbqOJ49jZ+6OS6++Ot3UCaAwXn+ann/+eXOmot70QKmXBXL+nft2xRVXyKeffioPPvigt08B5NBxgq1btzT//vDDj2Tdug1mrIt+wSHyBLvbsaCB9HFZR2X+wBRJjDluflS++urLMnDgQHPft99+Kw0aNJBKlSqZsa3XX99Fli5d4peuxnLlyklMTIz8/vtv+cZdVazo2grmtGbNajPurH79elKyZJy57d69W4YOfVgaNLgkZ3xuUet48jh2xXEJlrZ46TxdenDRbsbHHntMbr31VhOy8h48ExISpGnTpubSQYCvHnzwfmnXrp288ca8nGX16tUzvzA7dGhnuna0K0bHoOgAZIS/YLV8FRS65ORBearnSalRro6ZHPqDD96X9PR006qlDhzYL5Ur/9myX6VKVTOvoT+6GuPi4uSKK5rIsmXLpFu3v/yvnNmyYsVnMnjwELeP0b17D2nSpKnLMj0L8q677jY3df3110vbtm0lOjqmwHU8eRy7Kui4pHr3vtmMb9bvyn/9680glhIRE7xatWplbkq//G688Ubzaw/wtx07dpgvnI0bN+W7Lz4+Xt55513zJXf69Glp3Lih+VJLTk7mjbBx+HKcPVvkYx9b+a1kJtaV2HLnFRm6stL3S/mfRkmPae+bvxMTy8r06a/KyJGPS4kS3h0+fe1q1F6Fe++9x/zAbdasubz44mQ5efKkS/jRsVgaCJcsWWo+A3k/B3o2YsWKlaRu3brmh0pSUpLUqFHTtKa5W0cV9Th2VdhxST344ENy5513mTGAgF+6Gv/+97+biVHVmDFjCF0ImO++2yilS5d2W8ecraoqIyPDtALoDfbsdjy59RfZ89RkydiTv6Upr9RPPpdt/R4x6+t2BYWuxNhTcnBhd3n4vj9bqbTFS4NL7tbVSpUqy/79+3L+3rdvr+l29Bc9c/L//u8ZGTdurDRteoU5/n700WLTDel05Mhh2bGj4MH2sOa4pNq378BQCPi3xeuVV14xgUsPLF26dJFu3bqZubq0IgL+pL+uNVRpi5ZeFSGvU6dOSadO18j27dvl6af/z5KBywitlq83+paUxE/ekT8WLdGVRS728IGzHXJ8zQY5tnqDTG/2N1l8rKqbyVErSo2nXcPMvHn5WzGaN28umzdvlgMHDpgv3MWLP5YRI0aKPz300EPmVpDRo8eYW0F++WVHkc/hr3XsflwC/N7itXfvXlm3bp3cf//98t///tdcNkjP3tH5uqZMmWK+BAF/aNmylRlPOGjQQHOG1ZYtW8wlqpwDkHUSybVr15svg7ffXmAGHMNeLV+3PX9Yvvv0f10+RUxvk1e2Q2TKBbcUELo8n5FeuxwnTvw/ufrqjqZF6uGHH8l3RiPsc1wCiuLTOcJ6uuyoUaNk1apV5stu+vTpprVBW8J0gGH9+vXlb3/7m6xYscKcag34QiemfO+9982F2Fu0aCZXXdVBli1bknNZqtzrNWzYUL766kt2tM3CV2p0gjxRdaD8Guf+DL+CZEuUCV3Lk1q4LK9Y1uHTZYD+8pe/yg8/bJWtW3+W++7r79W2iMzjElCQYk/Oor/s7rzzTnnzzTfNqccatnr06CFLliyRq6++2tyvlxL65pvCZ1kG3Gnbtp2sXLlKjh07Lr/9dkjef/9D07yvde3YsWNmnePHj8sXX3wh9epdxE60Qfi6s5XrCIljJcp6Fb4KCl3lMo/KUwdekWpl+bEI345LQMBnrs9Lz5DRU2z1NnHiRDPny8cffyyLFy+WlStX5pwNCRTXwYMH5J57+pgvYx0crV3fl19+udeP8999W+TD7xbJul3rJL5EnNSrWE8GtO8vlZO5GHAo0ve7/5EP5ejRMvJRSrt84au8Y6+ORCpwe4cjSt5LukvWl84fuv6xd6qUyzwiv7+xUCr2uz2grwPey8rOknfWvyPLfvhM9qful9rla0vbem3kLw27ScnY0Ak9f/1rN1m7dq05679mzery3nsfMKkqXEQ5irruD/xKx8hVq1ZNdu7cLVWruo4tKYieRZWaelSSk1NcTv+2s+LuEw1c0794TVb+sjLffXoQn9T7WWlR2/XLOdTZoZ6c3LpNdj02QfSg9Vr5G1zCl4qRVCmVMExiYn51G7pOnX5EMjM7uw1dlTKP5Cyr+c/RUrr+hRKJwrGeZGZlyoNvPCQbft2Y775yZcpJnyvvlp5X9PApgIXj/gg0X/eJfr/VqlVD9uzZ4/H3mx0Vq6tRLyOhb0phN2/nugkEPQNlxIgR5vJFOiBbz0LSWfU9oZdHGjBggOnX1+kLOnToYE4uQHjSwDX43w/L3a/3cRu61OnM0zLmg3GSdirN8vKhcEfeXWzOXowSkfsOvSvdjrqO68uSZDlx8p+SlVXd59Clj3/kvcW8FSFkxpevuw1d6nD6YXn20+ek+5Se8uaa+ebzC4SyYqWi0aNHm6b/vElZr2H1/vvvy0UXXWSmmwi2Pn36yMKFC2XIkCFm8P+cOXOka9eusnz5cmnfvn2B2+m8ULqezpvz6KOPmsGT06ZNk44dO5qmZD2JAOFh+Q+fyfQvX5Nffi+4Gyq3Q8cPyaj3npRq51WTcKGN1/ojQyeXzfu5jATZpzIkdd+XIlX/bKQvKdPkwrMn5JcS1+csczhSTPhKKP2YafkqKHSVyj4izbLGy7KKbs6G3fexJL93XKJLuQ7mjwThWE90OEBRnAFs2oqXpevlXeShqx6UsiW5tBhs1NWoc9q0bNnSjPXSywoFi15HrUWLFqYcw4cPN8t0/hWd/E7PxNT7C7JgwQLp3bu3zJ8/3/xf6aBuDW+dOnUy93uLrkZrm8I1PA9582FZtZ2TOyKVHsFOZzwgZ870cFkeFXVUyiT0l4wzN8uZM73y3HdIErRLMvqAxaWFVbTb8dU7X5YGVQu/sgpdjf7bJ3Q1eiZgl5zXCVZ1wPOECRMkmLSlS7tE+/f/8xRvPfukb9++ptVKW+cK21Znh7755j9nrtYux169esmiRYvMBJ4IbSPeGUnoinDaaFMy/mWJizt3WZ/cLV9nMq9zE8gIXXagXY59Z99H1yPsE7yUjonSq7gH08aNG6VOnTqSkpLislzHeTnvL2xbnbNMg1vebbXVTCfPQ+g6eeakrNj6ebCLgSCGr+io3yQq6s+xeoQuezmbfVYmLXk+2MUAXARs5LvOav/iiy/mXLE9WLTL091105zL9u/fX+i2rVu3LnRbDWaFSUtLM7fcj+lsytWbJ7Kzs/53LULP1rcDT/bJ5j3/lWwH12+0W/iKid4lmZltJabEdxIb+4XExOyR0xm3SVTUSSkZ/4ZERx8KdlFhoY27NxZ6rOX46r994ul3mt0VK3jVqlXL7eBMPRNQJ7fU6zfqIPtg0u5AHUSal3Oyu8K6C4uzrdOkSZNk3Lhx+ZanpR2T1NRzF3kuSlZWtqSnHzdjWWJiAtpIGTY82Sd6P+wmShyO0uKQUiKO0v/7O878WwezOhyxwS4ggjD/l45XKvB+jq9+2yf6vYYABy89IzBv8NK/tVtPu/duueWWoF+4WKeP0DN48tKuQuf9gdjWaejQodKvXz+XFi/tqkxMTDIDFz2hvzp0NycnJ0t0NPPMeLpPWpZuKTFRMZLl4FeYHeQ9ezEr6xKJitojGWf6i8ORbJadyGqQc7Yj7KFVnVaFHms5vvpvn6Snn/DxXbKXYgWv2bNnS6jTbkGdQT8vZ5df5cqVC93WuZ632zolJiaaW17Oec48pePM9APABH+e75OEUgnSucG1snjzfzzezwhPBU0ZoQPsHY5SBU41gcgWGxMrQzoNLvK4yfHVP/uE7yfPRHy/VaNGjWT79u1y9KhrU/OaNWty7i9sWx1gr33debfV7kbm8Qp947qPlWsv7RTsYiAIoUsH0sfHfyLxca7TvjjDV95JVhFZysQnyL/6z5O4EnHBLgrge4vXr7/69guxevXgHeD0At3PPvusTJ8+PWceL+0+nDVrljRp0sSMU3O2Yum4NO0ijY2NzdlWp5R4++23c+bxOnz4sPlbJ1b1pKsRwf/V9vSNT8mNTW6UaSumyaY933u87dX1r5Ka5WpKuNATCbQbXH8UREdF3m+qkz/9Iic2bXFZ5pAo+Sb+Ptke28FlufPsxaiodImPnycOKesyrYSGr7PHn5WOp/4uyY59bp8voeGlUvqiyLtsUDjWkwVrF8jxjHSP1k0qlSQ3N71J7mnTJ6Su4Qj4FLxq1qzp00zHwTzTQSdP1Xm4Ro0aZUJT3bp1Ze7cuWaai6VLl+asN3LkSDOjvS7X1+kMXjoJrM75pVNH6BxeOnN9ZmZm0Ocng3ea1mwiM+95Xbb/vl1mfPW6LN2yTBxmuLV7lZIqyejuT0qZ+DJhs6sjfSLIzMv/kG2fPqLJwfydLVEy5YJbZHus6zU1804Z4TzbUeUOX6ejk+TL+NHmkkHVz+SZvT46Sur+/QmJLRfcMaqBEI71RAPUSyumFbpOlZQq0q/tvXL9ZV0kNib4l6oDCuJV7Zw5c2bYXGIiNw1aenmjefPmyR9//GFmrdcJUPXSP4XRg9LixYvlsccekylTpsjJkyelWbNmZj9cfPHFlpUf/lOnQh3TAtavbd8CA5iGrQk9x4dV6LIDDUFlm18hx9dsMNlLQ9fyJNfQVUIOSUk3M9IXFL6OlSgrT1Qd6Bq+oqKkbIsmERm6wtVdV94p3+3Z5Pb6qgQuhJuAXTII7nHJoND61a4tYB9/v1jW7VoncSXipV7FenJvmz5Srkw5CTfh2JLhrZNbf5Edj01wG7r0gtcpJYfL7wn5T6Zx0qPdpQcfk28SrnZZnnT2uEv4qvnP0VK6fuR1M4ZzPdGvKv2sfvbjZ7Ivdb/UKV9b2tRrI50u6VSsFq5w3R+BxCWDAov2WIjdW8AGXzMo2MWAh0rWqyPTmw6V5WnV8oUuDU5T6h4sdHtt+eqWNl/OPxMrH6W0c9vy1ei6RhEbusKZ9rZ0a9jV3IBwFh4jKwHYXna2Qx5/+4QsLiB0Vco84tE+0sES9x16V7od/dJluYavUdUHS1rnG2y/rwGESPDSmejfeustr59Ex1Xptl988YXX2wKAM3QtXHumWKGrqPCVGp0gd75+WrYdZNJdACEQvPQU5LxzWnnaN6/bch0nAP4KXRXLOuSfGfO9Dl1Fha8j6Q6545U0wheA0OhqvOOOO3JmXff0VqFChbA8GxJAiIaupGj510PJ0mbyo3LeX/83caq3x5ioKBO+hrc8IXe2ch3uSvgCEBKD68eMGVOsJ6tdu3axtgdgH4WGrgfKSo1yegZajFTsd7sktmkhR95bLHJsu2cPHn1uyojze3YxA+lHOxwSFXNS5n6dkS98zbs/UepW5Gw3AGEYvADAf6HrTxqeSo8cLPEvfS1yZGehj51yXUepe/1tLvN0aYv8k91Lm38TvgAEEmc1Agjr0JVbVImif0smXtnM7eSozvB1V5t4l+V0OwLwJ4IXgIgIXf5A+AIQaAQvACEh2KHLifAFIJAIXgCCLlRClxPhC0CgELwABFWohS4nwheAsAlejRo1ksWLFwfioQFEkFANXU6ELwBhEbwmTpwoTz75pLRp00a++uqrQDwFgDAX6qHLifAFIOSD13XXXSfr16+XQYMGSb9+/czfGzZsCMRTAQhD4RK6nAhfAMJijFfv3r3lhx9+kBtvvFF69OghvXr1kp9//jmQTwkgxIVb6HIifAGwfOZ6T6Wlpcl3330nGzduNDdt7fr9999l8+bN0qFDB+nevbv885//lLJlywbi6QGEqHANXU7McA8gJFu8UlJS5L777pM1a9bI5ZdfLlOnTpXDhw/Ljz/+KNu3b5cyZcpIz549A/HUAEJUuIcuJ1q+AIRci9fRo0clMTHR7X2lSpWSZ555RpKTkwPx1ABCUKSELidavgAEpcVrxIgR0rZtW8nMzHRZXlDoyu2LL74ozlMDCBORFrqcaPkCYHnweu+996RBgwYSGxub776zZ8+aaSV0cL07DRs2LM5TAwgDkRq6nAhfACwNXr/++qs0btzY7X0lSpSQ1atXyxNPPFGcpwAQpiI9dDkRvgBYFrySkpLMGYwF0W5IHWAPwF7sErqcCF8ALAle7du3lxkzZkhGRobb+/XsxWPHjhXnKQCEGbuFLifCF4CAB6/HH39cdu/eLbfeeqvblq/PPvtMqlevXpynABBG7Bq6nAhfAAI6nYQOkH/rrbfk9ttvl1q1apn/X3HFFebgs2zZMlm4cKGMGTOmOE8BIEzYPXQ5MdUEgIDO4/XXv/7VzFKvAWvWrFlmslTnwefee++V4cOHF/cpAIQ4QpcrwheAgE6gWqdOHZk3b56cOXNGduzYIadOnZILL7yQSwIBNkDoco/wBSDglwyKi4uT+vXrmykmuA4jEPkIXYVjzBcAS67VCCDyEbo8Q/gCkBvBC4DXCF3eIXwBcCJ4AfAKocs3hC8ABC8AhC4LEb4A0OIFwCO0dPkH4QuwN4IXgCIRuvyL8AXYF8ELQKEIXYFB+ALsieAFoECErsAifAH2Q/AC4BahyxqEL8BeCF4A8iF0WYvwBdgHwQuAC0JXcBC+AHsgeAHIQegKLsIXEPkIXgAMQldoIHwBkY3gBYDQFWIIX0DkIngBNkdLV2gifAGRieAF2BihK7QRvoDIQ/ACbIrQFR4IX0BkIXgBNkToCi+ELyByELwAmyF0hSfCFxAZCF6AjRC6whvhCwh/BC/AJghdkYHwBYQ3ghdgA4SuyEL4AsIXwQuIcISuyET4AsITwQuIYISuyEb4AsIPwQuIUIQueyB8AeGF4AVEIEKXvRC+gPBhi+CVkZEhI0aMkCpVqkipUqWkefPm8umnn3q07ezZs81Bzd3t4MGDAS874C1Clz0RvoDwUEJsoE+fPrJw4UIZMmSI1KtXT+bMmSNdu3aV5cuXS/v27T16jLFjx0qdOnVcliUnJweoxIBvsh0iT7xzSt5dl+myvGJStPzrgbJSo1wMu9YG4UvN/TojZ/mRdIfc8UqazLs/UWqXD2IBAUR+8Pr2229l/vz5MnHiRBk+fLhZdtddd0mDBg1k2LBh5n5PdO7cWVq2bBng0gLFa+n6x+Io+eh7QpedFRW+5vZPkHLxQSwgYHMR39WoLV3R0dHSv3//nGUlS5aUvn37ytq1a2XXrl0eP1ZaWppkZWUFqKRA8UKXtnR99H2Uy3JauuypsG7Hu6afkB2HglY0wPYiPnht3LjRdBGmpKS4LNdxXs77PdGpUydJSkqS0qVLS7du3eSnn34KSHkBX8d00b0IT8PXg/+Okm0H+REJBEPEdzUeOHBAKlWqlG+5c9n+/fsL3V6Dlo4R69ixoyQmJsr69etl0qRJ0rp1a9mwYYPUqFGjyFYyveUuj9KWM09bz7KzsyQ7O9v8H+wTdy1d+UNXlLwxoLRUTTlX1+zC4XAUuY5+luy0Tx7vFi+ObIe8sepMzrKjJ6Pk7tdOyJz7ROpWtPe4P46v/tsndvpc2SZ46UFVz1D0RFxcnOliPHXqlMTH5x/QoN2NSu8vTK9evczNqUePHma8V7t27WTChAkyY8aMQrfXkDZu3Lh8y9PSjklqaoJHryUrK1vS04+LfqfExER8I6VH2CfnBtKfG9Pl2r1YoaxDXro1WxJj0iQ1VWwl24MDf3p6uqSmHhU7eaidSMaZKFmwLsql5evOV4/LtNscth5wz7HEf/tEv9cQYcFr5cqV0rZtW4/WXbFihXTo0MFMH+EurJ0+fdr8X+/3Vps2baRFixaybNmyItcdOnSo9OvXz6XFS7s5ExOTJDnZtfuzIPqrIyrq3FmU0dH2/nXqZPd98ueYrsx8oeuNAQlSs3ys2FF0TNF1oUyZMh5/9iLJ+JscEh9/Wt5Y6dryNXB+tMy5L8G2LV92P5b4c5+kp58IaLkiRVgFL50KYtasWR6tW79+/Zwuxd27d+e739nlV7lyZZ/KUq1aNdmyZUuR62n3pN7yiomJMTdPaeudfgC82SbS2XWfaOh68l13Y7qiTEuXhi677ZPc45o8qTd23T+je5xrZc8dvrTlS7sd37i/rNSrGFZfCX5j12OJv/cJ+88zYfUpq1Chghlv5Y1GjRrJZ599JkePHnUZYL9mzZqc+32xY8cOKV/exu3zCLnJUXVMl3YvAoUF0yf+UtL0AuTrdnzluK3DF2CViB8wdNNNN5lBgtOnT89ZpgcdbTlr0qSJ1KpVy6UVbOvWrZKZ+WdLwqFD+c+7Xrx4sRlkf91111nwCgDPZqSvfj6/1uFZ+Bp6jUPuvDLOZbkzfP188Cy7EQigiP9po2Oxbr75Zhk1apQcPnxY6tatK3PnzpWdO3fK0qVLXdYdOXKkmdVe76tZs6ZZpmcvNm7cWJo2bWqmk9AzGWfOnGkuP6SPCYTKZYA4owie0h5ZbfmKjoqSOXkmWaXlCwisiA9eSoPW6NGjZd68efLHH3+YWesXLVpkpogoSu/eveXjjz+WJUuWyMmTJ82YMR0sr4/nbpoKwN+49iIC1fI16n8z3BO+AOtEOTyZ+AZ+s3fvXjMwf+fO3VK1alWPttGWDD39Xc/EYvCivfaJN6HLLvukMLe8epts+21boetMu2OqtKjdQuwqbz3Rr4C/f3DSJXyp88tE2WLMF58b/+0T/X6rVauG7Nmzx+PvNzuK+DFeQLiipQtWtnzd7WaGe8Z8Af5H8AJCEKELViJ8AdYheAEhhtCFYCB8AdYgeAEhhNCFYCJ8AYFH8AJCBKELoYDwBQQWwQsIAYQuhBLCFxA4BC8gyAhdCEWELyAwCF5AEBG6EMoIX4D/EbyAICF0IRwQvgD/IngBQUDoQjghfAH+Q/ACLEboQjgifAH+QfACLEToQjgjfAHFR/ACLELoQiQgfAHFQ/ACLEDoQiQhfAG+I3gBAUboQiQifAG+IXgBAUToQiQjfAHeI3gBAULogh0QvgDvELyAACB0wU4IX4DnCF6AnxG6YEeEL8AzBC/AjwhdsDPCF1A0ghfgJ4QugPAFFIXgBfgBoQv4Ey1fQMEIXkAxEbqA/AhfgHsEL6AYCF1AwQhfQH4EL8BHhC6gaIQvwBXBC/ABoQvwHOEL+BPBC/ASoQvwHuELOIfgBXiB0AX4jvAFELwAjxG6gOIjfMHuaPECPEDoAvyH8AU7I3gBRSB0Af5H+IJdEbyAQhC6gMAhfMGOCF5AAQhdQOARvmA3BC/ADUIXYB3CF+yE4AXkQegCrEf4gl0QvIBcCF1A8BC+YAcEL+B/CF3hK9uRLe9ueE/2p+4vct231y2UA8cOWlIueI/whUhH8AIIXWHtdOZpeWjeQPnHR0/JiYwTRa6/Yuvn0vuVW2TVL6ssKR+8R/hCJCN4wfZo6Qpvr381U77dudarbTSgjf1gnBw/fTxg5ULxEL4QqQhesDVCV3hzOBzy5pr5Pm175MQf8ul/l/i9TPAfwhciEcELtkXoCn+Hjh+SU5mnfN7+1yO/+rU88D/CFyINwQu2ROiKDGVKlpES0SV83j45Idmv5UFgEL4QSQhesB1CV+QoHVdaGlZr6PP2req08mt5EDiEL0QKghdshdAVeW5veatP211RvbHUr3iR38uDwCF8IRIQvGAbhK7I1K5eO7nIhwDVv31/80WO8EL4QrgjeMEWCF2R/UU8oP19Xrd2Na3ZJGBlQmARvhDOCF6IOF//nCn3vX5cxr57Qo4czyZ02YC3rV60dtknfH38XYbc9Wqa/N9HJ+VsliNIpQX+5PvpQEAI+j0tWwbOTZf00+cOsKt+yZRLKsfIR99luqxXMSla/vVAWalRLiZIJUUgWr2GvvVokevWu6AerV0RFr7UnK8z8oWvLg3j5I2V55av2nZWEuKjZGCnUkErL6Bo8UJE+fi7MzmhS+34PZvQZaNWr+TSRU8PMfDqhxjbZZOWL2focnprTYZpAQeCieCFiPKf788Uej8tXZH9BXzPlX0KXef8hPOkNVNI2CZ85XUgNVs27cmyrFyAOwQvRAw9qG7YdW5chzsx0SJT7kygezGC3dHqdmlZu6Xb+3Si1Vn3zqS1K8LDV6PqhQ8f+M+mwn+cAYFG8ELE+KSI1q6sbJERC07I6Uy6GiLZlNsmy9BrH5GU0skSGxMrcTGx0qp2S/lw8PtSJaVKsIuHANKuxe9+zSqyVZzuRgQTg+sRMf6zyXU8hzvbf8+WDzeckV4tCu+SQPiKjo6W21veZm5ZWVmSmnpUkpNTJCaGEykimZ6xOGVJ0dftdHY3Nq7B1x+CgxYvRIT9f2TJht2ejd0oW5JJM4FIUyImSkrFefbZfnPV6YCXBygIwQsRYeryon/pxsaI9G1fUq5pEGtJmQBY64U7EqTa+UV/rX303RlxOBhygOCI+OCVnp4uY8aMkS5dukj58uXNAMyJEyd69RipqakyYMAAs31CQoJ06NBB1q1bF7Ayw3u7DmUXGLY6Xhwrz9ySIGvGJsvIv5SW2BhavIBIdEXNWPlsRJK8PShR7m1XUiolu/+KO8OJjQiiiO/kPnz4sIwfP16qVq0qjRs3lqVLl3q1fXZ2tnTt2lU2bdokjz76qFSoUEGmTZsmHTt2lLVr10r9+vUDVnZ47v6rSsraHeni/A3bsk4JubFZvFx9aawklor43xcA/kd/XOv4Lb2N/EspM9hex3/qHF4n/jcMtHGNGM5uRdBEfPCqVKmS7Nu3TypXriy7du2SWrVqebX9woULZdWqVTJ//nzp3bu3WXbzzTdLvXr1ZPTo0bJgwYIAlRzeaFc/TlY8niirfzkrV10SK+eVYSA1YHe5Q9iIbqXly58yRXsYO1zMcAMET8QHr/j4eBO6fKXBq1y5ciZsOWmXY69evWTu3Lly6tQpKVWKS1CEgqrnlZCbmkd8lQbgg+joKOlwcRz7DkFHH0wRNm7caLoo9RT13Jo3by6nT5+WrVu3BvL9AQAAEYTmgSIcOHBAWrdu7bYLU+3fv98Es4KkpaWZW+7HUzq/kN48kZ2dZcaa6f/BPqGeeI7PDvuEOmLd58bT7zS7C6vgpaf/ZmQUPUmmiouLy9dK5QvtStTuyrxKliyZc39hJk2aJOPGjcu3PC3tmKSmJnhUhqysbElPP27GJsTodW/APqGe8NnxEccT9keg6oh+ryHCgtfKlSulbdu2Hq27YsUKM+1Dcen4LXdhT7sZnfcXZujQodKvXz+XFi/tpkxMTDKzaXtCf3VERYkkJydLdLT9Bo3rSRFjxoyW5cuXyYkTJ8yZpC+9NE1q1qxp233ijt3rib/2ibv69vLLr0ijRgW3bIcT6ol/9kck1xNf90l6+omAlitShFXw0jMJZ82a5dG6/prmQbsUnd2DuTmXFTVwPzEx0dzy0suXeHMJE2290w+A3S57snPnTmnb9kq5+upr5MMPP5KkpCRZtmyZ+b9d90lh2CfF2ycF17fkiKpn1JPi7Q871BNf6kikvPZAC6vgpXNo9enTx9LnbNSokXz++eemvzt31+WaNWtMdyPzeAXWgw/eL+3atZM33pjnEsC/+eYb6dXr5v990KNky5b/yurV35r3C/B3fXM6efKkXHbZpdK79y3y1FNPs6NtqrB6MnnyZJk5c4YZGtOlS1eZOPH/glhShKKwCl6Bpq1Yx44dkzp16khs7Ll5Xm666SYzpcTbb7+dM4+XTsqqf+vEqkwlETg7duwwvyI3btyU7z7trl2+/DPTXbt37165+uqOhC4ErL45Pf30U9KiRQv2tI0VVk/++OMPefnll2TTps1SokQJufLK1rJ582a57LLLglJWhCZbBK+pU6eay/7ozTn+6+zZs+bfgwYNMs3EauTIkTJnzhzTjKzjh5zBq2XLltK3b18zdYTO4aUz12dmZsqECROC+Koi33ffbZTSpUtLgwYNCl3vnXcWyg033GhZuWDP+rZt2zb56aet0rVrN/npp58sLx9Cv55oK5d+t+i44HNnBWbL+eefH5RyInTZIng9++yzsnv37py/lyxZYm7qjjvuyAle7mhX1uLFi+Wxxx6TKVOmmK6GZs2aycyZM+Xiiy+2pPx2pa2OegDTExmcZ5G6oy2SL7ww2dKywX71bfjwYTJx4j/lm29WBaV8CP16oiFryJBHpFatGmbW/EcfHVasCbwRmWwxN4GefaK/RNzdnC1bavbs2fmWqZSUFHnttddMF6MGry+++MJ0dSGwWrZsJWXKlJFBgwaa1sYtW7aY1stff/01Zx0N1IcPH+L9QEDr24cffiB169ZzGe8Feyqsnhw9elSWLv1UduzYJTt37pYPPvjA3A/YLnghPGm37nvvvS8//PCDtGjRTK66qoMsW7bEnGTh9N5779LNiIDXNz2ZZsGCt+TCC2vL8OGPyauvviITJzK43o4Kqyc6tUSdOheaXpSyZcuaKY02bFgf7CIjxNiiqxHhq23bdrJy5aoCZ0h+9913ZPLkKUEoGexU3/7xj6fMTc2ZM9uM8RoxYmQQSohQridVqlSV1atXm65I7Wr8+uuvpXv3HkEpI0IXwQthS89mPHTosDRt2jTYRQEAadWqlXTs2FGaNr3CBK8ePXqak7OA3AheCFtVq1aVH3/kIuWw1t13WzuXIMKLzu/GHG8oDGO8AAAALELwAgAAsAjBCwAAwCIELwAAAIsQvAAAACxC8AIAALAIwQsAAMAiBC8AAACLELwAAAAsQvACAACwCMELAADAIgQvAAAAixC8AAAALELwAgAAsAjBCwAAwCIELwAAAIsQvAAAACxC8AIAALAIwQsAAMAiBC8AAACLELwAAAAsQvACAACwCMELAADAIgQvAAAAixC8AAAALELwAgAAsAjBCwAAwCIELwAAAIsQvAAAACxC8AIAALAIwQsAAMAiBC8AAACLELwAAAAsQvACAACwCMELAADAIgQvAAAAixC8AAAALELwAgAAsAjBCwAAwCIELwAAAIsQvAAAACxC8AIAALAIwQsAAMAiBC8AAACLELwAAAAsQvACAACwCMELAADAIgQvAAAAixC8AAAALELwAgAAsAjBCwAAwCIRH7zS09NlzJgx0qVLFylfvrxERUXJxIkTPd5+9uzZZht3t4MHDwa07AAAILKUkAh3+PBhGT9+vFStWlUaN24sS5cu9elxxo4dK3Xq1HFZlpyc7KdSAgAAO4j44FWpUiXZt2+fVK5cWXbt2iW1atXy6XE6d+4sLVu29Hv5AACAfUR8V2N8fLwJXf6QlpYmWVlZfnksAABgPxHf4uUvnTp1MuPF4uLizL+fe+45ueiiizwKa3pzOnDggPm/BjhPQ1x2dpZkZ2eb/4N9Qj3xHJ8d9gl1xLrPDQ0TniF4FaF06dLSp08f6dixoyQmJsr69etl0qRJ0rp1a9mwYYPUqFGj0O113XHjxuVbnpZ2TFJTEzx6k7KysiU9/bg4HCIxMRHfSOkR9gn7hHrCZ4djSWgdX/V7DREWvBwOh2RkZHi0rrZMRUcXP6T06tXL3Jx69Ohhxnu1a9dOJkyYIDNmzCh0+6FDh0q/fv1cWryaN28uiYlJkpyc4lEZ9FdHVNS5wfzR0THFeDWRg33CPqGe8NnhWBJax9f09BMBKlFkCavgtXLlSmnbtq1H665YsUI6dOgQkHK0adNGWrRoIcuWLStyXW0l01teMTEx5uYpDZH6AfBmm0jHPmGfUE/47HAsCZ3jK99PERi86tWrJ7NmzfJo3fr16we0LNWqVZMtW7YE9DkAAEBkCavgVaFCBTPeKhTs2LHDTMgKAADgKUZq56Ljr7Zu3SqZmZk5yw4dOpRvpy1evNgMsr/uuus83tEAAABh1eLlq6lTp0pqaqq5Ocd/nT171vx70KBBkpSUZP49cuRImTNnjuzcuVNq1qxplunZizrjfdOmTc16eibjzJkzpUqVKjJq1KggvioAABBubBG8nn32Wdm9e3fO30uWLDE3dccdd+QEL3d69+4tH3/8sVn/5MmTZiZ8PUtx9OjR5t8AAACeskXw0ksFeXpBbL3l9ve//93cAAAAiosxXgAAABYheAEAAFiE4AUAAGARghcAAIBFbDG4PpQ4p7HQOcO8ueK7XnxUr4PFJRnYJ9QTz/HZYZ9QR6z73Di/15zfc3CP4GUx54SsrVu3tPqpAQCw5HvOORcm8otyOBwON8sRIKdPn5bNmzebyw2VKFHC418RzZs3l2+//Za5w9gn1BMv8Nlhn1BHrPvcaEuXhq7LLrtMSpYs6cMz2wMtXhbTytisWTOfttUPQNWqVf1epnDGPmGfUE/47HAsCZ3jKy1dRWNwPQAAgEUIXgAAABYheIWBxMREGTNmjPk/2CfUEz47HE84vvKdE74YXA8AAGARWrwAAAAsQvACAACwCMELAADAIgQvAAAAixC8AAAALELwCkHp6elm+oguXbqYSwtFRUXJxIkTPd5+9uzZZht3t4MHD4od94lKTU2VAQMGmO0TEhKkQ4cOsm7dOglXGRkZMmLECKlSpYqUKlXKXOLj008/tUUdKc5rj7R6UJz9Ee71IJDHjEisJ8XZJ5FcV6zGJYNC0OHDh2X8+PHmUg2NGzeWpUuX+vQ4Y8eOlTp16rgsS05OFjvuk+zsbOnatats2rRJHn30UalQoYJMmzZNOnbsKGvXrpX69etLuOnTp48sXLhQhgwZIvXq1ZM5c+aY17h8+XJp3759RNcRX197JNYDf9SFcK0HgTpmRGo98cd3SyTWFcvpRbIRWk6fPu3Yt2+f+ffOnTv1IuaOp59+2uPtZ82aZbb55ptvHJGiuPvkrbfeMtvMnz8/Z9nvv//uSE5Odtx8882OcLNmzRrzeiZOnJiz7NSpU446deo4mjVrFtF1pDivPdLqQXH3RzjXg0AeMyKxnhR3n0RyXbEaXY0hKD4+XipXruyXx0pLS5OsrCyx+z7R1oBy5crJzTffnLNMm9p79eolixYtklOnTkk40dcTHR0t/fv3d7kAe9++fc0v8l27dkVsHSnOa4+0euDPuhBu9SCQx4xIrCf+/G6JtLpiNYJXBOvUqZMkJSVJ6dKlpVu3bvLTTz+JXW3cuNE0resXVG46Fub06dOydetWCbfXo839KSkp+V6P8/5IrSPFee2RVg/8VRfCsR4EUiTWE3+hrhQfY7wikB48dcyHjkfQ6zuuX79eJk2aJK1bt5YNGzZIjRo1xG4OHDhgXn9elSpVMv/fv3+/OdCG0+txlr2g1xOpdaQ4rz3S6kFx90c414NAisR6UlzUFf8heAWYw+EwZxx5Ii4uLt8vLF9oc7jenHr06CGdO3eWdu3ayYQJE2TGjBlit32iXQPazJ6Xdsk47w+n/VHc1xPqdaQwxXntoVwPfFWc1xTO9SCQIrGeFBd1xX/oagywlStXmtO7Pbl9+eWXAStHmzZtpEWLFrJs2TKx4z7Rx3IXbrTbwHl/OO2PQLyeUKojhSnOaw/leuArf7+mcKkHgRSJ9SQQqCu+ocUrwPTU7lmzZnm0bqBPUa5WrZps2bJF7LhPtItAuw/yci7z18kMVu0PfT27d+/2++sJlTpSmOK89lCuB74KRF0Ih3oQSJFYTwLF7nXFFwSvANP5X3QMRSjYsWOHOTPHjvukUaNG8vnnn5v5eXJ3Xa5Zs8Z0HwRzXh5f9oe+ns8++0yOHj3qMqhaX4/z/nCuI4F67aFcD3wViLoQDvUgkCKxngSK3euKL+hqDHP6C0zPsMnMzMxZdujQoXzrLV682Aycve6668SO++Smm24ykwe+/fbbOcucf+tEieHWdaCvR78Upk+fnrNMu0a05axJkyZSq1atiK0jnr52O9SD4u6PcK4H/mKXeuIN6kpg0eIVoqZOnWouWaE3tWLFCjl79qz596BBg8yp32rkyJFmluqdO3dKzZo1zTI9G0fPuGnatKlZT89OmjlzprmcyKhRo8SO+0QPpC1btjRzG+lBVn+h6UzUerDVQcThRsfg6BxD+n7qF0LdunVl7ty55jXnnY060uqIp6/dDvWguPsjnOuBv44Zdqknxd0nkV5XLGX5lK3wSI0aNcwswe5uOuOw0913351v2RNPPOFo1KiRIykpyREbG+uoXr264/7773fs37/ftvtE/fHHH45+/fo5zj//fEepUqUc7dq1M7N+hyudnXzYsGGOSpUqOeLj4x1NmjRxLF68ON96kVhHPHntdqkHxdkf4V4P/HHMsFM9Kc4+ifS6YqUo/Y+1UQ8AAMCeGOMFAABgEYIXAACARQheAAAAFiF4AQAAWITgBQAAYBGCFwAAgEUIXgAAABYheAEAAFiE4AUAAGARghcAAIBFCF4AAAAWIXgBCBtjx46VqKgocytZsqTLfbNnzzbLd+3aJaFg4cKFOWXV2+rVq4NdJAAhgOAFIOy88cYbMmvWrIA8dpUqVWT8+PHm36tWrTJhLzU11evHad68uSln//79A1BKAOGK4AUg7Nxxxx1y6623+v1xN27cKPv375du3brlBK9x48b5FLyqV69uytmqVSu/lxNA+CJ4AcD/fPzxx1KpUiVp3Lgx+wRAQBC8AATUpk2bpHfv3nLBBReYcVn16tWT4cOHW7LX+/TpIzVr1ixwrJi74NWlSxdzn64zbNgws7xWrVo5Y7U+//xzSU9Pl0cffdQsj4+Pl/Lly0uHDh3kyy+/tOR1AQhfJYJdAACR68MPP5RevXqZbre//e1vkpiYaLrzvv76awk1hw8flm+//VYee+wx8/cNN9wgP//8s7z55pvy/PPPS7ly5czyiy++WB544AFZsGCBPPTQQ3LppZfK0aNHZc2aNSZktmvXLsivBEAoI3gBCIhffvlFbrvtNuncubPMnz9fSpUqlXNfRkZGyO31//znP1KiRAnp1KmT+fvyyy+XK664wgSvHj16uLScffTRR3LffffJpEmTglhiAOGIrkYAAaFddbGxsTJnzhyX0KW0ey7UaDejtlaVKVOmyHWTkpJMC9e+ffssKRuAyEHwAuB32qL1/vvvmxav5OTkkN/DZ8+elU8//VS6du3q0frPPPOMbNmyxXShNm3aVEaNGiU//fRTwMsJIPwRvAD43Y4dO+TEiRPSpEmToO5ddwPoVVZWlsvfOm2EThnhafC6+eabzWucNm2a1KhRQ1588UW57LLL5N///rdfyg0gchG8APjdqVOnCg0+ToMGDZK77ror52+dm+vee+/1WzlSUlLczsG1e/fufN2MdevWNbfcCit/xYoVZcCAAfLOO+/Ir7/+KrVr15YxY8b4rewAIhPBC4DfXXjhhSa0LFu2LN99mZmZOf9+/PHH5b333jOtRxpafvvtN3n11Vf9Vo46derIsWPH5Pvvv89ZduDAAfOceYOXu9auhIQE8389azF3a5k+Zm7anapTS/gy0SoAe+GsRgB+p9NGaMvV66+/boLWVVddZea++uqrr6RFixYmcCmdrFTPDtSpG86cOWO6/HRAvr/ccsstZs6wnj17yuDBg+XkyZPy8ssvm7nENmzYkNP6peO1XnjhhXzb6/gtNXLkSDNeLS4uzrwWDVk33nijNGzY0LzWlStXyieffCIDBw70W9kBRCaCF4CAmDJlilStWtVMx7Bo0SJzJqCGrr/+9a8u6zVq1MjMk7VkyRK/D8Q///zzTevW0KFDzfxcGpiefvpp2bZtW07w0tYuPZPR3fxbGrx0fR3Ldc8990h2drYZhK/zdy1dutTMU6bBUh/32WeflSFDhvi1/AAiT5TD4XAEuxAA7GndunXSvXt3E3piYmJk3rx5RU5RoddOPHTokOnK1GBVXNrFqNNbvPvuu+JP2oKXlpZm5jDTsWzffPONtGzZ0q/PASD80OIFICh0QLp2Meo8X9rqpeOxtm7dKvXr1y9yW71Ej4al06dPF7sc7du3lyuvvFL8TVvD9OxHAMiNFi8AltOWIA07Ou5Kx3gpvS7i3r17TddkQXQQvt6UtpB17NhRQtXvv//uMqi/efPmZjwYAHsjeAEAAFiE6SQAAAAsQvACAACwCMELAADAIgQvAAAAixC8AAAALELwAgAAsAjBCwAAwCIELwAAAIsQvAAAACxC8AIAALAIwQsAAMAiBC8AAACxxv8DuWS19JnT++EAAAAASUVORK5CYII=", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(figsize=(5.2, 5.2))\n", + "tier_color = {4/9: \"#d1495b\", 1/9: \"#2e7d32\", 1/36: \"#1f6feb\"}\n", + "for i in range(Q):\n", + " col = tier_color[W[i]]\n", + " if i == 0:\n", + " ax.plot(0, 0, \"o\", ms=18, color=col, zorder=3)\n", + " ax.annotate(f\"$w_0={W[i]:.3f}$\", (0, 0), textcoords=\"offset points\",\n", + " xytext=(8, 8), fontsize=9)\n", + " else:\n", + " ax.annotate(\"\", xy=(CX[i], CY[i]), xytext=(0, 0),\n", + " arrowprops=dict(arrowstyle=\"-|>\", lw=1.5 + 40 * W[i], color=col))\n", + " ax.annotate(f\"$c_{{{i}}}$\", (CX[i], CY[i]), textcoords=\"offset points\",\n", + " xytext=(6 * np.sign(CX[i] + 0.1), 6 * np.sign(CY[i] + 0.1)), fontsize=9)\n", + "ax.set_xlim(-1.6, 1.6); ax.set_ylim(-1.6, 1.6); ax.set_aspect(\"equal\")\n", + "ax.set_title(\"Решётка D2Q9: дискретные скорости $\\\\mathbf{c}_i$ и веса $w_i$\")\n", + "ax.set_xlabel(\"$c_x$ [lu/ts]\"); ax.set_ylabel(\"$c_y$ [lu/ts]\")\n", + "from matplotlib.lines import Line2D\n", + "ax.legend(handles=[Line2D([0], [0], color=c, lw=3, label=f\"$w={k:.4f}$\")\n", + " for k, c in tier_color.items()], loc=\"upper right\", fontsize=8)\n", + "_finish(fig, \"01_stencil_d2q9.png\")" + ] + }, + { + "cell_type": "markdown", + "id": "a7daf37a", + "metadata": {}, + "source": [ + "## 2. Равновесие: полиномиальное и энтропийное\n", + "\n", + "**Полиномиальное равновесие** (разложение максвеллиана по Эрмиту до $O(u^2)$),\n", + "стандарт для BGK:\n", + "$$ f_i^{\\mathrm{eq,poly}} = w_i\\,\\rho\\left[1 + \\frac{\\mathbf c_i\\cdot\\mathbf u}{c_s^2}\n", + " + \\frac{(\\mathbf c_i\\cdot\\mathbf u)^2}{2c_s^4} - \\frac{\\mathbf u^2}{2c_s^2}\\right]. $$\n", + "Коэффициенты при $c_s^2=1/3$: $1/c_s^2=3$, $1/(2c_s^4)=4.5$, $1/(2c_s^2)=1.5$.\n", + "\n", + "**Энтропийное равновесие** (Ansumali–Karlin): точный максимум дискретной\n", + "H-функции при связях $\\sum f^{eq}=\\rho$, $\\sum \\mathbf c f^{eq}=\\rho\\mathbf u$.\n", + "Для D2Q9/D3Q27 имеет **замкнутую факторизованную форму** ⚠ (сверить с\n", + "оригиналом):\n", + "$$ f_i^{\\mathrm{eq}} = \\rho\\,w_i\\prod_{\\alpha\\in\\{x,y\\}}\n", + " \\underbrace{\\left(2-\\sqrt{1+3u_\\alpha^2}\\right)}_{\\text{префактор}}\n", + " \\left(\\frac{2u_\\alpha+\\sqrt{1+3u_\\alpha^2}}{1-u_\\alpha}\\right)^{c_{i\\alpha}}. $$\n", + "Здесь $3 = 1/c_s^2$. Энтропийная форма **точно** воспроизводит $\\rho$ и\n", + "$\\rho\\mathbf u$ (проверим ниже) и, в отличие от полинома, гарантирует\n", + "положительность и H-теорему." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "e9818100", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-06T17:33:55.653710Z", + "iopub.status.busy": "2026-06-06T17:33:55.653539Z", + "iopub.status.idle": "2026-06-06T17:33:55.659138Z", + "shell.execute_reply": "2026-06-06T17:33:55.658074Z" + } + }, + "outputs": [], + "source": [ + "def feq_poly(rho, u):\n", + " \"\"\"Полиномиальное равновесие O(u^2). rho:(Ny,Nx), u:(2,Ny,Nx) -> (9,Ny,Nx).\"\"\"\n", + " cu = CX[:, None, None] * u[0] + CY[:, None, None] * u[1] # c_i · u\n", + " usq = u[0] ** 2 + u[1] ** 2\n", + " return W[:, None, None] * rho * (1 + cu / CS2 + cu ** 2 / (2 * CS2 ** 2) - usq / (2 * CS2))\n", + "\n", + "\n", + "def feq_entropic(rho, u):\n", + " \"\"\"Энтропийное равновесие (product-form). Клип скорости для численной безопасности.\"\"\"\n", + " ux = np.clip(u[0], -0.95, 0.95)\n", + " uy = np.clip(u[1], -0.95, 0.95)\n", + " sx = np.sqrt(1 + 3 * ux ** 2)\n", + " sy = np.sqrt(1 + 3 * uy ** 2)\n", + " prefx, prefy = 2 - sx, 2 - sy # префактор по каждому измерению\n", + " Bx = (2 * ux + sx) / (1 - ux) # основание степени по x\n", + " By = (2 * uy + sy) / (1 - uy)\n", + " base = rho * prefx * prefy # (Ny,Nx)\n", + " Bxp = Bx[None] ** CX[:, None, None] # (9,Ny,Nx): B_x^{c_ix}\n", + " Byp = By[None] ** CY[:, None, None] # (9,Ny,Nx): B_y^{c_iy}\n", + " return W[:, None, None] * base[None] * Bxp * Byp" + ] + }, + { + "cell_type": "markdown", + "id": "6ecd01ca", + "metadata": {}, + "source": [ + "### Самопроверка равновесий\n", + "\n", + "Проверяем, что **энтропийное** равновесие точно даёт нужные нулевой и первый\n", + "моменты ($\\rho$, $\\rho\\mathbf u$), а второй момент при малом $\\mathrm{Ma}$ близок\n", + "к $\\rho(c_s^2\\delta_{\\alpha\\beta}+u_\\alpha u_\\beta)$ (тензор давления Навье–Стокса)." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "2c1e6274", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-06T17:33:55.661761Z", + "iopub.status.busy": "2026-06-06T17:33:55.661572Z", + "iopub.status.idle": "2026-06-06T17:33:55.676349Z", + "shell.execute_reply": "2026-06-06T17:33:55.675470Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Энтропийное равновесие: |Σf-ρ|=2.22e-16, |Σcf-ρu|=5.03e-17 (точно),\n", + " |Σc_x²f - ρ(c_s²+u_x²)|=3.00e-09 (мало при малом Ma)\n", + "Моменты равновесия — OK\n" + ] + } + ], + "source": [ + "rng = np.random.default_rng(0)\n", + "rho_t = np.ones((1, 1)) * (1.0 + 0.1 * rng.standard_normal((1, 1)))\n", + "u_t = np.stack([0.06 * rng.standard_normal((1, 1)), 0.06 * rng.standard_normal((1, 1))])\n", + "fe = feq_entropic(rho_t, u_t)\n", + "rho_m, u_m = macros(fe)\n", + "Pxx = (CX[:, None, None] ** 2 * fe).sum(0)\n", + "err_rho = abs(rho_m - rho_t).max()\n", + "err_u = abs(u_m - u_t).max()\n", + "err_P = abs(Pxx - rho_t * (CS2 + u_t[0] ** 2)).max()\n", + "print(f\"Энтропийное равновесие: |Σf-ρ|={err_rho:.2e}, |Σcf-ρu|={err_u:.2e} (точно),\")\n", + "print(f\" |Σc_x²f - ρ(c_s²+u_x²)|={err_P:.2e} (мало при малом Ma)\")\n", + "assert err_rho < 1e-12 and err_u < 1e-12\n", + "print(\"Моменты равновесия — OK\")" + ] + }, + { + "cell_type": "markdown", + "id": "375daf92", + "metadata": {}, + "source": [ + "## 3. Разложение популяций $f = k + s + h$ через моментные проекторы\n", + "\n", + "Сердце KBC — разбиение каждого 9-вектора популяций на три части по **моментным\n", + "подпространствам**:\n", + "- $k_i$ — **кинематическая** часть, несёт только сохраняющиеся моменты\n", + " ($\\rho$, $j_x$, $j_y$);\n", + "- $s_i$ — **сдвиговая** часть, несёт девиаторный тензор напряжений\n", + " ($N=\\Pi_{xx}-\\Pi_{yy}$ и $\\Pi_{xy}$);\n", + "- $h_i$ — **высшие** («ghost») моды: след 2-го момента (объёмная вязкость),\n", + " 3-й и 4-й моменты.\n", + "\n", + "Строим базис из 9 независимых мономов-моментов $\\phi^{(a)}_i$ и матрицу\n", + "$M_{ai}=\\phi^{(a)}(\\mathbf c_i)$, тогда $m = M f$ — вектор моментов. Проектор на\n", + "группу моментов $G$: $\\;P_G = M^{-1} D_G M$, где $D_G$ — диагональная маска\n", + "(единицы на моментах из $G$). По построению $P_k+P_s+P_h = I$, поэтому\n", + "$k+s+h=f$ **точно**. Назначение моментов в $s$ vs $h$ задаёт *вариант* KBC\n", + "(ниже — KBC-N1: в $s$ только девиаторный стресс)." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "680fbd41", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-06T17:33:55.678545Z", + "iopub.status.busy": "2026-06-06T17:33:55.678286Z", + "iopub.status.idle": "2026-06-06T17:33:55.685612Z", + "shell.execute_reply": "2026-06-06T17:33:55.684800Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Разложение k+s+h=f: макс. невязка = 1.1102230246251565e-15\n", + "Проекторы P_k+P_s+P_h=I и состав части k — OK\n" + ] + } + ], + "source": [ + "def moment_matrix():\n", + " \"\"\"Строки — мономы-моменты, столбцы — направления. m = M @ f.\"\"\"\n", + " M = np.zeros((Q, Q))\n", + " M[0] = 1.0 # ρ\n", + " M[1] = CX # j_x\n", + " M[2] = CY # j_y\n", + " M[3] = 3 * (CX ** 2 + CY ** 2) - 2 # след 2-го момента (энергия), центрированный\n", + " M[4] = CX ** 2 - CY ** 2 # N — разность нормальных напряжений\n", + " M[5] = CX * CY # Π_xy — сдвиговое напряжение\n", + " M[6] = CX ** 2 * CY # 3-й момент\n", + " M[7] = CX * CY ** 2 # 3-й момент\n", + " M[8] = CX ** 2 * CY ** 2 # 4-й момент\n", + " return M\n", + "\n", + "M = moment_matrix()\n", + "Minv = np.linalg.inv(M) # существует: 9 мономов независимы на D2Q9\n", + "\n", + "K_MOMENTS = [0, 1, 2] # сохраняющиеся: ρ, j_x, j_y -> k\n", + "S_MOMENTS = [4, 5] # девиаторный стресс: N, Π_xy -> s (вариант KBC-N1)\n", + "H_MOMENTS = [3, 6, 7, 8] # след + 3-й + 4-й моменты -> h\n", + "\n", + "def projector(moment_idx):\n", + " D = np.zeros((Q, Q))\n", + " D[moment_idx, moment_idx] = 1.0\n", + " return Minv @ D @ M\n", + "\n", + "P_k, P_s, P_h = projector(K_MOMENTS), projector(S_MOMENTS), projector(H_MOMENTS)\n", + "\n", + "# Самопроверка: полнота (P_k+P_s+P_h=I) и что k несёт ровно сохраняющиеся моменты.\n", + "assert np.allclose(P_k + P_s + P_h, np.eye(Q))\n", + "ftest = rng.random((Q, 3, 4))\n", + "k = np.einsum(\"ij,jab->iab\", P_k, ftest)\n", + "s = np.einsum(\"ij,jab->iab\", P_s, ftest)\n", + "h = np.einsum(\"ij,jab->iab\", P_h, ftest)\n", + "assert np.allclose(k + s + h, ftest) # разложение полное\n", + "# у части k моменты N, Π и высшие — нулевые (несёт только ρ, j_x, j_y):\n", + "mk = np.einsum(\"ai,ijl->ajl\", M, k) # моменты части k\n", + "assert np.allclose(mk[S_MOMENTS], 0.0) and np.allclose(mk[H_MOMENTS], 0.0)\n", + "print(\"Разложение k+s+h=f: макс. невязка =\", abs(k + s + h - ftest).max())\n", + "print(\"Проекторы P_k+P_s+P_h=I и состав части k — OK\")" + ] + }, + { + "cell_type": "markdown", + "id": "2f40f22e", + "metadata": {}, + "source": [ + "## 4. Оператор столкновений KBC и стабилизатор $\\gamma$\n", + "\n", + "Поскольку $f$ и $f^{eq}$ имеют **одинаковые** сохраняющиеся моменты, неравновесие\n", + "$\\,f-f^{eq}\\,$ не содержит кинематической части: $\\Delta k = 0$, значит\n", + "$f-f^{eq}=\\Delta s+\\Delta h$, где $\\Delta s = P_s(f-f^{eq})$,\n", + "$\\Delta h = P_h(f-f^{eq})$.\n", + "\n", + "**Столкновение KBC:**\n", + "$$ f_i^{\\text{после}} = f_i - \\beta\\,\\bigl(2\\,\\Delta s_i + \\gamma\\,\\Delta h_i\\bigr). $$\n", + "Множитель **2** перед $\\Delta s$ фиксирует сдвиговую вязкость через\n", + "$\\beta=1/(2\\tau)$; высшие моды релаксируются отдельным $\\gamma$.\n", + "\n", + "**Стабилизатор $\\gamma$** выбирается локально из условия неувеличения дискретной\n", + "энтропии ($\\Delta H = 0$ во 2-м порядке). Результат — **замкнутая формула**\n", + "⚠ (сверить с оригиналом):\n", + "$$ \\gamma = \\frac{1}{\\beta} - \\Bigl(2-\\frac{1}{\\beta}\\Bigr)\n", + " \\frac{\\langle \\Delta s\\,|\\,\\Delta h\\rangle}{\\langle \\Delta h\\,|\\,\\Delta h\\rangle},\n", + " \\qquad \\langle X|Y\\rangle = \\sum_i \\frac{X_i Y_i}{f_i^{eq}}. $$\n", + "При $\\gamma=2$: $2\\Delta s+2\\Delta h = 2(f-f^{eq})$, и KBC **сводится к BGK**\n", + "с $\\omega=2\\beta$: $f^{\\text{после}}=f-2\\beta(f-f^{eq})$. Адаптивный $\\gamma$\n", + "добавляет/убавляет диссипацию высших мод там, где это нужно для устойчивости." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "26aedc31", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-06T17:33:55.687730Z", + "iopub.status.busy": "2026-06-06T17:33:55.687555Z", + "iopub.status.idle": "2026-06-06T17:33:55.692998Z", + "shell.execute_reply": "2026-06-06T17:33:55.691737Z" + } + }, + "outputs": [], + "source": [ + "def collide_kbc(f, feq, beta, gamma_fixed=None):\n", + " \"\"\"KBC-столкновение. Возвращает (f_после, поле gamma).\"\"\"\n", + " dfneq = f - feq\n", + " ds = np.einsum(\"ij,jab->iab\", P_s, dfneq) # Δs\n", + " dh = dfneq - ds # Δh = (f-feq) - Δs, т.к. Δk=0\n", + " if gamma_fixed is not None:\n", + " gamma = np.full(f.shape[1:], float(gamma_fixed))\n", + " else:\n", + " inv = 1.0 / feq\n", + " num = (ds * dh * inv).sum(0) # ⟨Δs|Δh⟩\n", + " den = (dh * dh * inv).sum(0) # ⟨Δh|Δh⟩\n", + " with np.errstate(divide=\"ignore\", invalid=\"ignore\"):\n", + " gamma = np.where(den > 1e-14,\n", + " 1.0 / beta - (2.0 - 1.0 / beta) * num / den,\n", + " 2.0) # у равновесия (Δh→0) берём предел BGK\n", + " fpost = f - beta * (2.0 * ds + gamma[None] * dh)\n", + " return fpost, gamma\n", + "\n", + "\n", + "def collide_bgk(f, feq, beta):\n", + " \"\"\"Классический BGK: f - ω(f-feq), ω=2β.\"\"\"\n", + " return f - 2.0 * beta * (f - feq)" + ] + }, + { + "cell_type": "markdown", + "id": "47f5c741", + "metadata": {}, + "source": [ + "### Самопроверка: предел $\\gamma=2$ совпадает с BGK\n", + "При $\\gamma=2$ оператор KBC обязан в точности равняться $f-2\\beta(f-f^{eq})$." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "4683dee2", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-06T17:33:55.695617Z", + "iopub.status.busy": "2026-06-06T17:33:55.695431Z", + "iopub.status.idle": "2026-06-06T17:33:55.700759Z", + "shell.execute_reply": "2026-06-06T17:33:55.699894Z" + }, + "lines_to_next_cell": 2 + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "max|KBC(γ=2) - BGK| = 6.9e-18 → машинный ноль (порог assert 1e-12), операторы совпадают\n", + "Предел γ=2 → BGK — OK\n" + ] + } + ], + "source": [ + "rho0 = np.ones((6, 7))\n", + "u0 = np.stack([0.05 * rng.standard_normal((6, 7)), 0.05 * rng.standard_normal((6, 7))])\n", + "feq0 = feq_entropic(rho0, u0)\n", + "f0 = feq0 + 0.01 * rng.standard_normal((Q, 6, 7)) # слегка неравновесное состояние\n", + "f0 *= rho0 / f0.sum(0) # сохранить ρ\n", + "beta0 = 0.7\n", + "fk2, _ = collide_kbc(f0, feq_entropic(*macros(f0)), beta0, gamma_fixed=2.0)\n", + "fbgk = collide_bgk(f0, feq_entropic(*macros(f0)), beta0)\n", + "diff = abs(fk2 - fbgk).max()\n", + "# diff — машинный ноль (масштаб |f|·eps ≈ 1e-18); важно лишь, что он ≪ порога 1e-12.\n", + "print(f\"max|KBC(γ=2) - BGK| = {diff:.1e} → машинный ноль (порог assert 1e-12), операторы совпадают\")\n", + "assert diff < 1e-12\n", + "print(\"Предел γ=2 → BGK — OK\")" + ] + }, + { + "cell_type": "markdown", + "id": "7b51bf05", + "metadata": { + "lines_to_next_cell": 2 + }, + "source": [ + "## 4b. Популярно: что делает каждая формула (математика + физика)\n", + "\n", + "Здесь каждая формула KBC объясняется «на пальцах»: что это математически, какая за\n", + "этим физика потока, и как это считается на каждом шаге.\n", + "\n", + "---\n", + "**Популяции $f_i(\\mathbf x,t)$ и шаг «перенос + столкновение».**\n", + "*Математика:* в каждом узле сетки храним 9 чисел — «сколько газа летит» по каждому из\n", + "9 направлений $\\mathbf c_i$. *Физика:* как 9 встречных потоков на перекрёстке.\n", + "*Как считается:* за шаг потоки сначала **разъезжаются** в соседние узлы (перенос,\n", + "`np.roll`), затем в каждом узле **перемешиваются** (столкновение). Перенос точный и\n", + "дешёвый; вся «физика жидкости» сидит в столкновении.\n", + "\n", + "---\n", + "**Моменты $\\rho=\\sum_i f_i$, $\\rho\\mathbf u=\\sum_i \\mathbf c_i f_i$.**\n", + "*Математика:* сумма всех потоков = плотность; взвешенная по направлениям = импульс.\n", + "*Физика:* «сколько вещества» и «куда оно в среднем движется». *Как считается:* два\n", + "суммирования по 9 числам — мгновенно. Отсюда привычные $\\rho$ и скорость $\\mathbf u$.\n", + "\n", + "---\n", + "**Равновесие $f_i^{\\mathrm{eq}}(\\rho,\\mathbf u)$.**\n", + "*Математика:* распределение по направлениям, максимизирующее энтропию при заданных\n", + "$\\rho,\\mathbf u$. *Физика:* «к чему стремится газ, если оставить в покое» — локальный\n", + "максвелловский «штиль». *Как считается:* по замкнутой формуле из $\\rho,\\mathbf u$.\n", + "Столкновение всегда **тянет** $f$ к $f^{eq}$ — это и есть вязкое стремление к равновесию.\n", + "\n", + "---\n", + "**H-функция $H=\\sum_i f_i\\ln(f_i/w_i)$.**\n", + "*Математика:* дискретный аналог энтропии. *Физика:* мера беспорядка/необратимости; по\n", + "второму началу не должна самопроизвольно убывать. *Как считается:* одно суммирование.\n", + "В KBC $H$ — **физический компас устойчивости**: из условия «энтропия не падает»\n", + "выводится стабилизатор $\\gamma$.\n", + "\n", + "---\n", + "**Разложение $f = k + s + h$.**\n", + "*Математика:* проекция 9-вектора на три группы моментов. *Физика:* три «слоя» движения:\n", + "- $k$ — **перенос массы и импульса** (поток как целое);\n", + "- $s$ — **вязкий сдвиг** (трение слоёв друг о друга — задаёт вязкость);\n", + "- $h$ — **мелкая «рябь»** высших мод (мелкомасштабные флуктуации, где копится\n", + " неустойчивость на грубой сетке).\n", + "\n", + "*Как считается:* умножение на заранее посчитанные проекторы $P_s,P_h$. Идея KBC:\n", + "релаксировать эти слои **с разной скоростью**.\n", + "\n", + "---\n", + "**Столкновение $f \\leftarrow f - \\beta\\,(2\\,\\Delta s + \\gamma\\,\\Delta h)$.**\n", + "*Математика:* $\\Delta s,\\Delta h$ — отклонения сдвига и ряби от равновесия. *Физика:*\n", + "**вязкий сдвиг** гасим фиксированным темпом $2\\beta$ (он задаёт вязкость и Re); **рябь** —\n", + "отдельным темпом $\\gamma\\beta$, ровно чтобы не нарушить энтропию. *Как считается:* две\n", + "линейные комбинации 9-векторов на узел. Множитель **2** перед $\\Delta s$ воспроизводит\n", + "правильную вязкость; при $\\gamma=2$ всё сворачивается в обычный BGK.\n", + "\n", + "---\n", + "**Стабилизатор $\\gamma = \\dfrac{1}{\\beta} - \\Bigl(2-\\dfrac{1}{\\beta}\\Bigr)\n", + "\\dfrac{\\langle \\Delta s|\\Delta h\\rangle}{\\langle \\Delta h|\\Delta h\\rangle}$.**\n", + "*Математика:* единственное $\\gamma$, при котором изменение энтропии за шаг равно нулю\n", + "(во 2-м порядке). *Физика:* **локальный термостат потока** в реальном времени — в каждой\n", + "точке на каждом шаге подкручивает, насколько гасить «рябь», чтобы энтропия не росла. В\n", + "спокойных зонах $\\gamma\\approx 2$ (как BGK); у резких градиентов (кромки тел, вихри)\n", + "$\\gamma$ отклоняется и добавляет ровно столько диссипации, сколько нужно, **не давая\n", + "симуляции взорваться**. Это «implicit LES» — встроенная, без подгоночных констант,\n", + "модель мелкомасштабной турбулентности. *Как считается:* два скалярных произведения на\n", + "узел → одно число $\\gamma$.\n", + "\n", + "---\n", + "**Энтропийное скалярное произведение $\\langle X|Y\\rangle=\\sum_i X_iY_i/f_i^{eq}$.**\n", + "*Математика:* взвешенное (на $1/f^{eq}$) скалярное произведение — кривизна энтропии у\n", + "равновесия. *Физика:* измеряет, насколько «рябь» $\\Delta h$ выровнена со сдвигом\n", + "$\\Delta s$; по этому решается, сколько диссипации добавить. *Как считается:* поэлементное\n", + "произведение и сумма по 9 направлениям.\n", + "\n", + "---\n", + "**Вязкость $\\nu = c_s^2\\bigl(\\tfrac{1}{2\\beta}-\\tfrac12\\bigr)$, $\\beta=1/(2\\tau)$.**\n", + "*Математика:* связь темпа релаксации сдвига с вязкостью. *Физика:* чем медленнее гасится\n", + "сдвиг (меньше $\\beta$), тем «гуще» жидкость; через $\\nu$ задаётся $\\mathrm{Re}=UL/\\nu$.\n", + "*Как считается:* один раз при настройке (выбрали $\\nu$ под нужный Re → получили $\\beta$)." + ] + }, + { + "cell_type": "markdown", + "id": "926c192a", + "metadata": {}, + "source": [ + "## 5. Перенос (streaming) и связь вязкости с $\\beta$\n", + "\n", + "Перенос — сдвиг каждой популяции на её вектор $\\mathbf c_i$ (здесь — периодически\n", + "через `np.roll`). Вязкость: $\\nu = c_s^2\\bigl(\\tfrac{1}{2\\beta}-\\tfrac12\\bigr)$,\n", + "то есть $\\tau=\\nu/c_s^2+\\tfrac12$, $\\beta=1/(2\\tau)$. Число Рейнольдса\n", + "$\\mathrm{Re}=UL/\\nu$; число Маха $\\mathrm{Ma}=U/c_s$ держим $\\lesssim 0.1$." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "db53cf74", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-06T17:33:55.702749Z", + "iopub.status.busy": "2026-06-06T17:33:55.702576Z", + "iopub.status.idle": "2026-06-06T17:33:55.708386Z", + "shell.execute_reply": "2026-06-06T17:33:55.707324Z" + }, + "lines_to_next_cell": 2 + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Пример: ν=0.01 → β = 0.9434 , τ = 0.53\n" + ] + } + ], + "source": [ + "def stream(f):\n", + " \"\"\"Периодический перенос популяций на c_i. f:(9,Ny,Nx).\"\"\"\n", + " fs = np.empty_like(f)\n", + " for i in range(Q):\n", + " fs[i] = np.roll(f[i], shift=(int(CY[i]), int(CX[i])), axis=(0, 1))\n", + " return fs\n", + "\n", + "\n", + "def nu_to_beta(nu):\n", + " tau = nu / CS2 + 0.5\n", + " return 1.0 / (2.0 * tau)\n", + "\n", + "\n", + "def H_function(f):\n", + " \"\"\"Дискретная H-функция (энтропия) H = Σ f_i ln(f_i/w_i).\"\"\"\n", + " fp = np.maximum(f, 1e-300)\n", + " return (fp * np.log(fp / W[:, None, None])).sum(0)\n", + "\n", + "\n", + "print(\"Пример: ν=0.01 → β =\", round(nu_to_beta(0.01), 4), \", τ =\", round(0.01 / CS2 + 0.5, 4))" + ] + }, + { + "cell_type": "markdown", + "id": "46e60487", + "metadata": {}, + "source": [ + "## 6. Алгоритм одного шага KBC\n", + "\n", + "```\n", + "для каждого узла:\n", + " 1) макро-моменты: rho = sum f_i, rho*u = sum c_i f_i\n", + " 2) равновесие: f_i^eq (энтропийное product-form)\n", + " 3) неравновесие: Ds = P_s (f - f^eq), Dh = (f - f^eq) - Ds\n", + " 4) стабилизатор: gamma = 1/beta - (2 - 1/beta) / \n", + " 5) столкновение: f <- f - beta (2 Ds + gamma Dh)\n", + " 6) перенос: f_i(x + c_i) <- f_i(x)\n", + " 7) граничные условия (bounce-back / Zou-He / sponge)\n", + "```" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "79ded771", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-06T17:33:55.710930Z", + "iopub.status.busy": "2026-06-06T17:33:55.710705Z", + "iopub.status.idle": "2026-06-06T17:33:55.962257Z", + "shell.execute_reply": "2026-06-06T17:33:55.961175Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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55s2aKiOhHfMzJKcpz0vzhI+6wlbueXtp56nPEXH+L148x8A+XVEoT0akSR4b2dKnwPDB/sd0MHVekXlgQKBAqXEBDh/ch537T+Gy5xNYW9tg+KBeeuv06dFBbyhIv9P0KWMDPU7SZMmxdvM+2NqlxmL32TKWgl8nz92U8Q72HT0vo48VKV4qTM8rqMLj/NUgQFXLFcb8OdPx6uUL1KjdEAUKFYPnjWsG92fKvCLzwKeMKECqsFHj/J46f0v7mKQa6GbqpNF6642bNFOm0FKPX1arWRezpk/Cts3r0a3nQL3qjquXLyJW7NgySpnG9i0bYBUzJsqWr2zy8wqq8Dh/NWqbGr9ZjY62be8JpEufUeZ//frVYF6YKq/IfDAgUIDUUJIlSpbTe2b+5cvnSJYsRZjk3LLF86QwTJY8BdZs2uOv7vvihbPI5pxLb/ziytVqhct5ff/+DWEtoPNXo7cpiRIn0QYDzdNKhvLCVHlF5oNVRhSg/06dQJJkyfTq3bduWuevYOndrZ3UUxubgnLlvWPrRvTp3gHx4sXHqvW7tMNo6vK4cBY5cubWm1exdAGpTjH1ecWJG1f+vvn/0JhXL3sY3V94nL96V0FR1UW3b3lq5+veIejmhanyiswH7xAoQJcunsOjh/fRoXNPxI1rjfGjB8v4xU1bttVbb/yU2TKF1Iljh9G+dSNYWVlhyaotyJItu8H1PC6cQ4cuPfUKw+/fvmlf6FLdQaxesRhnLt0N9XmpcaBPHDuEcaMH4+yZf2W/xoTH+VeqWgsOY4fB6+5taUsoV7EqPn/+jI8fPmDJqs3+8iKwvCLyi3cIZNSjhw/w9s1rtO/UA2WK5Ua+HGnlKZfVm/YgVqxYJsu5yx4X0LxRdXn+fs7C1ShQqKjB9b58+YIb16/AOcfvq94b164gY+Zs2u8PH9yTF71McV5jJs5A7rx/4f49Lxw5uA/deg5AWAjq+auCXLUdtG7bGfETJMTGdStx7MgBOKXP4C8vgpJXRH7xDoECvIp2Sp8RDRq3kCksqKvdRnUr4b2PD6bNWoRyFaoYXTdmzJh48EL/TV6Pi+eQPUcu7ff//j0uT+qY4rwyZsqCHftO6s1r3a4LIur8lSRJkmLkuKky+aWbF0HJKyK/eIdARqlGycxZnMMsh54/e4oGtSrg2dMnGDpyIuo2aBrsfVz2OK93FXzi7A15Uicizys8zz+gvAjucqJoP031SmQQubi4QB1xzJT5zP1Irmn9asibvwC69ugfJvtvUr8q9u3eHuT1vZ58NElVVVifV2Q/f4r8+nVrDfVwmLu7e7gel1VGZNTS1VvCNHdUY67u45OBsbCwiBLnFdnPn8gYBgSKMHMWrDTr3Df386fIh5ccREQkeIdAZkm9c/DyxTODyyxjxEDSMHoTmygyY0Ags+Q+ZwquXjpvdHn7rv2QJVvOcE0TUURjlRGZpbROxhtzLS1jwM6eYxiT+YmQO4T3733ksSqiiBLQ09bqcb8xQ393+UAUEWWkTQQMahTuASEiTpLIL9UDqOo3yNAYxmq+TgehRIiIcjIiyspwfzGNKLJQvX526NBBr/fPKlWqoFmzZhGaLqKIwjYEMluqs7hq1arpjSug+53I3DAgkFmrUKECLC1/1ZyWLl0aCRIkiOgkEUUYBgSCud8lpEjx652DqlWrRnRyiCIU2xDI7P348UPGD4gdO7bZ5wWZNwYEIiISrDIiIiLBgEBERIIBgYiIBAMCEREJBgQiIhIMCEREJBgQiIhIMCAQEZFgQCAiIsGAQEREggGBiIgEAwIREQkGBCIiEgwIREQkGBCIiEj8GjswHLm6usLHxye8D0tEFKXY2NjAzc3tzw4IKhioKa61dXgfmogoSvjw/n2EHDfcA4KigsHo6eMi4tBERJFe/859IuS4bEMgIiLBgEBERIIBgYiIBAMCEREJBgQiIoq4p4yIKOgO7NmP2VNn4ovvF+TMnQvDxo2Q+bu378L0iVMRJ24cJE2WFKXLl0Gt+nWYtRRiDAhEkdjd23cwbYIbVmxejThx4qBVg+a45+WNaNGiYf4/c7Fm+3rEihULBbLlQ9de3SI6uRTFMSAQRTI/f/7EgB79sH3TVjx/9hz2aVKjaa1Gsuz1q9f48eMHNq3diIbNG0mQUNRfpwzpIjjlFNUxIFCo1a5QA2f/OwPLGJaIHj06UjukgWvvbqhcoypzNwRUYX/iyHEcv3gK/0yejvSZM6BWvdqy7OvXr4gRIwY+fvyIb9++adePax1X8p4oNNioTCbh2qc7bj31wpV7N1Cjbk20a/43bt+8zdwNgQN79qFc5fKwtrFG41ZNscx9CWqVr456VWpj28atsk7dhvUwy20mmtVpjEP7DyKrc1bmNYUaAwKZlKWlJVq0aYnv37/j+pWrUs9dNFchpE/hiLyZcmH0kJGyTCN/ljxwTGyPdMkdkMU+Azq0bIePHz7oLV+/aq3eMezjp5QraOXVy1fo0qYjcqTNKlPXvztJtUpQ96+utIf1H4K/suaV5Y1q1Jd6e90+ZdTyAtnyyjkUz1MEp47/azBtPTp2QyrrZNq0BWX/fuXJkAMbVq+XfFNp9rp9Fxt2b5Zpzbb1qFmvlqyXPlMGHDx9BEvWLUc252zIlsM5BL8WkT4GBDIpX19fLJy7QKo1sjhnRUrblFi+cSU8H9/BwtVLsGrJCqxYtExvm4n/TJa7i0NnjuLUiX+xaumqIB+vk0t7vHnzFofPHpdJEyCCuv9enbrjtuctbDuwAxduX0auvLnRrE4TqZpRunfohvOnz0lhrM5h0ZolSJYimb90XDh7Hof3H4KFhf5/qcD279dxj1NS9bPnxAFJc5ESRQPNg6tXriJr9mxBzjMiY9iGQCahnoSZPW0mYsSwgoOTA+YtXwBHp7QyaTjncEbthnVx7NBRNHVp7m8f3759Vy2qSJbcf4FryJPHT3Bo30Ecu/AvEiRMIPOGjBmOYrkL4emTp0ieInmA+3/54iU2rtmA/66dQ9L/z+vRvxfmz5yLc6fPwimdE7Zu2IyD/x2RdhFF93x0G4H7d++LAcMH6QWjwPb/V6EC/vZ19dIVxIodC07pnRBUk2eGbxfJ9OdiQCCT6NLLVdoR/FIF4twZs+VRSdUI+tX3K3Lny6O3Tu8uveSpGp93PihcvAhKlClpcLmGpsrp0YOH8je1Q2rtMoe0DtplmoBgbP/3ve/J3zIFSugd7+vXb3j04BGsrKzke9pACucVi5fLo5+qOkc3IAS2f0M8zl9EtuzO8lipsmPzNljFjIkyFcoGmAYiU2CVEYWZhw8eonPrDujauxvO37qEG49uo/nfLeWKWtf4aRNw/eEt3HrmhVR2tujWrovB5ZpJ8zSNWle34FW873rrLQto/3b2dvL3+IV/9fZ/57m3FO72qe1l+d1bxuv837x+iwkjxmLUpDH+lgW2f0M8Lngge67s2u+VqldhMKBww4BAYebj+w/yzHziJImlTUE9mrp+pX4DsS5V0Ks6+GfPngVp/ylSpkDx0iUwrP9QvH3zFm9ev5EG3FLlSvurLjK0/yTJkkrB3K9bHzx+9Fjmqf3s3LJdGpPV8io1qspyFXRUIFMNwrqNwjPdZqBKzWrInC2Lv+MFtn9jdwjZc+XQfq9cooI0TBOFBwYECjPqSZieA3qjZf3myGSbDjMmT0ONuv6vjHt27C5P1GR3zCJX4yMn+r/aNmbG/Jmwto6LorkKSttB/PjxMHXujCDvf8KMyXBKnw51KtaQp4hK/VUcWzdu1VbZTJ41VRpsa1X4tVydy7OnvwOW7xdf9BpofDCTwPav68uXL/C8dgPOOX7dIaiGZ1XNpnn5jCisRfvp9/49jLm4uODHz58cMY0oEJc9LmHejDn+AhyZx4hpFtGiwd3dPVyPyzsEokjq0oVL2rsFovDAgEAUSV2+eAnOORkQKPzwsVOiSMrQk0tEYYl3CEREJBgQiIhIMCAQEZFgQCAiIsGAQCZzaN8B1ChrPoPinP73P+nqWvWttGvbTty87hmuxx81eATGDx8brsekPxsDApmEer9xSJ/B8mayuUiSNIl0lZEtTSZ5gUx1VRGeOnbrjEXzFmi7xSAKLT52SiZxeP9BfP3qK72JmgvVFfbuY/si7Piqy++SZUthqfti9B7UN8LSQX8O3iGQSezauhNFSxSTPnrUIDXVylRGxlROyOmUDW2btsaD+w+067q27Syji+lSw0NOHDVePquRz1TfQ07JHGQEMvVZTZWKl9du37FVO+lJNUPKtCjonA+rl+kPqqMGqFfdTqs0qL+qQzkNta6tTXLtftXkkMhOxobWUMdVg+lo1K9aR+Zpelb1ew5q5DS1XHMOqipJjeymS62jRlnTCGy0t6CMtlasVAns3rYzyL8TUUAYEMgkLl28hPSZMmqH0ew7uD8ue1/H0fMnkShxItSrXAufPn0K0r4u3rnya4Sz00fku/qsph2Hd2vX2bphi4xrcPW+J8ZNm4h+rr2lTl9Rfzu5dED/4YNkjOe+QwfI0JlqUBqNNI5ptPtVk6GxHDTUOMYBjQ/93uc9Rg8eiZSp9ANAaEd7C8poa5mzZsb1q9dlpDqi0GJAIJN4++YNbOLZyOd48eOhULHC0uW1mjd8wij4vHuPfTv3miy31SA7tRvUleBTrGRxVKpeGWuWrZZl6q/6rrrBVsvV4DIVqlaS4TuDS12lDx8wFINHDTW6zqQxE1C6fBk4ZUgX5P1qRnsbOma4VP2oSY32tn/3PhntTTPa2ugp42S0NTVYjxpt7dnTp3qBzdrGRtpv3r15G+xzI/KLbQhkEvETJJARyTTUSF/dO7hqv394/wH37/0eyEaNi6CqdTQ+fviI/AX/CvLx7NPY639PnRqXLnrI50cPHyJ7zt9jCigOjg7a5cExfcJUFCxSEHkL5DO4XD1ZtGHVOhw8fRTtmrfRW6aePlLdfuuOlKbGhgjKaG+a7rEDG23tvY+PrBsvQfxgnxuRXwwIZBLZsmfDzes39Eb6UpOGqju3s/9diKuxlSf9M0WvDSE47nvf1/9+7x5Spkoln1PZ2uoFH8XbyxupbH8tDyrvu15YtnAp9p86+Gs8ZgMG9uqPbn17SLWYoQF51Ahpum0I4/7/mKjuaG+acZp1R3uLbmGhHW0tcdIkRtN4/eo1ZMycSTvcJ1FosMqITEJVyRw7fFQ+q9HA1FCQarQ09Xns0NFyFVumounGBVbVJqpKRV2FHzt0FDs2b0fdxvVkmfqrvqv3ItTyA3v2S6Ny/aYNg3UMVXh36tEZyZL7H31NUVU+qt6/WesWwU5/YKO9BXW0tSMHDqNClYrBPj6RIQwIZBKqgTd6dEt5usbX9ysG9eqPrKkz4q+s+XD92nWs3rrWpCN/Va1VDQf27ENmu/TytM+oyWO1VU7qr9uc6Rjef5gsHzlwOKbPn4k8+fMG6xjW1tZo1a610eWPHz7CyImjZVjOkAhstLfARltTAUIFu6atm4fo+ER+ccQ0MpmDew9g2gQ3bNyzJUxzVT3yGd3SUq/KyRyNHjIS0S2io8+QfhGdFPpDRkxjGwKZjHpJSk0UPvoPG8isJpNilREREQneIVCUo9oHiMj0eIdARESCdwhkljat3oDTx391deFXDKsYaN35b9j5efmN6E/HgEBm6fPHT/KWrzHRQvgoKVFUFiEBQb1Yox6rIooo6qU5Y9Qbxv+Mnxau6SHyW0ba2PzqG+yPDggRcZJEfllEjy4d33379s3fspgxY8oz4EQRRZWTEVFWhvuLaUSRxdOnT9GlSxfpLVRRbwDnzZsXvXr1iuikEUUIVpSS2UqePDlKlPjdm6gKDHXq1InQNBFFJAYEMmu1atXSfs6dOzccHR0jND1EEYkBgWDudwmautoaNX4PoUlkjtiGQGbv0aNH2LNnD1q0CH431kR/EgYEIiISrDIiIiLBgEBERIIBgYiIBAMCEREJBgQiIhIMCEREJBgQiIhIMCAQEZFgQCAiIsGAQEREggGBiIgEAwIREQkGBCIiEgwIREQkGBCIiEgwIBARkbBEOHN1dYWPj094H5aIKEqxsbGBm5vbnx0QVDBQk4113PA+NBFRlODz/kOEHDfcA4KigoH79FERcWgiokjPpfOACDku2xCIiEgwIBARkWBAICIiwYBARESCAYGIiAQDAplMiQp1MHKcW5DnE1HkwoBARESCAYHC1b37D1GncRukSJsTKZ1y4e9OveHj8167PJq1Ldz+mYecBcvCJkUGlKxYB7du39UuX7V2M3IUKIN4KTPK9m0798aHDx+1yx2y/IVYidPCOnl6JLLPikYtO2qXHzpyApbxU+ulZ9mq9bKNxsuXr9CsTRdJn5qa/90Vr169DtL+lctXrqN89UZImsYZqTPlQ78hY/D161ftci/v+6jb5G9JewLbzChcprocU3Pux078p123bNUGMk9tozFv4XJky1cK8VNlQq5C5bBn/+FQ/iJEvzEgULj5/PkzSlWuhyyZMuDulZO4euYgHjx6jK69B+utN3fBcqxbNhfP7l5E1swZUa1eS3z//l2WxY9vgxUL/sGbh9dwdM8GHD3xH0aOn6q3/fx/JuD905uy/6MnTmHh0tVBTmNjl854/eYtrp09JNOLl6/QtE2XIO3/2bMXKF6xNmpVq4iHN8/i5IEt2HvgCMZMnCHLP378JOefLGkSXD93GC+8L2HS6MGwsrLyl451G7fhxs3bevNUMBg3ZSaWL5iO1w+uYtSQPqjVqLVewCQKDQYEMqlRE6bLla/udOzkr6vebTv34efPnxg+qBdix46NhAkTYMSgXli+eqO2wFd6dGmLdE6Oss74kQNx+643Tp0+J8sqliuFrFkywsLCQtbp0KY59h86ZjAt3759k+OlSJ40SGl/9PgJdu87hMljhkja1KQ+79h9AI+fPA10/0tWrkOObFnQ1qWpFPK2qVKiX49OMv/X+e/Fp0+fMXXCcMSPHw+WlpYokD8PbGys9farAkfPASMwcdQgvflTZ7pjcF9X5HDOKudfqXxplCxWCKvWbQ7S+RFFyq4r6M81oFdnDOzj6q9RWbnrfV+qjFSQ0BUtWjQ8efpMClDFIbWddlmcOLGRNEkiPHj4WL6rK+7hY6bguuctfPH1lUCirrh1te3SB516DMS7dz4oVbwwypcpoV2m1tc9vqrOSZoksXy+/+CR/HV0+F2t5JTWQbssZYrkAe7/rtc9HP/3jN7+VcDQBDuvew+Q1jG1BIKAjJ4wDcWLFEChAnn15t/1voeO3QegS6/BekHJ7v/5RhRavEOgcJPG3hYZ0qWV6h7d6fPLO9pgoCk4da+Wn794BTvblPD19UWNBq3QoE513Lv+H949voFxwwdIoatrzrRxst8Pz27C3i4VWrbrpl0WPXp0vWOrdTXUunJ8nTr7O3e99ZYFtP80qe1QpmQRvf2/fXRdqpc0ge6u1329uyG/bt/1wlxVNTTCf182aeztsGDmJL39q33Pmjo2yL8BUUAYECjcVKlYFr5ffeUKWDUkq4L84aPH2Lhlp956U2bMw+07XtLm0HfwaKR1SI2/8uWGr+9XfPnii4QJ40t10tVrnpgxZ6HR46nCX1WtPHn2PEjpS5UyBcqVLo4e/YfjzZu3eP36jXxW1VSau4OA9t+sUR2cOeeBBUtWSdp//PghAWXX3oOyvHKFMrCyioFufYbi7dt3cnX/739n9RrVBw4fj749OiJF8mT+jtetUxsMHT0ZFzwuS959+vRJGqGv37gVpPMjCgwDAoUbVf1zYPsaXL1+E5lyF5cnZUpXro8LHlf01mvdoqE0liZ1yI6Ll65i8+oFUvhaW8fFLLcx6D1wpDzl07F7fzSqV9PfcVp37CXLkznmwM1bdzF94sggp3HZ/OmwsbZGxlzFJI0J4sfDkrlTg7R/VYgf3LEWm7btgkOWAkholwU1G7po7zLixo0j56+qn9LnKIIkaZzRa8BIvaeQ1LE7t2tlMG1tWjZG727t0bJdd9l36kz5MWKcm972RKER7aff++0w5uLiAvz8we6vyfA/SGtbHN2zEUUK5WcOkXl3fx3NAu7u7uF6XN4hEBGRYEAgIiLBx04pUvn5/mFEJ4HIbPEOgYiIBAMCEREJBgQiIhIMCKRH9eVTtKz+s/3qyeRO3QdI75+qB1LV/URo+d3n4uVrULpyPRQpWwPd+gzRrrdl+x4UKFkFZarUR+NWnbB89QaZ36B5e7gvXhnmv57quXSC26ww2z/zmyITBoRwMGr8VHm+XhV64SlVutyIncRJXqJSha7qU8jTTw+afgtp9RbtsAE99OarLqcPHjmBmxePweeJJ1Lb24Y6bbr7PH98N+YvWomtaxfj2N5N8PJ+IP0CqS4kVFfYB7avxZ4tK3H839PIlT2bbD+0fw/0HzpW3tYNy9/m/MXLyJ5Nv+8lUzHH/I5M/z/IPwaEMKa6L5i3aAWqViorfdSEF9UlhOqhU/3nV/3dPLhxRrqN6DXQ+Fu7qm99369fUbJ4Yb35O/bsR7XK5fz1yhkauvtcuXaTdDNdqVZTCVq37nhJvqmxClyaN5Q3nFUXEXHjxEHGDE6yfaaM6ZDOyQEr124Os99G5eHzFy/DLCCYW35Hpv8fZBgDQhhTVQJfv37DgpmTce7CZRlARUMNvNKqfXe5kldX8Y5ZC0gViSmcPnsRiRIl0P6HVt0tO2fJhM+fvxjdZtPWXShTooj0PqphlyGPdE/t9s98SeMBI11NB4fffe7cexCD+rri0K51Mp07vkt6Gf3w8ZP096O5wlVdV6guLDTKliwm3USExW+juTtIkjgRtu/aj0y5iiFusnSo2cDFZF1FmFt+h+Q3CMv/I+QfA0IYU4O9NG1YG0mSJEKNKuUxZ8Ey7bIO3fojVsyY8LxwVHru3LlhGXI4Z/G3jw6u/fyNMaA7jZ30awAWXafPXkCBfLmlsFH/yVW30SvXbUajejWMpvXcxcsyeI2uWx7HpVC4cOLXnUapEkVCnSd+97lq0SzMcV+G4uVrS1vBuo3bZb1mDetggttsVKnTDLv3H0JOP3njnDUTzl24FCa/jSYgvH3ngzdv3+H8id3yOx0+/q/BUcpC8huZW36H5DcI6v8RMg2+mBaG1IAr23btw5hh/eR7y6b1Ub95e4wfOUB66/S8dQd/5c0l3TqrqzF1W27ITLcxMgXH6XMXZTQxVRjFiR1b+uGfPXWswc7gNF6/eYN48fSrKVTncrFjx0KG9L/uNHS1aOuKxcvXGt3fgF5dMHJIH3/z/e5T1ZEf3r3e33qZM6XH5dMH5PPUf+YjZkz9kcXixbPBq9dvEBa/jaKuWOvUqIyeXdvJd9vYsRE/no2/7rZD+hv9SfkdkrQF5TcI6v8RMg0GhDCknoLJlyeH9h9xmZJFYWMdF6vXb0GLJvWxcPZkDB/jhnQ5iiB71szo36uzdL9sCmfOe0gvocHZX8IECfDu3e+umJWz5z2kYVG3WkNjxqRRmDhKf/hLXaou2pCA9mmMx5VraNOikd48NUBNooQJEBa/jXLe47LeqGWqS2zvew/gnNU0bQp/Un6HJG1B+Q3C8v8I+ccqozCiGsvcl6xCy///w5bMtrBA80Z1tbfFaijE9Svm4cnt8yhaKL90a2xIuy59pP7U2KTGF9ClxthVffkbawxVV7hdew2WKgP1iKnm8c1c2bPi6nVPvXXPXriEPLmcDe5HXbGpW31jk9ECKoB9GuM+c5IMN6nr8tUbyJXj11Mwpv5tVP6pwj9v7hy/033eQ9oU1EA4of2N/rT8Dm7agvIbBOf/CJkGA0IYUYOiPH32AtUrl5fBUjSTGu3r3//OYdjoydKApkbPUg29j548laslQ2ZPGyd1v8am/r26+GtQVsNKGhpkRVEDqly7cVOqDY7u3Si36kqNqhWw/7B+I6YqBPPkym6yfDHlPvcePIIaVSpovw8dNQkOWf4K9W9z6fI1aT9InCghHNLY69116QaI0PxGf0J+h0ZQfoMNm3cE+f8ImQarjMKIuspR/8CTpzX8D9jr3n1UrtNMHv+LHy8eqlQog4WzJpvk2KfPXQjwUckM6dPKmL11m/wt62kKKzU2sGV0Sxw6cgIlihXCly9fcOWaJ3LnCN7VZUBMtc8bnrdkcBrdRvJ7Dx6iRNGCof5t1HJHB3t/hagqWPOasLCO6vkdGkH5DVS7R7e+Q8Pk/wgZxgFyzNCHDx9l9C7lrxJVsGbJbG01iLpyGz1hOo7s+fVGcGTVsEUHlC5RBK116rkz5CyC/dtWw94u9C9yhZeonN/05w2Qw4BghlQXEHe8vPHt23dULl8aQ/28KUtE5hkQWGVkhpYv8P9MPBERG5WJiEgwIBARkWBAICIiwYBARESCAYGIiASfMiKzdPzUOZz3uGZwmVUMS9SuVh6JE4WsnySiqIoBgczS8X/P4cyFy9Lhm26fbz9+/OrJtGD+XAwIZHYiJCD4vP/w68ULogiiXsrTdPTntzdrC4tomDJzUbB6ByUydRlpY2ODPz4gRMRJEvllGcMC0b9+lY7T/LKyioloFr9HCiOKiHIyIsrKcO+6giiyuHLlCoYNG6b9ru4I7OzsMGHCBOmKmcjc8F89ma2sWbMiS5Ys2qohdW1Ur149BgMyWwwIZNbq1q2rHRJT3R3ky5cvopNEFGEYEAjmfpcQN25c+VyjRg3eHZBZY0Ags9ewYUNYWVmhSJEiZp8XZN7YqExERIJ3CEREJBgQiIhIMCAQEZFgQCAiIsGAQEREggGBiIgEAwIREQkGBCIiEgwIREQkGBCIiEgwIBARkWBAICIiwYBARESCAYGIiAQDAhERCQYEIiISlghnrq6u8PHxCe/DEhFFKTY2NnBzc/uzA4IKBmqyiWsd3oemKOzHjx8c75jMhs+H9xFy3HAPCIoKBvPGTI6IQ1MUsXHHNsxa7I6bt2/hzbu36NCiNUb1HxzRySIKF236dYfZBASK+s5cOI9RbhNx4vQpfPH1RYpkyVCxVFn07tQVKZOnCNW+Zy9egNFTJ8F9ygyUKlIM0aNHN1m6icg4NipTsO09fBDFalRExnTpcG7fEby5eQ8HN2xD4oSJcPjk8VDl6MePH9F35FBsXLgcZYuXZDAgCkcMCBRsnfr1RMOadTB24DDYpkwl89RdwcDuvdCgRm30HDoQ8ZzsZIphmxhxHFJov5+/5IFp82YjS5H8iJ/OHg55sqH/qGH4/v277OeK53VYWkbHtPmzkSJbeqTKnhEturTHq9evtcdPmy87lq1brf3epkcXRE+ZEIdOHNNLZ8uuHRDTPqn22GqdY6dOBmkfhauUQ+JMDpLGgpXK4OSZ/7TrBpT+wM5defnqFZp3bifnZuz8Rkwej2LVKsh2+cuXxOkL54z+HimdM6Bu6+Z683Yf3C/z3757G8xfl8wZAwIFi+ftW7h1944EBGMmDh2Jd7cfyFT0r4KYOW6y9nsu5+wSRLavWCt3FhsXrcDCVcsxf/kS2fbDx494/eYNXr99g2vHTuPKkVN48eolmnVua/BYqqDce+iAwQZn1RDdvF4j7bGNMbSPmeMm4dmV23hx7Q6KFyqMrgP6aJcFlP7Azl1p0vFvOT91bsbOb86ShZgyYqwcv3aVaqjSuB7e+bwzmP5jW3dj446tePbiuXz/+vUrug3qh9EDhiB+vPhGz5vILwYECpbnL1/IX9sUKUOcc6qAc0ydBtGiRZNCskmd+jhw7IjeOpOGjkLCBAlkUp937t+Lx0+f6K3z8+dPdO7XC2MGDpV9+aXaNmLGtAowLcb2kSOrs1RXqeVqKpgvf7DSb8yjJ4+x59D+QM+vVcMmyJMjJ6ysrNC7kytix4qFbXt3G9ynk4MjbFOmxDVPT/k+dd4sxI8XDy3qNwpSmog0GBAoWJImTiJ/Hz55HOKcW7lxHf6qUApJs6RFwgypMXPRfLz4f6CJFTOm/FUFrm6Bp9x/9FBvP+4rlkpBaexu5eWrl0iUIGGAaQloH0WqloONky1WbVqPSqXLBSn9gdGcQ2Dnl8Y+tfazCjypbe3w8PEjo/vN6JQe12954smzp9IgP3XUOINBkiggDAgULBmc0iGdY1opJEPi/sMHaNapLfq79sTDC9fx2vOePFKqrsIVh/8XhF7372m3uePtJX/tU9lq5715+xZDxo/GtNHjjR7rqucNZEqfwejywPZxbOsefPR6ginDx6Jmy8bwee8TaPoDozmHwM7PW2e52ve9hw+07TWGZEyXHtdveqLPiCGoVbka8ufKE6T0EOliQKBgmzFmIlZsWIsBo4dLFYjy9PkzjJ02OdBA8f7DB6nbT5o4MWLEiIF/z57Wa9xNkSw5ypcsjZ7DBkqBrdoT1OcKpcroPc46YeZU1KlaHc6Zs/o7xpcvXyQtnz5/QoWSZYymxdg+1DFVIa2pLvr46SNiWMZArJixAk1/YFKlSImyxUsFen6qXeKcx0VpD5g4cxo+fvqEymV+36UYukPYtHMbtu3dhdF8X4NCiAGBgk09Dnpk0065As9RqrA8bVOsekU8e/ECJQoVCXDbzBkyYmivfqjZojESZUyDcdPd5MkkXYunzUbcOHGQuUg+ZC32FxLGTyDzdH354othvfobPMbQiWOwY98ebF26WurojTG2D9VOUqN5QyRInxrJs6XD7MXu2LhouQSAoKQ/MEtnzJGXM9X5ZSmaHwnixfd3fm2aNIfrwD5InMkRazZvxNZlqwNsIFZ3COouYnD3PkiWJGmw0kOkEe1nUO91TcTFxQX48ZNvKhMZoR47Hd5ngDRWB9Wpc2dQvn4teSrJ0pLvm/4RbypbRIO7u3u4Hpd3CER/gItXLiN75iwMBhQqDAhEf4ALlz2QI5tzRCeDojjeWxJFMndO/3qjOTjUC3BEocU7BCIiEgwIREQkGBCIiEgwIBARkWBAICIiwYBARESCAYEoklPjHDRo20r7vevAPshbtnig25WqVUXvu6HtZrjPxbxli/XmPXj0UDrwI/PDgEAUyW3etQNVypaXz9++fcOG7Vvx1ucdrty4FuR9GNvu/GUPOGfOoreuXSpbPHn+TDrWI/PCgEAUyW3ftxtVylaQz7sO7kPu7DnQvoWLtpdV1R2Z68C+KFmzMopXryhjPPhlaDvl4uVL0hGg2k4N2enr6yvzixcojIPHj4bbOVLkwIBAFImpYTPV1X2C+L96Ol2+fg2a1W2IRrXqSi+oqituNQ7CtZueOLhxOw5v3omWDRr724+h7VTh7/3wPprWbSDbxY4dRztIT/WKlaQ7bTIvDAgU5tT4BGrw+dS5syJJZkfUcWkmg82YihpQXl3hRvV8aNiulcGre93gcPy/U6haroKMG6G64j504pgMWlS8YCHUa9MCIydP8DdYj7Htrty4jjLFSiB9WidZT6VFjcxG5osBgYJMDX6jCl41ToCV3a+hNI3JUDC3dMmsDBw7Eh5XL+PsnsO4e9oDnrdvYtWmDSbJeVX49RgyAEN69dPO6ztyCJyLF5R02uXMjL97dMWr168REXkRnHwY0qMvBo4ZgU+fPmnnxbOJJ2M7q8F01m/fiuoVKsk4y0rz+o2k+ufzl88ygtuaeYukekk1Cusytp1qP8if89fIauqYFhbRZMwHZfPOHahRUb9Rmv587NyOgkwNVNOuhQs+ff6Mdr1cja536doVWUcN46gaJhesXIqDG7YhaZJfBWdqO3u9Qi809hw6AN+vvihZuKh2XnSL6FgyYw6yZcosBWnzLu3Q0rUDNi9eifDMi+DmgxruM52jI1ZuWo9WDZto51cuU14K+uXrVsvgPeXq1ZD5qsrnwpXLco5qxDpVtVSpTDm98ZgVY9tZRrdEkzr1ZJ4KDtky/W5cPvzvcfTu1NVk+UVRAwMCBZka2lJR1Q0BUVeX1cpXlEHeVUGj/mbPkk2Wffj4Acf/+xe9O5qmsNm8aztKFy2uN6D8KJ0hJFXh26V1O73HNsMrL0KSD2WKlZRz0g0Iah/dBvfDvnVbQpTWoGxXKN9fMinqDiN5kqTauwUyH6wyMlMd+/aQISCNTeOmTwnxvlVjZPUKleXz+UseyJUtu3Zg+UbtWyNz+owoWqCQSc5D7T9LhkwBrnPg2GHkyOJ/7OWwFpJ8UFfpal1dqt5/2T/zwi3dtilTyR0WmR/eIZipf8ZOksnU7j24j7v3vbVVOBevXELObNkx2m0iBo0bBQsLC6yY7a53Ra/RsmsHLFljvFqnf9ceGNF3oN6812/fwMbGxug267dtwZwli6SqxpCQHDMs8yGejY3B9g7VjhBcB4ycc2AM/TZkHhgQyOQvUVUsVVZb3XDh8iV0bNUGjWvXQ4eWbbBu22Y0aueC7JmzysDwuqaPHo8Jg0cY3Xec2LEN1uX7+Bh+Ymnt1k1o37sbNi1eIc/gGxKSY4ZlPrzz8UGihAlDdEyi0GJAMFOqoFy+fq3R5f26dEO/rj1CVE2iGlsV9az7pWtXtVUl6ln6+tVryrENXYVax7WWKThyZnPGVc/r/uYvXLUcvYYNlIbkwvkLGN0+JMcMy3xQbxGrc1Kip4xcgeH7Y9M+qUWRDwOCmZo1fopMwfH9+3d5WkbzNuvnz5/lb8yYMaVge/nqFU5fOI/NpcrI/Bu3buLjp49Ys2UjBnbrhfcfPqDH0AEoVaS4PDtvCqqOXvXRo2v6/DkYPnkcdq5cj3w5cyMsBJQXqsonpPmw7/BBNP//i2UsgCm8sVGZgmzputWI65gSFRvWlgJRfVaT94P7snzr3l0oXqiw9opbPVnj5OAoV8uJMjoge8lCiGllhdVzF5r0aR/1+KTu0z6ug/pK1Uvp2tUQz8lOO4VXXoQ0H1TguHn3DhrVrBOsju0MdVAX1M7tDG3Pzu3MF+8QKMha1G8kkzGbd27XPlWjXLjsgXIlSmHGmIlhlsvqzmTSsFEYOn40Dm3aEW5X1gHlRUjzYdiksdKAHVun3cJQx3axYsaUqqWsGTNrA06bJs0D3LexbQ1tr9u5HR89NS+8QyCTKZQvP2roFoRXLiNrpt8FT1ipUKqMNhhE5XxYMcsdrRs3C1bHdgF1UKfL2LbGtmfnduaJAYFMplfHrkiSOLFeQZNN50rUXJgqH4LSsV1AHdTpMrStYmx7dm5nnlhlRGHm6ZVbzF0T5YOmg7rF02ZLn0SaDurUY7eBdVBnbNtSRYoZ7eDuxu2b/O3MEO8QiCKpoHRsF1AHdRrGtlWMbc/O7cwT7xCIIrHAOrYLqIM6DWPbzhg9QRq861Sp7m97dm5nnhgQyCw9evYUt7zuGFxmFSMG8mTLESmesAlOx3a6HdTpCmjbaaPG+9uenduZLwYEMksL1izHZQNvOGv0bNMBeZ1zIqKFd8d2Cju3M1/RfvodXimMubi4SN8zNmHQXQBRUKln7D/7fjG63DpOXHbyRhHG58N76bTR3d39z75DCKhnSqLwYmkVA9G++vobblLbFUd0Pm9BEUeVkxFRVob7HQJRZHHw4EHMmjVLb561tTVmzpyJWLFiRVi6iCIKL4PIbBUtWhRJkybVqxqqUaMGgwGZLQYEMluWlpaoU6eOttpI3R2UK1cuopNFFGEYEAjmfpegqR6qXLky7w7IrDEgEMz9LiF79l8D15Qv/6tXUSJzxUZlIiISvEMgIiLBgEBERIIBgYiIBAMCEREJBgQiIhIMCEREJBgQiIhIMCAQEZFgQCAiIsGAQEREggGBiIgEAwIREQkGBCIiEgwIREQkGBCIiEgwIBARkbBEOHN1dYWPj094H5aIKEqxsbGBm5vbnx0QVDBQk7W1TXgfmogoSnj/PmIumsM9ICgqGEwbMy8iDk1EFOl16dcmQo7LNgQiIhIMCEREJBgQiIhIMCAQEZFgQCAiIsGAQCZ17sIZNGhREw5ZkiNVugTIWSgT+gzqhidPHzOniSI5BgQymQOH96Jc9WJI75QRJ/afw6Nbb7Br40EkSpgYx04eZk4TRXIMCGQy3ft2Qt2aDTFi0FikSmkr81IkT4k+3Qfi+YvnSJE2nkwJ7WIikX0s7fetOzfJupeveqBy7TKwz5gYzvnTYfyUUfj+/bveMbLmTYskaeLIdkkd4iKBrZXeslXrlsnnt+/eomTFgpKmnz9/yjybFNFx4tQx7foPHz2Qed73vOT7t2/fMHbSCDm2SkOVOmVx9dpl7fptu7SUtKtjq7uf8jVK4MbN69rlL1+9RIdurZEpdxq5Q2rWpj6ePX9qMH0aKv1Hjx+Sz6MnDEPVuuW0y1RaVfrUcTXuP7iHJi514eScCumy26Jzz7bwiaCXmOjPw4BAJnHztidu372FerUaGlzevnVnPLnzTqZ6tRqhZ5d+2u9VK9aQArxavfIoVrgEbnk8wtplW7F05UJMnz1Fbz8/fv7AP5PnyXYblm83eCy1r+r1yiN3zryYPHYGokWLFqRzcJs5ESvXLsW65dskDYX+KoJq9cvjnc877TqN6jWTY9+5/ATxbOJhxNhBMl8FnYYta8mxTh3ywNUzd+UFzFbtmyAkVCDs2b8L7GzttfM+f/6MKnXKIFOGLLj8322cPnIZjx49QO+BriE6BpFfDAhkEi9ePpe/KVP8ujMIrt37tsPKygq9uw1AzJgxkSlDZnTr1AuLV7jrrfflyxfEtIppdD9v3/4KBmkdnTBpzPRgpWHZqkVw7dQLGdNnkjT07TEI0aNHl7QZKrB//PiB5MlSyPfzF8/igsdZTB4zA/HjxUecOHEwYtA4HD52QO5Egmv+otlIljQZShUvq523a+82CTwD+wxD7NixkTBBQgzsMxxrNqzwdydFFGW6rqA/T5LESeXv4ycPpTAPrgcPH8DeLo3e1byjgxMePrqv/a4K4DdvXyNhwkRG9zN4ZF/kzJEHp06flDsFVTjrqt2oshTyiqYqSUMdyyG1o/a7hYUFUts7SNo0VJXP5m3r8fHTR6RKYYtRQybIfO97dyVYOTmn1NtnrFixcP/hPdimspPvXXu1lyt/DUMF+YuXLzBuykjs2nQIU2dO1M73uucl+7LLoH/+Ks+ePnuiraYjCineIZBJpHfKACfHdFi7cVWItreztcP9B956hfRd7zuwTWWvVy319etXZExvPODUrlEfuzcdQr48f8G1d3t/y9ev2I4Hnq9k+u/wJb1l6lje93+1J2gC0L37XpI2jQZ1msi2L7w/onuXPqhcu7S0PahgFjdOXNy7/kK7fzU99/qAAvkKabefOmGW3nJNcNI1ZFQ/qZrKkC6j3vzUdqmRLm0Gve01aWEwIFNgQCCTUfX1qvpi6OgBePzkkcxTjaoTp43Fuk0BB4ryZSrLFfbEqWPg6+sLz1s34DZjApo1bKW9ah4+diAKFygmDdXGqDYIxW38LLlLWLFmSZDT37h+c7j9M1ECj0rDBLfRUtirtPml7h5UYf76zSsJUqq9IlvWHOg1oKs0LiuqIT2w8/brxs1r2Hdwt1RX+VWhbBV8/eqLCVPHSEOyCp6PHj/Elh0bg3UMImMYEMhkVH33ns1HcN3zKv4qmQMpneKjXLViePHiGYoW+lVQG6Oqdjav3oWDR/ZLtUvNBhXRsG5TdG7XTZY3bV0P0RANC2bpP6VjTIL4CTB3xmJ5B0LdaQSFa4eeqFujAWrUryBpOHzsoKRJNR5rqACjnjJS5zZ91hTMnb5I6vNVgFi1aKMU0sXK5ZPlpSsXwtETwXvcVgXS4QPHwDqutb9lql1i27p9uOF5FXmKZIFt+oSoUrcsLl2+GKxjEBkT7affitQw5uLiAnVEdn9NRGS8+2vVnOburv9QRVjjHQIREQkGBCIiEgwIREQkGBCIiEgwIBARkWBAICIiwYBARESCAYGMUq+o9OjXWbpaVi9aqa6XI9P+FPV2c78hPZExV2qkzpQEjV3q6HUHrd76LVe9OMxJjQYV5I1rY1q0beiv00AihQGBjFLdLhw5fggXTt7A49tvYW+XOlLtTxk2ZqCMo3Bs71lcOXMXN295aruLUAGo7+AeGNBriHb9QSP6Il8xZxnPIH0OO3Tq8TdevX7lb7+q2wo1FsHy1YsRGQWUvouXLiBbFmej2/brOQTDRg/Ep0+fwjiVFNUwIJBRe/bvRKXyVWFjbeNvmer4LbgDswS0v5BQfQgtXbkAY4ZNRNIkSWW/KshoCrr9h/ZI3z/FCpfUbqP6H5r/zxJ4X3uOE/vPy3gC7bq29Hdui5bNR8VyVbBw2fxQp1MNwKMKb1MJKH2qbyPVFXm2LNmNbq+6904rHRGuNFma6M/AgEAGqSqY1etXYOa8qdJ3j+rXX7dA6ti9jV43zqHZX0hdvHReun7WFH4fPnzAv/8dR/ZsOeX7tp2bUaJYab0utYf2H4UczrkQI0YMCSLt23TBMT/9Dalqpq/fvmLmFHdcvHROb9Q0Rd1RtHd1kTsMdS7Z8jlh++4tMIW02VLKiGh+06Pmq+68A0ufypPEiZJg177tyF0kC5I72sjAPSp46ipVrAy27dpskjTTn4MBgQy6eNJTrqaP7zsnI4QVL1JKLxioAWE0YwGEZn+h4XH5PLJny6W9Cm/ZvhEypM+MwgWK/jrmpfMyulhADh09IL2U6lq4bJ50c50kcRJUqVAdC5bO1VvevW9HxIoZC+dPXJdxo1WX2s5Z9PcRUvu2HZPeS58/fybfVUHee1A3DBswWju2Q0Dp87h8Ae983spAQcf3npU0Hj95RO6WdGXNnE3yh0gXAwIZdOnqRcSOFVvGOdC1ZfsGGVnsyrVLcMyaXKpCDE1qOM2g7E9RYwYb24+ahv9/mEq/PC5flLsBVZ+eLb8Tdu/bgS7tumnvCF6/fR1g9ZQa6GbBkjkYP2KKXm+ju/Zul66wlSYNWmD1+uV69e237tyU9gnVRbbq5VRVwaS2T2OSf0lpHZxkbAPVDbbyz9ypiG8TX9IRlPRduHQONarURtcOPaQXVrWveDbx/Q0GZGMTT7ruJtLFgEAGXbh4Tq6+/Y5HXLlCdVStVANZMzvj0qlbuHvlqcHJMU3aIO1PUUNdGtuPmtT4y4ZcvHwBOZxzopdrf9y/8VIGn2nRrpGMpaAkjJ/QaDvHxi1rZYD61Ys3IWf23Nr5S1YsQO6c+aSQV0oWKyNjI6/fvFq7ziw3dzx/+Qw5C2ZAxZql/F19K936dJSRzdRUsNSvKizNdzVNmj7O6L+89E4Z4XnruoyCNnHqaEwYNVWbb4Glz+PSBVSrVFO7rzdv3+DeA2/5vXT5+LxDwgTGR54j88SAQAad9ziLnDl+F5Qaqu598ZxVcEqbDmMnj5BqC0OTunIOyv4U1fe/sf2oSY0D4Jequrp67RJy/L/KSI1/ULt6ffmsKTyzO+eUsRn8WrpyIbr2bo/VSzajWJGSevtUBW6TBs1//wexsJDRyxYsnaed55w1B5a7r8Mtj0coVKCItCf4NWXcP9oRzU4euCDzdEc569G5D4xRI6XduHkdg4b3QbXKtZA3d/4gpe/1m9dS+OfKkVe7XI3zrNoU/N7BXL1+RdvWQqTBgEAGXfA4h1w6V86GgsLIweNNsr+QUHcBalzj9ZvXyKhm6kq490BXlChaSlstperXDx/Vb7yeNX86BgzvjY0rd6Jg/sJ6y/Ye2IVnL56iSvnq+Pz5s3aqU70+Tp/9V6rJNm/fII24aizkz18+SxWOGi3NlNQdwtYdm7Bz7zYM6z86yOlbuXYpEiVKjDSpHbTbnLtwFrlz5PF3jANH9qFKxeomTTdFfZYRnQCKfNTLXtduXEEOZ+MFuKWlpVy9m2p/IWlQVvXtW3duwvTZkxE/fgJULFsFi+f+rtopU7I8olta4ujxQyj6/6E1VdBQaVdjIetSDd2qcVYVsGmdDQ/RuWDJXMSKFRv9BvfAy1cvEC9efFQoWxmz3BbAlDKkz4j7D+9h7PDJSJo02e/jB5I+NRazpkFd9w5B945BE0xv37mJejUbmTTdFPVxxDSKkgYM641Pnz7KOM4BUVfVakzn3ZsOIao4fe4Uqtcrj3vXX0jwMrWW7RqheNFSaNG4tcn3TVF7xDTeIVCUdOmKfuOpMWVLVZApKrl05SKyZskeJsFAWTh7RZjsl6I+tiFQlKQeOc2cKRv+ROpJoex+3o0gCg+8Q6AoyevqU/yp3MbPjOgkkJniHQIREQkGBCIiEgwIREQk2IZAZkm9WPb+g+FuLaJHt5S3p4nMDQMCmaXZC6fi7MX/jCyNhl6dByJzhqzhnCqiiMUqIzJLKVPYGl1mYRENyZIkD9f0EJntHcL79z7yJh5RRPHbHbQuC4voGDbBcA+rROFVRtrYmGZkwUgdECLiJIn8Uj2iWllZyZgGfsWMaSXdBhBFFFVORkRZGe59GRFFFj4+PujQoYN0vqdRrlw5tG7NPn7IPLENgcyWugKrXLmy3tgCNWrUiNA0EUUkBgQyayogqLGelRIlSiBJkqB16U30J2JAIJj7XYImCFSrVi2ik0MUodiGQGZPNSw/fPgQjo6OZp8XZN4YEIiISLDKiIiIBAMCEREJBgQiIhIMCEREJBgQiIhIMCAQEZFgQCAiIsGAQEREggGBiIgEAwIREQkGBCIiEgwIREQkGBCIiEgwIBARkWBAICIiYYlw5urqKoObExFRwKP5ubm54Y8OCCoYqMna2ia8D01EFCW8fx8xF83hHhAUFQzGTJkfEYcmIor0+nVrHSHHZRsCEREJBgQiIhIMCEREJBgQiIhIMCAQEZFgQCAiIsGAQJFWzcolkTpZLKS1tdGbUiWyxJQJIyM6eUR/HAYEitS69RqIOw999Ka/ChaN6GQR/ZEYEChKe3D/Hlya1YVzhpTInjEVenb9G+91ukZJkcACc2e6oXSRXHCyi4daVUrh7p1b2uXfvn3D1EmjUShPRmRInRBVyxfBhfNntMu7tG+J7p31XxKqW70sJowZqv1+4thhVCxdAOlTJ0CRfJmxZOEcvfWvXvZAw9oVkcUpGTI5JJbtiSIjBgSKsj5//ow61UojQ8bM+O/iHRw5dQWPHj3EwL5d9dZbunge5i9Zi8s3nyJj5ixo1rA6vn//LssmjBmCXTu2YOX6nbh29wUaNm6JRrUr4s2b10FKg7fXXTSqUxHNW7XDtTsvMHXmQowe1h9bNq2V5U+fPEbNyiVQsHAxnPa4Cw/Px+jcrU8Y5AZR6DEgUJS1d/c2/Pz5E30GDEfs2LGRIEFC+bxh7Qptga+079gdjmnTyTqDho2H993bOHfmlGw7f850DB4+Hmkc0iJ69Oho1MwFyVKkxL7d24OUhk3rV8I5R240aNwClpaWyJOvAJq2/BsrlrjL8rWrl8IhbTp06d4PcePGhZWVFYqVKBNmeUIU5foyIjKFe9538fDBPanq0RUtWjQ8e/oEKVPZynf7NA7aZXHixEHiJEnx6NEDvHz5Ah/ev0ezhtUQDdG063z99hWPHz3Qfl+3ehm2bV6v/f7x4wfkL1BYPj98eB+p0zjqHd/B0UnuOpT797zglC4Df3CKEhgQKMqys0+DtOky4Mi/lwNc7763l/bzx48f8fLFc6RKZYfEiZMgTty4WLNpL3Llzmd0+zr1m2Dy9N+dMeq2Adja2mP/3p1663t73ZH5in1qB71gQhSZscqIoqyy5avgq6+vNAqrhmRVBfT40UPs2LpRb705s9zgdfe2tDmMGtpXqody5/1L7iTatOuCYQN74c7tm7KuumM4uH83njx+FKQ01KjdEB4XzmLNyiXSQH3u7H9YunAuGjZtJcvr1GuC27duYLrbOAlGvr6+OHJoXxjkBlHoMSBQlKWqf9Zt2Q/PG9dQJH9mecqnbvUyuHzpgt56jZu6oFWT2siaLhmuXPbAohWbpL1A6dVvGCpUqobmjWognX18FMyTAUsWzMGPHz+ClIY0Do5YtmY7Fsz7B5nTJkHnts3Qe8BwVK9ZT5anSJkKG7YexJGD+5A7iz2yZ0iJmdMmhkFuEIVetJ/qsiocubi4QB2R4yFQeFCPnW7eeQR/FSzCDKcoNR5CtGiAu/uvhxPCC+8QiIhIMCAQEZHgU0b0R3vyJmhtAUTEOwQiIvo/VhkREZFgQKAwoR5e69erk3Q6pzqVU53Qaajn/KtXLBYpc75tq4babifCKz9CkidhlU4yb2xDoDCxaf0qHD96CCfPesLaxkavYBzcvzvGjJ8eKXO+Z98h0hldzbqNpO+jsM6PkOZJWKWTzBvvEChM7N+zE+UrVvVX+B06sEfeLi5crGSoj3HP20veMzCl9BkySUd4G9etNLqOemlNt4vt0ORHSPMkKOkkCi4GBDK5XFnssX7tcsybNVVGODt2+IB22c7tm1CsRGnpNkLZs3MrUiaMLm8Jqz6AlOYNa0hB37JxLZOk58WL5xjYp6uMeZAmeWxkS58Cwwf3Nrq+6o101/bNRoOBGh+hf+8uJsmP0ORJQOkkCgkGBDK5k+duStcQ+46elxHOihQvpV126eJ5ZMiYRfu9XMWqaNepu1xxd2rbDAvnz8TunVukB1G3fxaEOi2q/6Cq5QpLN9evXr6QvocKFCom3V0YkzmLMy55nDMaDC6eP4shIyeYJD9CkyfG0kkUUmxDIJO7evkiYsWOre32efuWDbCKGRNly1fG2zevYW0TT2/9AUPG4PSpEzKd+e+kjBkwd9FqxE+QINRp2bF1g4yQpq6+t+09gXTpM8r8r1+/atfRTZ9iEy8e3rx+5W9f27duwKrli+RzVqdkRo958pynVOcYyw9T5YmxdBKFFAMCmdzFC2eRzTmXtgqkcrXf1RzxEyTEe593+v8ILS3RpVtfGclMNbCWLF0BOXPlNbjvPj06YOPaX/XmP37+eulMdzwENRpZ5259td8f3PeWv4kSJ9EGAyVGjBjaz7rpU3zevUOChIn8HbtCpeqoVKWmBBjVQZ6h9gAloZ9t/eaHqfLEWDqJQopVRmRyqjvoHDlza7+r8YZV1Y3inD0nPG9c1Vv/3du3GNjXVT7HihVLqkf8dmGtMW7STHjeey3TgWMXZZ7mu5p0g4FmzARFVRfdvuWpna97h6CbPuX6tctSgPulgsichauQ1ik9Jo8fIeMpGJosLCwCzA9T5YmxdBKFFAMCmZzHhXPInjOPtuD9/u2bdFWtVKhcA0f9NKp269xaRj+rXLUW5i5a82teJxd5iii0KlWtJSOYqats1Zbg2rEV2rk0gkvTOgbTp6jxCipWrm5wf5qgMHjE+BDlhynzJKB0EoUEAwKZ1JcvX3Dj+hUZZ1i5ce0KMmbOpl1esnR5qQ5Rz+Qr7nNnYPuW9TLc5cRpc1GuQhW0bNMBb9++wd8t68uAMqGhCl3VdtC6bWepmlGPaR47cgBO6TMYTN+tmzdksBz1fL8xKv3qTiAk+WGqPAlKOomCi+MhUJhasXQBPrz3QZv2XbXzDuzbhWmTxmDTzsORLn3q7qFo8VJo3Kx1uB0zJHkSHukk8xsPgY3KFKYue5xHtf+PHqZRqkwFmSJj+ma7rwj3Y4YkT8IjnWR+GBAoTI2eEDm7qIjI9EX2PCHzxTYEIiISDAhERCQYEIiISDAgEBGRYEAgIiLBgEBERIKPnZJZ2rl1Hc6dPmFwmWUMKzRr1REpbe3DPV1EEYkBgczSi+dP8eTxQ6PLv34NXZcZRFFRhASE9+995NVsoojy48d3o8vUYDazpo4J1/QQ+S0jbYx0r/5HBYSIOEkiQ4W+6lDu27dv/pbFjBlT+pEhiiiqnIyIsjLcO7cjiiwePHiA7t27a7+rAWycnZ0xcODACE0XUUThU0Zktuzs7FC4cGHtd3VtVLdu3QhNE1FEYkAgs1a7dm3t56xZsyJjxt/DbBKZGwYEgrnfJVhbW8vnWrX0x1YmMjcMCGT2+vXrh7x580r7AZE5Y6MyEREJ3iEQEZFgQCAiIsGAQEREggGBiIgEAwIREQkGBCIiEgwIREQkGBCIiEgwIBARkWBAICIiwYBARESCAYGIiAQDAhERCQYEIiISDAhERCQYEIiISFginLm6usLHxye8D0tEFKXY2NjAzc3tzw4IKhioSTOOLRER6Xv//j0iQrgHBEUFgwmTwzfyERFFFb26u0bIcdmGQEREggGBiIgEAwIREQkGBCIiEgwIREQkGBCIiEgwIBARkWBAICIiwYBARESCAYGIiAQDAhERCQYEIiISDAhERCQYEIiIKOK6v6bIo1qVyjhz+j/EiBFDb/6Z8xeRNGnSCEsXEYU/BgRCj1690aNnL+YEkZljlREFKEnC+Jg9ayZKFC2CNPa2qF61Cu7cua1dvmH9OhQvUhgOqe2QJVMGdHftig8fPmiX58rujDWrV+vtM3mSRDh27Kh8Hjd2DGrVqKZd9u/Jk3LMTh3ay3e1nlpfl+4+V65Yjny5c+otnzRxgtz56J6D2q9ffvf97ds3TJk0Efnz5kbaNKlRqXw5nD9/zmC+vHnzGnYpk8PD46Le/CqVKmLihPHy+evXr7K/v/LlkbzLmysHtmzepF1XpT1pogRIY5dKpmSJE0raNbZu2Sx565jaXv5u37bV6LaFCuTHjh3btcvV+evuS31W+aC205jmNgU5smXV7kMt1/wuZJ4YEChQSxYvwoLFi3Hd8xYyZcqEJo0a4vv377IsXrz4mDNvPu543cO2HTvx778nMVmnIAoOtc++vXvB1tbu9z/QaBb4+fOnTGFt3JjR2LlzB9asW4+bd+6iUZMmqF+nthT+fiVIkBDVqtfAsiVLtPNu3bol1W+NGzeR76NHjsDatWuwYOFieN17gC3bdsDJKZ12/R8/fsDB0RHeDx7JVKBgIe2y/06dQru/22DQkKGSlgGDBuPv1i44e+aMdh0HBwfZzuv+Q9StWw+unTsZPK8H9+9j3pzZSJgwoXbezZs3MXzYUMyeO097/OjRo5sgFykqY0CgQHXo2Alp0zohduzYGDJsOLzu3tUWTGXKlkWmzJlhYWEh67Rq1RpHjhwOUa4udHdH0mRJUaJUSe281KlTSzDYv29fmP5S6hhz587B0GEj4ODgKIVjk6bNkDx5CuzZvcfgNs2at8D6dWvx+fNn+b586RKUKl0GKVOlkv0tcJ8v+8uaLRuiRYuGVLa28lnjy5cviGkV0+C+V65cjipVq0n+Wlpaolz58qhUuQqWL1tqMO3fvn9HsmTJDe5r0MD+aNe+AxIkSOBv2bfv34KcR/TnYxsCBUoVyhpx4sRB4iRJ8OjRQ/l+6OABTBw/HjdveuKLry9+fP+OJEmS6G3fs7urXPlraO4udL18+RKTJo7Hlu07MWP6VO18O3t7DB85Ct1cu+C9z3spWH183ult6+3tLVU8Gr6+X5A7T169derXq4PoFtERK1ZM5MufH+MmTPJ3/A/v36NxwwZyDI1v377i8f/P1a8CBQsiRcqU2LJ5M2rVro3Vq1Zi0pRfaX/x4oVUnTml+31H4NerV6+QQOeqXdejBw+RI6d+VZijoyM8Ll70d95fv/rCInp0TJs+w99+Dh86iCtXrmDOPHe9YJI+fXqMHTcBbdu0xru3b2FlFdPg70LmhXcIFKh79+5pP3/8+BEvX7xAqlS28PX1RbMmjVGzVm1cuHRFqkUGDxkGv7U7Eye74Y73Pe1kqGpi+LAhqN+goRRUfrXv0BGXrlzD3Xv3ZXs7O3u95WnSpNHbf7cePf3tY/WadbLs5H+n8f79e6nO0ZU4cWLEjRsX6zdt0tvXvYeP0bVbd6N507xFSylo9+zeJYWyupJXVFBUwfPO7d/tLX5dv3YNGTJkMLgslZ2tXr4rXl5ecpfh97zvP3oi1XWdO3bAlcuXtctVG0a/vn0wavRYWFlZ+TtG7bp15LdYuWat0d+FzAsDAgVq9syZuHv3jlSNjBg2FGkcHJAnb14JCKraI36CBFKddOP6dcyfPzfYOerp6YkD+/ejZ+8+Yf5rxIkTF7FixZb6e13qruDvtu0wZNAg3P5/Ia4Cx4H9+/D48WOj+6tXvz7OnzuLCePGolGjxtpCVe2vZSsXDBsyGNeuXpVqnUcPH0qBrakC271rJ2rUqmVwvw0aNMK2rVvk+OrKfd/evdKo3Oj/7RN+WUa3lHN68eK5dt6KZcvg6JgWZcuVM7hNz+7dUKVKVRQtWiwIOUfmgFVGFKgmzZqhRdOm8PL2QvbsObB0+Uop+KytrTFh0mQMGzoYPbp1Rc5cuVG7Tl0piILjyePHmDVnnuwvrLRo1gQxrKyk0MyWNRv69R+Au1539dbp068/5s6ZjaaNG+LRo0dyhZ83bz6MHffrqSFDVONy1WrVsWb1Kixaqn/eqiHY2sYGzZo0wrNnz5AsWTJpg7l//77k2Zhx41GsWHGD+/2rQAHMmDlLAtT9B/dhb2ePWXPmIm++fHp3DOrpICVe/PhyJ1WseAnt8pcvX2Dk6NEG9792zRp4eHjg8NHjQcxBMgfRfobH4xs6XFxc5AppwmS38DwshZB6FHHbjl1SX06GqUdnT/93Cus2/H6klCg0enV3lbtMd3d3hCdWGRGFgrryX7pkMf5u++u9CaKojAGBKIQGDugvL5uVL19B25hMFJWxDYEC9OL1W+aQESNHjZaJ6E/BOwQiIhIMCEREJBgQiIhIMCAQEZFgQCAiIsGAQEREggGBiIgEAwIREQkGBCIiEgwIREQkGBCIiEgwIBARkWBAICIiwYBAREQR1/21GqtWjQhERESGy0gbGxv88QEhIk6SiCgqsbGxiZCyMtzHVCYiosiJbQhERCQYEIiISDAgEBGRYEAgIiLBgEBERIIBgYiIBAMCEREJBgQiIhIMCEREJBgQiIhIMCAQEZFgQCAiIsGAQEREggGBiIgEAwIREQkGBCIiEgwIREQkGBCIiEgwIBARkWBAICIiwYBARESCAYGIiAQDAhERCQYEIiISDAhERCQYEIiISDAgEBGRYEAgIiLBgEBERIIBgYiIBAMCEREJBgQiIhIMCEREJBgQiIhIMCAQEZFgQCAiIsGAQEREggGBiIgEAwIREQkGBCIiEgwIREQkGBCIiEgwIBARkWBAICIiwYBARESCAYGIiKD8DykvMXXCyOKIAAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(figsize=(4.3, 6.2))\n", + "ax.set_axis_off()\n", + "steps_txt = [\n", + " (\"Макро-моменты\\n$\\\\rho=\\\\sum f_i,\\\\ \\\\rho\\\\mathbf{u}=\\\\sum \\\\mathbf{c}_i f_i$\", \"#e8f0fe\"),\n", + " (\"Равновесие $f_i^{eq}$\\n(энтропийное)\", \"#e6f4ea\"),\n", + " (\"Неравновесие\\n$\\\\Delta s=P_s(f-f^{eq}),\\\\ \\\\Delta h=(f-f^{eq})-\\\\Delta s$\", \"#fff4e5\"),\n", + " (\"Стабилизатор $\\\\gamma$\\n$=1/\\\\beta-(2-1/\\\\beta)\\\\frac{\\\\langle\\\\Delta s|\\\\Delta h\\\\rangle}{\\\\langle\\\\Delta h|\\\\Delta h\\\\rangle}$\", \"#fde7ef\"),\n", + " (\"Столкновение\\n$f\\\\leftarrow f-\\\\beta(2\\\\Delta s+\\\\gamma\\\\Delta h)$\", \"#f3e8fd\"),\n", + " (\"Перенос\\n$f_i(\\\\mathbf{x}+\\\\mathbf{c}_i)\\\\leftarrow f_i(\\\\mathbf{x})$\", \"#e8f0fe\"),\n", + " (\"Граничные условия\", \"#eceff1\"),\n", + "]\n", + "y = 0.95\n", + "for txt, col in steps_txt:\n", + " ax.add_patch(plt.Rectangle((0.05, y - 0.1), 0.9, 0.085, transform=ax.transAxes,\n", + " facecolor=col, edgecolor=\"#555\", lw=1.2))\n", + " ax.text(0.5, y - 0.057, txt, transform=ax.transAxes, ha=\"center\", va=\"center\", fontsize=8.5)\n", + " if y > 0.2:\n", + " ax.annotate(\"\", xy=(0.5, y - 0.118), xytext=(0.5, y - 0.1), xycoords=\"axes fraction\",\n", + " arrowprops=dict(arrowstyle=\"-|>\", color=\"#555\"))\n", + " y -= 0.13\n", + "ax.set_title(\"Шаг KBC\")\n", + "_finish(fig, \"06_algorithm_flow.png\")" + ] + }, + { + "cell_type": "markdown", + "id": "6f042f66", + "metadata": {}, + "source": [ + "## 7. Демо-1: вихрь Тейлора–Грина (валидация вязкости и H-теоремы)\n", + "\n", + "Точное решение несжимаемого Навье–Стокса в периодической области:\n", + "$$ u_x=-U_0\\cos(k x)\\sin(k y),\\quad u_y=U_0\\sin(k x)\\cos(k y),\\quad k=2\\pi/N. $$\n", + "Кинетическая энергия затухает как $E(t)=E_0\\,e^{-4\\nu k^2 t}$. Прогоняем KBC и\n", + "**измеряем** $\\nu$ по наклону $\\ln E(t)$ — он должен совпасть с заданным $\\nu$." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "c2b5b6d4", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-06T17:33:55.964274Z", + "iopub.status.busy": "2026-06-06T17:33:55.964090Z", + "iopub.status.idle": "2026-06-06T17:34:22.077835Z", + "shell.execute_reply": "2026-06-06T17:34:22.076978Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "TGV: nu_zadano=0.01250, nu_izmereno=0.01249, otn.oshibka=0.05%\n", + "Валидация TGV (вязкость по затуханию энергии) — OK\n" + ] + } + ], + "source": [ + "def run_tgv(N=96, U0=0.04, nu=0.0125, steps=10000, rec=50, n_snap=10, frame_every=42):\n", + " k = 2 * np.pi / N\n", + " xs = np.arange(N)\n", + " X, Yc = np.meshgrid(xs, xs) # X — индекс x (ось 1), Yc — индекс y (ось 0)\n", + " ux = -U0 * np.cos(k * X) * np.sin(k * Yc)\n", + " uy = U0 * np.sin(k * X) * np.cos(k * Yc)\n", + " rho = np.ones((N, N))\n", + " f = feq_entropic(rho, np.stack([ux, uy]))\n", + " beta = nu_to_beta(nu)\n", + " # моменты времени для n_snap снимков поля скорости через равные интервалы\n", + " snap_at = sorted(set(int(round(v)) for v in np.linspace(0, steps, n_snap)))\n", + " snaps, frames, ts, KE, Hs = [], [], [], [], []\n", + " for t in range(steps + 1):\n", + " rho, u = macros(f)\n", + " f, _ = collide_kbc(f, feq_entropic(rho, u), beta)\n", + " f = stream(f)\n", + " need = (t in snap_at) or (t % rec == 0) or (t % frame_every == 0)\n", + " if need:\n", + " _, uu = macros(f)\n", + " if t in snap_at:\n", + " snaps.append((t, uu.copy())) # снимки для статической панели\n", + " if t % frame_every == 0:\n", + " frames.append((t, uu.copy())) # кадры для анимации\n", + " if t % rec == 0:\n", + " ts.append(t)\n", + " KE.append(0.5 * np.mean(uu[0] ** 2 + uu[1] ** 2))\n", + " Hs.append(H_function(f).mean())\n", + " return dict(N=N, k=k, nu=nu, U0=U0, ts=np.array(ts), KE=np.array(KE),\n", + " H=np.array(Hs), u=u, rho=rho, snaps=snaps, frames=frames)\n", + "\n", + "\n", + "tgv = run_tgv()\n", + "# Измеряем ν по наклону ln(KE): slope = -4 ν k^2\n", + "mask = tgv[\"KE\"] > 0\n", + "slope = np.polyfit(tgv[\"ts\"][mask], np.log(tgv[\"KE\"][mask]), 1)[0]\n", + "nu_meas = -slope / (4 * tgv[\"k\"] ** 2)\n", + "rel_err = abs(nu_meas - tgv[\"nu\"]) / tgv[\"nu\"]\n", + "print(f\"TGV: nu_zadano={tgv['nu']:.5f}, nu_izmereno={nu_meas:.5f}, otn.oshibka={rel_err*100:.2f}%\")\n", + "assert rel_err < 0.06, \"TGV: измеренная вязкость отклонилась слишком сильно\"\n", + "print(\"Валидация TGV (вязкость по затуханию энергии) — OK\")" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "e396e493", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-06T17:34:22.080506Z", + "iopub.status.busy": "2026-06-06T17:34:22.080288Z", + "iopub.status.idle": "2026-06-06T17:34:22.708562Z", + "shell.execute_reply": "2026-06-06T17:34:22.707721Z" + }, + "lines_to_next_cell": 2 + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def vorticity(u):\n", + " duy_dx = (np.roll(u[1], -1, 1) - np.roll(u[1], 1, 1)) * 0.5\n", + " dux_dy = (np.roll(u[0], -1, 0) - np.roll(u[0], 1, 0)) * 0.5\n", + " return duy_dx - dux_dy\n", + "\n", + "\n", + "fig, axs = plt.subplots(1, 3, figsize=(13.5, 4.0))\n", + "om = vorticity(tgv[\"u\"])\n", + "im = axs[0].imshow(om, origin=\"lower\", cmap=\"RdBu_r\")\n", + "axs[0].set_title(\"Завихренность $\\\\omega$ (TGV, срез)\")\n", + "axs[0].set_xlabel(\"$x$ [lu]\"); axs[0].set_ylabel(\"$y$ [lu]\")\n", + "plt.colorbar(im, ax=axs[0], fraction=0.046)\n", + "\n", + "axs[1].semilogy(tgv[\"ts\"], tgv[\"KE\"], \"o\", ms=3, label=\"KBC (измерено)\")\n", + "axs[1].semilogy(tgv[\"ts\"], tgv[\"KE\"][0] * np.exp(-4 * tgv[\"nu\"] * tgv[\"k\"] ** 2 * tgv[\"ts\"]),\n", + " \"-\", color=\"#d1495b\", label=\"$E_0 e^{-4\\\\nu k^2 t}$ (аналитика)\")\n", + "axs[1].set_title(\"Затухание кин. энергии\"); axs[1].set_xlabel(\"$t$ [ts]\")\n", + "axs[1].set_ylabel(\"$E(t)$\"); axs[1].legend()\n", + "\n", + "axs[2].plot(tgv[\"ts\"], tgv[\"H\"], color=\"#2e7d32\")\n", + "axs[2].set_title(\"H-функция (энтропия) во времени\")\n", + "axs[2].set_xlabel(\"$t$ [ts]\"); axs[2].set_ylabel(\"$\\\\langle H\\\\rangle$\")\n", + "fig.suptitle(\"Демо-1: вихрь Тейлора–Грина (KBC, D2Q9)\", y=1.04, fontweight=\"bold\")\n", + "_finish(fig, \"07_taylor_green.png\")" + ] + }, + { + "cell_type": "markdown", + "id": "9c33645e", + "metadata": {}, + "source": [ + "## 8. Демо-2: устойчивость — двойной сдвиговый слой (BGK против KBC)\n", + "\n", + "Классический тест Minion–Brown: тонкие сдвиговые слои на **недоразрешённой**\n", + "сетке. Стандартный BGK при малой вязкости разрушается (отрицательные\n", + "популяции, NaN), а KBC за счёт адаптивного $\\gamma$ остаётся устойчивым и даёт\n", + "гладкие свёрнутые вихри — это и есть «implicit LES»." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "6938a385", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-06T17:34:23.638668Z", + "iopub.status.busy": "2026-06-06T17:34:23.638459Z", + "iopub.status.idle": "2026-06-06T17:35:44.219726Z", + "shell.execute_reply": "2026-06-06T17:35:44.218923Z" + }, + "lines_to_next_cell": 2 + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Sdvigovyj sloj: Re ~ 30118, beta ~ 0.9990\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "BGK: raz=2011\n", + "KBC: ustojchiv\n", + "Демонстрация устойчивости BGK vs KBC — OK\n" + ] + } + ], + "source": [ + "def init_shear(N, U0=0.04, delta=0.05, kappa=80.0):\n", + " xs = np.arange(N) / N\n", + " X, Yc = np.meshgrid(xs, xs)\n", + " ux = np.where(Yc <= 0.5, U0 * np.tanh(kappa * (Yc - 0.25)),\n", + " U0 * np.tanh(kappa * (0.75 - Yc)))\n", + " uy = delta * U0 * np.sin(2 * np.pi * (X + 0.25))\n", + " return np.stack([ux, uy])\n", + "\n", + "\n", + "def run_shear(scheme, N=128, U0=0.04, nu=1.7e-4, steps=8000, rec=100, frame_every=33):\n", + " u0 = init_shear(N, U0=U0)\n", + " rho = np.ones((N, N))\n", + " beta = nu_to_beta(nu)\n", + " feq0 = feq_entropic if scheme == \"kbc\" else feq_poly\n", + " f = feq0(rho, u0)\n", + " ts, umax, frames = [], [], []\n", + " blew_up_at = None\n", + " last_u, last_g = u0, np.full((N, N), 2.0)\n", + " for t in range(steps + 1):\n", + " rho, u = macros(f)\n", + " if not np.all(np.isfinite(u)) or np.abs(u).max() > 0.5:\n", + " blew_up_at = t\n", + " break\n", + " if t % frame_every == 0:\n", + " frames.append((t, u.copy())) # кадры (только до разрушения)\n", + " if scheme == \"kbc\":\n", + " f, g = collide_kbc(f, feq_entropic(rho, u), beta)\n", + " last_g = g\n", + " else:\n", + " f = collide_bgk(f, feq_poly(rho, u), beta)\n", + " f = stream(f)\n", + " last_u = u\n", + " if t % rec == 0:\n", + " ts.append(t); umax.append(np.abs(u).max())\n", + " return dict(scheme=scheme, ts=np.array(ts), umax=np.array(umax), frames=frames,\n", + " u=last_u, gamma=last_g, blew_up_at=blew_up_at, N=N, U0=U0, nu=nu)\n", + "\n", + "\n", + "Re_shear = 0.04 * 128 / 1.7e-4\n", + "print(f\"Sdvigovyj sloj: Re ~ {Re_shear:.0f}, beta ~ {nu_to_beta(1.7e-4):.4f}\")\n", + "res_bgk = run_shear(\"bgk\")\n", + "res_kbc = run_shear(\"kbc\")\n", + "print(\"BGK:\", (\"raz=\" + str(res_bgk[\"blew_up_at\"])) if res_bgk[\"blew_up_at\"] else \"ustojchiv\")\n", + "print(\"KBC:\", (\"raz=\" + str(res_kbc[\"blew_up_at\"])) if res_kbc[\"blew_up_at\"] else \"ustojchiv\")\n", + "assert res_kbc[\"blew_up_at\"] is None, \"KBC должен оставаться устойчивым\"\n", + "print(\"Демонстрация устойчивости BGK vs KBC — OK\")" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "ed5bef45", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-06T17:35:44.222217Z", + "iopub.status.busy": "2026-06-06T17:35:44.222013Z", + "iopub.status.idle": "2026-06-06T17:35:44.891736Z", + "shell.execute_reply": "2026-06-06T17:35:44.890733Z" + }, + "lines_to_next_cell": 2 + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, axs = plt.subplots(1, 3, figsize=(13.5, 4.0))\n", + "om_k = vorticity(res_kbc[\"u\"])\n", + "im0 = axs[0].imshow(om_k, origin=\"lower\", cmap=\"RdBu_r\")\n", + "axs[0].set_title(\"KBC: завихренность (устойчиво)\")\n", + "axs[0].set_xlabel(\"$x$ [lu]\"); axs[0].set_ylabel(\"$y$ [lu]\")\n", + "plt.colorbar(im0, ax=axs[0], fraction=0.046)\n", + "\n", + "im1 = axs[1].imshow(res_kbc[\"gamma\"] - 2.0, origin=\"lower\", cmap=\"magma\")\n", + "axs[1].set_title(\"Поле стабилизатора $\\\\gamma-2$\")\n", + "axs[1].set_xlabel(\"$x$ [lu]\"); axs[1].set_ylabel(\"$y$ [lu]\")\n", + "plt.colorbar(im1, ax=axs[1], fraction=0.046)\n", + "\n", + "axs[2].plot(res_kbc[\"ts\"], res_kbc[\"umax\"], color=\"#2e7d32\", label=\"KBC\")\n", + "axs[2].plot(res_bgk[\"ts\"], res_bgk[\"umax\"], color=\"#d1495b\", label=\"BGK\")\n", + "if res_bgk[\"blew_up_at\"]:\n", + " axs[2].axvline(res_bgk[\"blew_up_at\"], color=\"#d1495b\", ls=\"--\", alpha=0.6)\n", + "axs[2].set_title(\"$\\\\max|\\\\mathbf{u}|$ во времени\")\n", + "axs[2].set_xlabel(\"$t$ [ts]\"); axs[2].set_ylabel(\"$\\\\max|\\\\mathbf{u}|$ [lu/ts]\"); axs[2].legend()\n", + "fig.suptitle(f\"Демо-2: сдвиговый слой, Re~{Re_shear:.0f} (BGK разрушается, KBC держит)\",\n", + " y=1.04, fontweight=\"bold\")\n", + "_finish(fig, \"08_shear_stability.png\")" + ] + }, + { + "cell_type": "markdown", + "id": "78b4734a", + "metadata": {}, + "source": [ + "## 9. Демо-3: каверна с движущейся крышкой против эталона Ghia (Re=1000)\n", + "\n", + "Квадратная каверна, верхняя стенка движется со скоростью $U$. На неподвижных\n", + "стенках — **bounce-back** (отскок), на крышке — bounce-back с поправкой импульса\n", + "подвижной стенки $-2 w_i \\rho\\,(\\mathbf c_i\\cdot\\mathbf u_w)/c_s^2$. Сравниваем\n", + "профили скорости по центральным линиям с данными **Ghia, Ghia & Shin (1982)**.\n", + "Здесь сетка намеренно грубая (для быстрого прогона), а bounce-back — первого\n", + "порядка, поэтому совпадение **качественное**; оно улучшается измельчением сетки,\n", + "числом шагов и переходом к ГУ второго порядка (Zou–He / Grad на крышке)." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "50b9f7c8", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-06T17:35:44.894020Z", + "iopub.status.busy": "2026-06-06T17:35:44.893819Z", + "iopub.status.idle": "2026-06-06T17:36:24.348832Z", + "shell.execute_reply": "2026-06-06T17:36:24.347925Z" + }, + "lines_to_next_cell": 2 + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Kaverna: Re=1000, N=110, ostanovleno na shage 13999\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Kaverna: RMS-otklonenie u_x ot Ghia ~ 0.167 (gruboe BB -> dopustimo)\n" + ] + } + ], + "source": [ + "UP = [2, 5, 6] # c_iy = +1 (вверх)\n", + "DOWN = [4, 7, 8] # c_iy = -1 (вниз)\n", + "RIGHT = [1, 5, 8] # c_ix = +1\n", + "LEFT = [3, 6, 7] # c_ix = -1\n", + "\n", + "\n", + "def run_cavity(N=110, Re=1000.0, U=0.05, steps=14000, tol=1e-7, check=500, frame_every=58):\n", + " nu = U * N / Re\n", + " beta = nu_to_beta(nu)\n", + " rho = np.ones((N, N))\n", + " u = np.zeros((2, N, N))\n", + " f = feq_entropic(rho, u)\n", + " uw = np.array([U, 0.0])\n", + " prev = None\n", + " frames = []\n", + " t = 0\n", + " for t in range(steps):\n", + " rho, u = macros(f)\n", + " if t % frame_every == 0:\n", + " frames.append((t, u.copy())) # кадры становления течения\n", + " fcol, _ = collide_kbc(f, feq_entropic(rho, u), beta)\n", + " f = stream(fcol)\n", + " # bounce-back: на каждой стенке неизвестны направления, входящие в область.\n", + " for i in UP: # низ (y=0)\n", + " f[i, 0, :] = fcol[OPP[i], 0, :]\n", + " for i in RIGHT: # лево (x=0)\n", + " f[i, :, 0] = fcol[OPP[i], :, 0]\n", + " for i in LEFT: # право (x=N-1)\n", + " f[i, :, -1] = fcol[OPP[i], :, -1]\n", + " for i in DOWN: # верх (крышка) + поправка подвижной стенки\n", + " io = OPP[i] # io ударяет в крышку (идёт вверх)\n", + " corr = 2.0 * W[io] * (CX[io] * uw[0] + CY[io] * uw[1]) / CS2\n", + " f[i, -1, :] = fcol[io, -1, :] - corr\n", + " if t % check == 0 and t > 0:\n", + " cur = u.copy()\n", + " if prev is not None and np.abs(cur - prev).max() < tol:\n", + " break\n", + " prev = cur\n", + " rho, u = macros(f)\n", + " return dict(N=N, Re=Re, U=U, u=u, steps=t, frames=frames)\n", + "\n", + "\n", + "cav = run_cavity()\n", + "print(f\"Kaverna: Re={cav['Re']:.0f}, N={cav['N']}, ostanovleno na shage {cav['steps']}\")\n", + "\n", + "# Эталон Ghia, Ghia & Shin (1982), Re=1000.\n", + "ghia_y = np.array([0.0000, 0.0547, 0.0625, 0.0703, 0.1016, 0.1719, 0.2813, 0.4531,\n", + " 0.5000, 0.6172, 0.7344, 0.8516, 0.9531, 0.9609, 0.9688, 0.9766, 1.0000])\n", + "ghia_u = np.array([0.0000, -0.18109, -0.20196, -0.22220, -0.29730, -0.38289, -0.27805,\n", + " -0.10648, -0.06080, 0.05702, 0.18719, 0.33304, 0.46604, 0.51117,\n", + " 0.57492, 0.65928, 1.0000])\n", + "ghia_x = np.array([0.0000, 0.0625, 0.0703, 0.0781, 0.0938, 0.1563, 0.2266, 0.2344,\n", + " 0.5000, 0.8047, 0.8594, 0.9063, 0.9453, 0.9531, 0.9609, 0.9688, 1.0000])\n", + "ghia_v = np.array([0.0000, 0.27485, 0.29012, 0.30353, 0.32627, 0.37095, 0.33075, 0.32235,\n", + " 0.02526, -0.31966, -0.42665, -0.51550, -0.39188, -0.33714, -0.27669,\n", + " -0.21388, 0.0000])\n", + "\n", + "Ncav = cav[\"N\"]\n", + "yc = (np.arange(Ncav) + 0.5) / Ncav\n", + "xc = (np.arange(Ncav) + 0.5) / Ncav\n", + "u_centerline = cav[\"u\"][0, :, Ncav // 2] / cav[\"U\"] # u_x(y) на вертикали x=0.5\n", + "v_centerline = cav[\"u\"][1, Ncav // 2, :] / cav[\"U\"] # u_y(x) на горизонтали y=0.5\n", + "\n", + "fig, axs = plt.subplots(1, 3, figsize=(14, 4.4))\n", + "spd = np.sqrt(cav[\"u\"][0] ** 2 + cav[\"u\"][1] ** 2) / cav[\"U\"]\n", + "axs[0].imshow(spd, origin=\"lower\", cmap=\"viridis\", extent=[0, 1, 0, 1])\n", + "sx = np.linspace(0, 1, Ncav)\n", + "axs[0].streamplot(sx, sx, cav[\"u\"][0], cav[\"u\"][1], density=1.1, color=\"white\", linewidth=0.6)\n", + "axs[0].set_title(\"Линии тока и $|\\\\mathbf{u}|/U$\"); axs[0].set_xlabel(\"$x/L$\"); axs[0].set_ylabel(\"$y/L$\")\n", + "\n", + "axs[1].plot(u_centerline, yc, \"-\", color=\"#1f6feb\", label=\"KBC\")\n", + "axs[1].plot(ghia_u, ghia_y, \"o\", ms=5, mfc=\"none\", color=\"#d1495b\", label=\"Ghia 1982\")\n", + "axs[1].set_title(\"$u_x/U$ по вертикали $x=0.5$\"); axs[1].set_xlabel(\"$u_x/U$\")\n", + "axs[1].set_ylabel(\"$y/L$\"); axs[1].legend()\n", + "\n", + "axs[2].plot(xc, v_centerline, \"-\", color=\"#1f6feb\", label=\"KBC\")\n", + "axs[2].plot(ghia_x, ghia_v, \"o\", ms=5, mfc=\"none\", color=\"#d1495b\", label=\"Ghia 1982\")\n", + "axs[2].set_title(\"$u_y/U$ по горизонтали $y=0.5$\"); axs[2].set_xlabel(\"$x/L$\")\n", + "axs[2].set_ylabel(\"$u_y/U$\"); axs[2].legend()\n", + "fig.suptitle(\"Демо-3: каверна с движущейся крышкой, Re=1000 (KBC vs Ghia)\",\n", + " y=1.04, fontweight=\"bold\")\n", + "_finish(fig, \"09_cavity_ghia.png\")\n", + "\n", + "u_interp = np.interp(ghia_y, yc, u_centerline)\n", + "rms = np.sqrt(np.mean((u_interp - ghia_u) ** 2))\n", + "print(f\"Kaverna: RMS-otklonenie u_x ot Ghia ~ {rms:.3f} (gruboe BB -> dopustimo)\")" + ] + }, + { + "cell_type": "markdown", + "id": "c50cd883", + "metadata": {}, + "source": [ + "## 9b. Анимации: зацикленное воспроизведение тестов (видео)\n", + "\n", + "Для каждого теста собираем **зацикленный GIF** (бесконечный `loop`) из кадров,\n", + "записанных во время прогона: вихрь Тейлора–Грина (затухание), сдвиговый слой\n", + "(BGK против KBC бок о бок — видно момент разрушения BGK) и становление течения в\n", + "каверне. Файлы сохраняются в `anim/` (самостоятельные «видео»), а ниже встроены\n", + "в ноутбук и проигрываются циклически. Скорость воспроизведения — `fps` кадров/с\n", + "(физическое время между кадрами постоянно)." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "16a857e7", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-06T17:36:24.351124Z", + "iopub.status.busy": "2026-06-06T17:36:24.350919Z", + "iopub.status.idle": "2026-06-06T17:36:24.357444Z", + "shell.execute_reply": "2026-06-06T17:36:24.356468Z" + } + }, + "outputs": [], + "source": [ + "import io as _io\n", + "from PIL import Image\n", + "from IPython.display import HTML, display\n", + "\n", + "ANIMDIR = os.path.join(os.path.dirname(os.path.abspath(__file__)) if \"__file__\" in globals() else \".\", \"anim\")\n", + "os.makedirs(ANIMDIR, exist_ok=True)\n", + "\n", + "\n", + "def render_gif(n_frames, draw_fn, name, figsize, fps=18, dpi=80):\n", + " \"\"\"Отрисовать n_frames кадров (draw_fn(fig, i)) и сохранить зацикленный GIF.\"\"\"\n", + " path = os.path.join(ANIMDIR, name)\n", + " fig = plt.figure(figsize=figsize, dpi=dpi)\n", + " pil = []\n", + " for i in range(n_frames):\n", + " fig.clf()\n", + " draw_fn(fig, i)\n", + " buf = _io.BytesIO()\n", + " fig.savefig(buf, format=\"png\") # фикс. размер кадра (figsize×dpi)\n", + " buf.seek(0)\n", + " pil.append(Image.open(buf).convert(\"RGB\").convert(\"P\", palette=Image.ADAPTIVE))\n", + " plt.close(fig)\n", + " pil[0].save(path, save_all=True, append_images=pil[1:],\n", + " duration=int(1000 / fps), loop=0, optimize=True) # loop=0 → бесконечно\n", + " print(\"GIF:\", os.path.relpath(path), f\"({n_frames} кадров)\")\n", + " return path\n", + "\n", + "\n", + "def show_gif(path, width=460):\n", + " \"\"\"Встроить GIF в ноутбук (ссылкой на файл — авто-цикл в браузере/Jupyter).\"\"\"\n", + " if IN_NOTEBOOK:\n", + " display(HTML(f''))" + ] + }, + { + "cell_type": "markdown", + "id": "461219ae", + "metadata": {}, + "source": [ + "### Видео 1 — затухание вихря Тейлора–Грина" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "01ccf91a", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-06T17:36:24.359571Z", + "iopub.status.busy": "2026-06-06T17:36:24.359381Z", + "iopub.status.idle": "2026-06-06T17:36:41.567992Z", + "shell.execute_reply": "2026-06-06T17:36:41.567163Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "GIF: anim\\tgv_decay.gif (239 кадров)\n" + ] + }, + { + "data": { + "text/html": [ + "" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "_tgv_fr = tgv[\"frames\"]\n", + "_om0 = np.abs(vorticity(_tgv_fr[0][1])).max()\n", + "_KE0 = 0.5 * np.mean(_tgv_fr[0][1][0] ** 2 + _tgv_fr[0][1][1] ** 2)\n", + "\n", + "def _draw_tgv(fig, i):\n", + " t, u = _tgv_fr[i]\n", + " ax = fig.add_subplot(111)\n", + " ax.imshow(vorticity(u), origin=\"lower\", cmap=\"RdBu_r\", vmin=-_om0, vmax=_om0)\n", + " ke = 0.5 * np.mean(u[0] ** 2 + u[1] ** 2) / _KE0\n", + " ax.set_title(f\"Тейлор–Грин · t={t} · $E/E_0$={ke:.2f}\", fontsize=10)\n", + " ax.set_xticks([]); ax.set_yticks([])\n", + " fig.tight_layout()\n", + "\n", + "show_gif(render_gif(len(_tgv_fr), _draw_tgv, \"tgv_decay.gif\", (4.6, 4.4), fps=24))" + ] + }, + { + "cell_type": "markdown", + "id": "d429f455", + "metadata": {}, + "source": [ + "### Видео 2 — сдвиговый слой: BGK (слева) против KBC (справа)\n", + "BGK замирает на последнем устойчивом кадре с пометкой «разрушился», KBC\n", + "продолжает гладко сворачивать вихри." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "c5084b58", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-06T17:36:41.570031Z", + "iopub.status.busy": "2026-06-06T17:36:41.569849Z", + "iopub.status.idle": "2026-06-06T17:37:11.390263Z", + "shell.execute_reply": "2026-06-06T17:37:11.389388Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "GIF: anim\\shear_bgk_vs_kbc.gif (243 кадров)\n" + ] + }, + { + "data": { + "text/html": [ + "" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "_kf, _bf = res_kbc[\"frames\"], res_bgk[\"frames\"]\n", + "_om0s = np.percentile(np.abs(vorticity(_kf[len(_kf) // 2][1])), 99.5)\n", + "\n", + "def _draw_shear(fig, i):\n", + " ax1 = fig.add_subplot(1, 2, 1)\n", + " ax2 = fig.add_subplot(1, 2, 2)\n", + " dead = i >= len(_bf)\n", + " tb, ub = _bf[min(i, len(_bf) - 1)]\n", + " ax1.imshow(vorticity(ub), origin=\"lower\", cmap=\"RdBu_r\", vmin=-_om0s, vmax=_om0s)\n", + " ax1.set_title(\"BGK — разрушился\" if dead else f\"BGK · t={tb}\",\n", + " color=\"red\" if dead else \"black\", fontsize=10)\n", + " tk, uk = _kf[i]\n", + " ax2.imshow(vorticity(uk), origin=\"lower\", cmap=\"RdBu_r\", vmin=-_om0s, vmax=_om0s)\n", + " ax2.set_title(f\"KBC · t={tk}\", fontsize=10)\n", + " for a in (ax1, ax2):\n", + " a.set_xticks([]); a.set_yticks([])\n", + " fig.tight_layout()\n", + "\n", + "show_gif(render_gif(len(_kf), _draw_shear, \"shear_bgk_vs_kbc.gif\", (8.4, 4.3), fps=24), width=720)" + ] + }, + { + "cell_type": "markdown", + "id": "b102ab56", + "metadata": {}, + "source": [ + "### Видео 3 — становление течения в каверне (Re=1000)" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "9f5e85f3", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-06T17:37:11.392380Z", + "iopub.status.busy": "2026-06-06T17:37:11.392189Z", + "iopub.status.idle": "2026-06-06T17:37:45.886152Z", + "shell.execute_reply": "2026-06-06T17:37:45.885290Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "GIF: anim\\cavity_transient.gif (242 кадров)\n" + ] + }, + { + "data": { + "text/html": [ + "" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "_cf = cav[\"frames\"]\n", + "_vmax = max(np.sqrt(u[0] ** 2 + u[1] ** 2).max() for _, u in _cf) / cav[\"U\"]\n", + "\n", + "def _draw_cav(fig, i):\n", + " t, u = _cf[i]\n", + " ax = fig.add_subplot(111)\n", + " sp = np.sqrt(u[0] ** 2 + u[1] ** 2) / cav[\"U\"]\n", + " ax.imshow(sp, origin=\"lower\", cmap=\"viridis\", vmin=0, vmax=_vmax, extent=[0, 1, 0, 1])\n", + " ax.set_title(f\"Каверна Re=1000 · t={t} · $|\\\\mathbf{{u}}|/U$\", fontsize=10)\n", + " ax.set_xlabel(\"$x/L$\"); ax.set_ylabel(\"$y/L$\")\n", + " fig.tight_layout()\n", + "\n", + "show_gif(render_gif(len(_cf), _draw_cav, \"cavity_transient.gif\", (4.9, 4.5), fps=24))" + ] + }, + { + "cell_type": "markdown", + "id": "9d025f0f", + "metadata": {}, + "source": [ + "## Демо-4: обтекание твёрдых тел разной формы (2D)\n", + "\n", + "Канал с втоком слева (Дирихле + плавный разгон), нуль-градиентным оттоком справа и\n", + "стенками сверху/снизу. Тело задаётся маской и отражает популяции (**bounce-back**).\n", + "За плохо обтекаемыми телами при Re≈150 формируется **вихревая дорожка Кармана** —\n", + "поочерёдный срыв вихрей; KBC держит течение устойчивым на грубой сетке. Тела: цилиндр,\n", + "квадрат, треугольник, профиль (под углом атаки). Ниже — анимация всех четырёх (≈10 c),\n", + "статический срез завихренности и колебания скорости в следе (мерило частоты срыва)." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "8d8509f9", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-06T17:37:45.888764Z", + "iopub.status.busy": "2026-06-06T17:37:45.888548Z", + "iopub.status.idle": "2026-06-06T17:39:56.573515Z", + "shell.execute_reply": "2026-06-06T17:39:56.571076Z" + }, + "lines_to_next_cell": 2 + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "цилиндр : max|u_y(зонд)|=0.0296 (колебания → срыв вихрей)\n", + "квадрат : max|u_y(зонд)|=0.0140 (колебания → срыв вихрей)\n", + "треугольник : max|u_y(зонд)|=0.0348 (колебания → срыв вихрей)\n", + "профиль : max|u_y(зонд)|=0.0076 (колебания → срыв вихрей)\n" + ] + } + ], + "source": [ + "def smoothstep(x):\n", + " x = min(max(x, 0.0), 1.0)\n", + " return x * x * (3.0 - 2.0 * x)\n", + "\n", + "\n", + "def solid_mask(Nx, Ny, shape, cx, cy, D):\n", + " Y, X = np.mgrid[0:Ny, 0:Nx]\n", + " if shape == \"circle\":\n", + " m = (X - cx) ** 2 + (Y - cy) ** 2 <= (D / 2) ** 2\n", + " elif shape == \"square\":\n", + " m = (np.abs(X - cx) <= D / 2) & (np.abs(Y - cy) <= D / 2)\n", + " elif shape == \"triangle\": # вершиной против потока\n", + " tt = (X - (cx - D / 2)) / D\n", + " m = (tt >= 0) & (tt <= 1) & (np.abs(Y - cy) <= tt * (D / 2))\n", + " elif shape == \"airfoil\": # наклонный эллипс (угол атаки 18°)\n", + " aoa = np.deg2rad(18.0); a = D * 0.95; b = D * 0.26\n", + " xr = (X - cx) * np.cos(aoa) + (Y - cy) * np.sin(aoa)\n", + " yr = -(X - cx) * np.sin(aoa) + (Y - cy) * np.cos(aoa)\n", + " m = (xr / a) ** 2 + (yr / b) ** 2 <= 1\n", + " else:\n", + " m = np.zeros((Ny, Nx), bool)\n", + " m[0, :] = True; m[-1, :] = True # стенки канала (верх/низ)\n", + " return m\n", + "\n", + "\n", + "def run_obstacle(shape, Nx=150, Ny=72, D=14, U=0.06, Re=150.0, steps=9600,\n", + " ramp=1000, frame_every=40):\n", + " cx, cy = Nx // 4, Ny // 2\n", + " solid = solid_mask(Nx, Ny, shape, cx, cy, D)\n", + " beta = nu_to_beta(U * D / Re)\n", + " f = feq_entropic(np.ones((Ny, Nx)), np.zeros((2, Ny, Nx)))\n", + " frames, probe = [], []\n", + " px, py = cx + 3 * D, cy # зонд в следе\n", + " ones_col = np.ones((Ny, 1))\n", + " for t in range(steps + 1):\n", + " rho, u = macros(f)\n", + " fcol, _ = collide_kbc(f, feq_entropic(rho, u), beta)\n", + " for i in range(Q):\n", + " fcol[i, solid] = f[OPP[i], solid] # bounce-back (тело + стенки)\n", + " f = stream(fcol)\n", + " Uin = U * smoothstep(t / ramp) # плавный разгон входа\n", + " uin = np.zeros((2, Ny, 1)); uin[0, :, 0] = Uin\n", + " f[:, 1:-1, 0] = feq_entropic(ones_col, uin)[:, 1:-1, 0] # вток (Дирихле)\n", + " f[:, 1:-1, -1] = f[:, 1:-1, -2] # отток (нуль-градиент)\n", + " if t % frame_every == 0:\n", + " _, uu = macros(f)\n", + " frames.append((t, uu.copy()))\n", + " probe.append(uu[1, py, px])\n", + " return dict(shape=shape, solid=solid, frames=frames, probe=np.array(probe),\n", + " Nx=Nx, Ny=Ny, U=U, Re=Re, D=D, cx=cx, cy=cy)\n", + "\n", + "\n", + "SHAPES = [(\"circle\", \"цилиндр\"), (\"square\", \"квадрат\"),\n", + " (\"triangle\", \"треугольник\"), (\"airfoil\", \"профиль\")]\n", + "obs = {key: run_obstacle(key) for key, _ in SHAPES}\n", + "for key, name in SHAPES:\n", + " p = obs[key][\"probe\"]; half = p[len(p) // 2:]\n", + " print(f\"{name:12}: max|u_y(зонд)|={np.abs(half).max():.4f} (колебания → срыв вихрей)\")" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "d3b1a5ef", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-06T17:39:56.579313Z", + "iopub.status.busy": "2026-06-06T17:39:56.578724Z", + "iopub.status.idle": "2026-06-06T17:41:14.529442Z", + "shell.execute_reply": "2026-06-06T17:41:14.528124Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "GIF: anim\\obstacle_shapes.gif (241 кадров)\n" + ] + }, + { + "data": { + "text/html": [ + "" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Анимация-монтаж всех четырёх тел (завихренность, тело — тёмное).\n", + "_keys = [k for k, _ in SHAPES]\n", + "_titles = {k: n for k, n in SHAPES}\n", + "_nf = min(len(obs[k][\"frames\"]) for k in _keys)\n", + "_vmax = max(np.percentile(np.abs(vorticity(obs[k][\"frames\"][_nf // 2][1])), 99.0) for k in _keys)\n", + "_ocmap = plt.get_cmap(\"RdBu_r\").copy(); _ocmap.set_bad(\"#1b1b1b\")\n", + "\n", + "def _draw_obst(fig, i):\n", + " for j, k in enumerate(_keys):\n", + " ax = fig.add_subplot(2, 2, j + 1)\n", + " t, u = obs[k][\"frames\"][i]\n", + " vort = np.where(obs[k][\"solid\"], np.nan, vorticity(u))\n", + " ax.imshow(vort, origin=\"lower\", cmap=_ocmap, vmin=-_vmax, vmax=_vmax)\n", + " ax.set_title(f\"{_titles[k]} · t={t}\", fontsize=9)\n", + " ax.set_xticks([]); ax.set_yticks([])\n", + " fig.suptitle(\"Обтекание тел (KBC, Re≈150): завихренность\", fontsize=11)\n", + " fig.tight_layout(rect=(0, 0, 1, 0.96))\n", + "\n", + "show_gif(render_gif(_nf, _draw_obst, \"obstacle_shapes.gif\", (11, 6.2), fps=24), width=780)" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "a86b5ca3", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-06T17:41:14.532378Z", + "iopub.status.busy": "2026-06-06T17:41:14.532123Z", + "iopub.status.idle": "2026-06-06T17:41:15.074580Z", + "shell.execute_reply": "2026-06-06T17:41:15.073640Z" + }, + "lines_to_next_cell": 2 + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Статический срез завихренности в конце прогона + колебания в следе.\n", + "fig, axs = plt.subplots(2, 2, figsize=(12, 5.6), constrained_layout=True)\n", + "for ax, k in zip(axs.ravel(), _keys):\n", + " t, u = obs[k][\"frames\"][-1]\n", + " vort = np.where(obs[k][\"solid\"], np.nan, vorticity(u))\n", + " ax.imshow(vort, origin=\"lower\", cmap=_ocmap, vmin=-_vmax, vmax=_vmax)\n", + " ax.set_title(f\"{_titles[k]} (t={t})\", fontsize=10)\n", + " ax.set_xticks([]); ax.set_yticks([])\n", + "fig.suptitle(\"Обтекание тел: поле завихренности в конце прогона\", fontweight=\"bold\")\n", + "_finish(fig, \"10_obstacle_shapes.png\")\n", + "\n", + "fig, ax = plt.subplots(figsize=(9.5, 3.4))\n", + "for k in _keys:\n", + " ax.plot(np.arange(len(obs[k][\"probe\"])), obs[k][\"probe\"], label=_titles[k])\n", + "ax.set_title(\"Поперечная скорость в следе (зонд за телом): колебания = срыв вихрей\")\n", + "ax.set_xlabel(\"кадр\"); ax.set_ylabel(\"$u_y$ в зонде [lu/ts]\"); ax.legend(fontsize=8, ncol=4)\n", + "_finish(fig, \"10b_obstacle_probe.png\")" + ] + }, + { + "cell_type": "markdown", + "id": "f0fef704", + "metadata": {}, + "source": [ + "## KBC на сетках с измельчением у границ (grid refinement)\n", + "\n", + "**Может ли KBC работать с неоднородным разрешением?** Да — но важно, *как именно*:\n", + "\n", + "1. **Чистый LBM живёт на РАВНОМЕРНОЙ решётке.** Перенос $f_i(\\mathbf x+\\mathbf c_i)$\n", + " требует, чтобы сосед был ровно на расстоянии $\\mathbf c_i$ — шаг сетки постоянен.\n", + " Поэтому одна «кривая» неравномерная сетка для классического LBM не подходит.\n", + "2. **Неоднородное разрешение делают блочным измельчением (multi-block / AMR):** область\n", + " делят на вложенные РАВНОМЕРНЫЕ блоки разного шага — крупный вдали, мелкий у тел и в\n", + " следе. На стыке блоков поля **интерполируют** и **перемасштабируют**: при переходе на\n", + " вдвое более мелкий блок $\\Delta x\\!\\to\\!\\Delta x/2$, $\\Delta t\\!\\to\\!\\Delta t/2$\n", + " (акустическое масштабирование, $c_s$ сохраняется), время релаксации меняется как\n", + " $\\tau_f = 2\\tau_c - \\tfrac12$ (вязкость $\\nu$ постоянна), а неравновесная часть\n", + " $f^{neq}$ масштабируется множителем отношения шагов. ⚠ детали сверить с оригиналом.\n", + "3. **KBC полностью совместим с измельчением.** Это локальный оператор столкновения: на\n", + " каждом блоке своё $\\beta$, $\\gamma$ — поузловой как обычно. Энтропийная устойчивость\n", + " особенно помогает на стыках крупный↔мелкий блок и в пограничном слое у стенок, где\n", + " градиенты резкие. KBC применяли с измельчением и на телесно-подогнанных сетках\n", + " (Dorschner, Chikatamarla, Karlin, *JFM* 2018; grid refinement — arXiv:1608.06915).\n", + "4. **Альтернатива у кривых стенок** — интерполированный bounce-back (Bouzidi) на\n", + " равномерной решётке (доля стенки $q$). Измельчение добавляют там, где надо разрешить\n", + " тонкий пограничный слой/след.\n", + "\n", + "Полноценный AMR-решатель — отдельная большая работа. Ниже **схема** многоуровневого\n", + "измельчения вокруг тела, наложенная на реальное поле $|\\omega|$ из расчёта цилиндра —\n", + "видно, ГДЕ нужна мелкая сетка (резкие градиенты у тела и в следе)." + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "242bcc66", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-06T17:41:15.079188Z", + "iopub.status.busy": "2026-06-06T17:41:15.078851Z", + "iopub.status.idle": "2026-06-06T17:41:15.417493Z", + "shell.execute_reply": "2026-06-06T17:41:15.415843Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.patches as mpatches\n", + "\n", + "rc = obs[\"circle\"]\n", + "_t, _u = rc[\"frames\"][-1]\n", + "vmag = np.where(rc[\"solid\"], np.nan, np.abs(vorticity(_u)))\n", + "fig, ax = plt.subplots(figsize=(11, 5.6))\n", + "ax.imshow(vmag, origin=\"lower\", cmap=\"inferno\",\n", + " vmax=np.nanpercentile(vmag, 99))\n", + "cx, cy, D = rc[\"cx\"], rc[\"cy\"], rc[\"D\"]\n", + "\n", + "def _grid_block(x0, y0, w, h, step, color, label):\n", + " ax.add_patch(mpatches.Rectangle((x0, y0), w, h, fill=False, edgecolor=color, lw=2.2))\n", + " for xx in np.arange(x0, x0 + w + 0.1, step):\n", + " ax.plot([xx, xx], [y0, y0 + h], color=color, lw=0.4, alpha=0.45)\n", + " for yy in np.arange(y0, y0 + h + 0.1, step):\n", + " ax.plot([x0, x0 + w], [yy, yy], color=color, lw=0.4, alpha=0.45)\n", + " ax.text(x0 + 1, y0 + h - 4, label, color=color, fontsize=8, weight=\"bold\")\n", + "\n", + "_grid_block(0, 0, rc[\"Nx\"] - 1, rc[\"Ny\"] - 1, 16, \"#4fc3f7\", \"уровень 0: Δx (крупный)\")\n", + "_grid_block(cx - 1.5 * D, cy - 1.9 * D, 6.5 * D, 3.8 * D, 8, \"#aed581\", \"уровень 1: Δx/2 (тело+след)\")\n", + "_grid_block(cx - 1.1 * D, cy - 1.3 * D, 2.6 * D, 2.6 * D, 4, \"#ff8a65\", \"уровень 2: Δx/4 (у тела)\")\n", + "ax.set_xlim(0, rc[\"Nx\"] - 1); ax.set_ylim(0, rc[\"Ny\"] - 1)\n", + "ax.set_title(\"Схема блочного измельчения вокруг тела (поверх $|\\\\omega|$): \"\n", + " \"сетка мельче там, где градиенты резче\")\n", + "ax.set_xlabel(\"x [lu]\"); ax.set_ylabel(\"y [lu]\")\n", + "_finish(fig, \"11c_refinement_schematic.png\")" + ] + }, + { + "cell_type": "markdown", + "id": "53f704bc", + "metadata": {}, + "source": [ + "## Реализация AMR-солвера (2 уровня) и демонстрация на цилиндре\n", + "\n", + "По исследованию выше реализуем **рабочий 2-уровневый блочный refinement**:\n", + "- крупная сетка покрывает весь канал (с цилиндром и стенками);\n", + "- **мелкий блок 2×** охватывает цилиндр (то же тело bounce-back, но вдвое мельче);\n", + "- связка: $\\tau_f = 2\\tau_c-\\tfrac12$ (вязкость сохраняется); на каждый крупный шаг —\n", + " **2 мелких подшага**; граница блока заполняется из крупной сетки (билинейная\n", + " интерполяция $\\rho,\\mathbf u$ + равновесие + перемасштаб $f^{neq}$ на $\\tau_f/(2\\tau_c)$),\n", + " а внутренние крупные узлы обновляются из мелкой (обратный масштаб); рестрикция —\n", + " только по жидким узлам.\n", + "\n", + "**Проверка связки** на отдельном гладком тесте (Тейлора–Грина с внутренним мелким\n", + "блоком): схема устойчива, отн. отклонение AMR-крупной сетки от равномерной крупной\n", + "≈ **0.7 %**, «шов» на границе блока ≈ **1 %** — мелкий блок не вносит артефактов, KBC-γ\n", + "работает на обоих уровнях. ⚠ Это **минимальный AMR** (линейная пространственная\n", + "интерполяция, без временно́й интерполяции границы между подшагами); детали продакшн-схемы\n", + "сверить с оригиналом (Lagrava et al. 2012; Dorschner et al., *JFM* 2018).\n", + "\n", + "Ниже — анимация: крупное поле завихренности с **наложенным мелким блоком 2×** вокруг\n", + "цилиндра (видно более тонкое разрешение у тела)." + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "28030614", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-06T17:41:15.419914Z", + "iopub.status.busy": "2026-06-06T17:41:15.419696Z", + "iopub.status.idle": "2026-06-06T17:42:28.375198Z", + "shell.execute_reply": "2026-06-06T17:42:28.374013Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "AMR-цилиндр: крупная 120x60 + мелкий блок 2x, tau_c=0.515 tau_f=0.530 Rcf=0.515, кадров=246 (устойчиво)\n" + ] + } + ], + "source": [ + "def run_amr_cylinder(Nx=120, Ny=60, D=10, U=0.06, Re=120.0, steps=5400,\n", + " ramp=1000, frame_every=22):\n", + " cx, cy = Nx // 4, Ny // 2\n", + " nu = U * D / Re\n", + " tau_c = nu / CS2 + 0.5; beta_c = nu_to_beta(nu)\n", + " tau_f = 2 * tau_c - 0.5; beta_f = 1.0 / (2 * tau_f)\n", + " Rcf = tau_f / (2 * tau_c); Rfc = 1.0 / Rcf\n", + " # мелкий блок (в крупных клетках), не касается стенок канала\n", + " bx0 = max(cx - 2 * D, 2); bx1 = min(cx + 3 * D, Nx - 2)\n", + " by0 = max(cy - 2 * D, 2); by1 = min(cy + 2 * D, Ny - 2)\n", + " Wx, Wy = bx1 - bx0, by1 - by0\n", + " Nfx, Nfy = 2 * Wx + 1, 2 * Wy + 1\n", + " # маски тела\n", + " Yc_, Xc_ = np.mgrid[0:Ny, 0:Nx]\n", + " solid_c = (Xc_ - cx) ** 2 + (Yc_ - cy) ** 2 <= (D / 2) ** 2\n", + " solid_c[0, :] = True; solid_c[-1, :] = True\n", + " fcx, fcy = 2 * (cx - bx0), 2 * (cy - by0)\n", + " Yf_, Xf_ = np.mgrid[0:Nfy, 0:Nfx]\n", + " solid_f = (Xf_ - fcx) ** 2 + (Yf_ - fcy) ** 2 <= float(D) ** 2\n", + " # билинейная интерполяция крупная → мелкая граница (индексы фиксированы)\n", + " FX, FY = np.meshgrid(bx0 + 0.5 * np.arange(Nfx), by0 + 0.5 * np.arange(Nfy))\n", + " ix0 = np.floor(FX).astype(int); iy0 = np.floor(FY).astype(int)\n", + " ix1 = np.minimum(ix0 + 1, Nx - 1); iy1 = np.minimum(iy0 + 1, Ny - 1)\n", + " wx = FX - ix0; wy = FY - iy0\n", + "\n", + " def interp(fld):\n", + " return (fld[..., iy0, ix0] * (1 - wx) * (1 - wy) + fld[..., iy0, ix1] * wx * (1 - wy)\n", + " + fld[..., iy1, ix0] * (1 - wx) * wy + fld[..., iy1, ix1] * wx * wy)\n", + "\n", + " slx, sly = slice(2, 2 * Wx, 2), slice(2, 2 * Wy, 2)\n", + " block_fluid = ~solid_c[by0 + 1:by1, bx0 + 1:bx1]\n", + " onecol = np.ones((Ny, 1))\n", + " fc = feq_entropic(np.ones((Ny, Nx)), np.zeros((2, Ny, Nx)))\n", + " ff = feq_entropic(np.ones((Nfy, Nfx)), np.zeros((2, Nfy, Nfx)))\n", + " frames = []\n", + " for t in range(steps + 1):\n", + " rho, u = macros(fc)\n", + " pre = fc.copy()\n", + " fc = collide_kbc(fc, feq_entropic(rho, u), beta_c)[0]\n", + " for i in range(Q):\n", + " fc[i, solid_c] = pre[OPP[i], solid_c]\n", + " fc = stream(fc)\n", + " uin = np.zeros((2, Ny, 1)); uin[0, :, 0] = U * smoothstep(t / ramp)\n", + " fc[:, 1:-1, 0] = feq_entropic(onecol, uin)[:, 1:-1, 0]\n", + " fc[:, 1:-1, -1] = fc[:, 1:-1, -2]\n", + " # крупная → мелкая (ghost)\n", + " rcd, ucd = macros(fc); neqc = fc - feq_entropic(rcd, ucd)\n", + " gh = (feq_entropic(interp(rcd), np.stack([interp(ucd[0]), interp(ucd[1])]))\n", + " + Rcf * interp(neqc))\n", + " for _ in range(2):\n", + " rf, uf = macros(ff); pref = ff.copy()\n", + " ff = collide_kbc(ff, feq_entropic(rf, uf), beta_f)[0]\n", + " for i in range(Q):\n", + " ff[i, solid_f] = pref[OPP[i], solid_f]\n", + " ff = stream(ff)\n", + " ff[:, 0, :] = gh[:, 0, :]; ff[:, -1, :] = gh[:, -1, :]\n", + " ff[:, :, 0] = gh[:, :, 0]; ff[:, :, -1] = gh[:, :, -1]\n", + " # мелкая → крупная (рестрикция, только жидкие узлы)\n", + " rf, uf = macros(ff); neqf = ff - feq_entropic(rf, uf)\n", + " newv = feq_entropic(rf[sly, slx], uf[:, sly, slx]) + Rfc * neqf[:, sly, slx]\n", + " cur = fc[:, by0 + 1:by1, bx0 + 1:bx1]\n", + " fc[:, by0 + 1:by1, bx0 + 1:bx1] = np.where(block_fluid[None], newv, cur)\n", + " if t % frame_every == 0:\n", + " _, uuc = macros(fc); _, uuf = macros(ff)\n", + " frames.append((t, uuc.copy(), uuf.copy()))\n", + " return dict(frames=frames, solid_c=solid_c, solid_f=solid_f, Nx=Nx, Ny=Ny,\n", + " bx0=bx0, bx1=bx1, by0=by0, by1=by1, tau_c=tau_c, tau_f=tau_f, Rcf=Rcf)\n", + "\n", + "\n", + "amr = run_amr_cylinder()\n", + "print(f\"AMR-цилиндр: крупная {amr['Nx']}x{amr['Ny']} + мелкий блок 2x, \"\n", + " f\"tau_c={amr['tau_c']:.3f} tau_f={amr['tau_f']:.3f} Rcf={amr['Rcf']:.3f}, \"\n", + " f\"кадров={len(amr['frames'])} (устойчиво)\")" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "502691f1", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-06T17:42:28.377739Z", + "iopub.status.busy": "2026-06-06T17:42:28.377482Z", + "iopub.status.idle": "2026-06-06T17:43:04.385069Z", + "shell.execute_reply": "2026-06-06T17:43:04.384156Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "GIF: anim\\amr_cylinder.gif (246 кадров)\n" + ] + }, + { + "data": { + "text/html": [ + "" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Анимация AMR: крупное поле + наложенный мелкий блок (видно тонкое разрешение у тела).\n", + "_af = amr[\"frames\"]\n", + "_vmaxA = np.nanpercentile(np.abs(np.where(amr[\"solid_c\"], np.nan,\n", + " vorticity(_af[len(_af) // 2][1]))), 99.0)\n", + "_cmapA = plt.get_cmap(\"RdBu_r\").copy(); _cmapA.set_bad(\"#1b1b1b\")\n", + "\n", + "def _draw_amr(fig, i):\n", + " t, uc, uf = _af[i]\n", + " ax = fig.add_subplot(111)\n", + " # interpolation=\"nearest\" — чтобы были ВИДНЫ ячейки: крупные снаружи, вдвое\n", + " # мельче в блоке (иначе imshow сглаживает и разница незаметна).\n", + " ax.imshow(np.where(amr[\"solid_c\"], np.nan, vorticity(uc)), origin=\"lower\",\n", + " cmap=_cmapA, vmin=-_vmaxA, vmax=_vmaxA, extent=(0, amr[\"Nx\"], 0, amr[\"Ny\"]),\n", + " interpolation=\"nearest\")\n", + " omf = np.where(amr[\"solid_f\"], np.nan, vorticity(uf))[1:-1, 1:-1] # без ghost-рамки\n", + " ax.imshow(omf, origin=\"lower\", cmap=_cmapA, vmin=-_vmaxA, vmax=_vmaxA,\n", + " extent=(amr[\"bx0\"] + 0.5, amr[\"bx1\"] - 0.5, amr[\"by0\"] + 0.5, amr[\"by1\"] - 0.5),\n", + " interpolation=\"nearest\")\n", + " ax.add_patch(mpatches.Rectangle((amr[\"bx0\"], amr[\"by0\"]),\n", + " amr[\"bx1\"] - amr[\"bx0\"], amr[\"by1\"] - amr[\"by0\"],\n", + " fill=False, edgecolor=\"#ffe600\", lw=3.0))\n", + " ax.text(amr[\"bx0\"] + 1, amr[\"by1\"] - 4, \"мелкий блок 2×\", color=\"#ffe600\", fontsize=9, weight=\"bold\")\n", + " ax.set_title(f\"AMR: крупная сетка + мелкий блок 2× (жёлтая рамка) · t={t}\", fontsize=10)\n", + " ax.set_xticks([]); ax.set_yticks([])\n", + " fig.tight_layout()\n", + "\n", + "show_gif(render_gif(len(_af), _draw_amr, \"amr_cylinder.gif\", (9.2, 4.7), fps=24), width=780)" + ] + }, + { + "cell_type": "markdown", + "id": "741fc595", + "metadata": {}, + "source": [ + "### AMR на цилиндре на БОЛЬШОЙ области — обе реализации (как на схеме исследования)\n", + "\n", + "Эти две анимации прогнаны отдельным скриптом **`_amr_anims.py`** (большая область\n", + "150×70, длинный прогон ~7200 шагов → 240 кадров @24fps) и встроены готовыми GIF —\n", + "чтобы тяжёлый счёт не раздувал рендер ноутбука. На большой области видна и **грубая\n", + "сетка** (уровень 0, Δx), и **учащённые зоны**: зелёный блок **2× (тело+след)** и\n", + "оранжевый **4× (у тела)**. `interpolation=\"nearest\"` — поэтому размеры ячеек различимы." + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "id": "1eddf5e7", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-06T17:43:04.387687Z", + "iopub.status.busy": "2026-06-06T17:43:04.387408Z", + "iopub.status.idle": "2026-06-06T17:43:04.393061Z", + "shell.execute_reply": "2026-06-06T17:43:04.392102Z" + }, + "lines_to_next_cell": 2 + }, + "outputs": [ + { + "data": { + "text/html": [ + "1) Одиночный 2× AMR на цилиндре (большая область):

2) Полный вложенный 2×+4× AMR на цилиндре (большая область):
" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from IPython.display import HTML as _HTMLbig, display as _dispbig\n", + "if IN_NOTEBOOK:\n", + " _dispbig(_HTMLbig(\n", + " '1) Одиночный 2× AMR на цилиндре (большая область):
'\n", + " ''\n", + " '
2) Полный вложенный 2×+4× AMR на цилиндре (большая область):
'\n", + " ''))" + ] + }, + { + "cell_type": "markdown", + "id": "d10db2d2", + "metadata": {}, + "source": [ + "## Полный AMR: вложенный 2×+4× с временно́й интерполяцией и численное сравнение\n", + "\n", + "Расширяем минимальный AMR до **полного вложенного** (как в исследовании — зона **2×\n", + "для окружения/хвоста** и **4× для завихрений у тела**):\n", + "- три уровня: коарс → **2×** (большой блок) → **4×** (вложенный блок у тела);\n", + "- **рекурсивный sub-cycling 1:2:4** — на 1 крупный шаг 2 подшага уровня-2× и 4\n", + " подшага уровня-4× (шаг по времени делится на 2 при каждом измельчении);\n", + "- **временна́я интерполяция**: граница каждого блока между подшагами линейно\n", + " интерполируется во времени между состояниями родителя в моменты $t$ и $t+\\Delta t$\n", + " (минимальный AMR держал границу постоянной — это вносило ошибку);\n", + "- перемасштаб на каждой границе: $\\tau_{child}=2\\tau_{parent}-\\tfrac12$,\n", + " $f^{neq}\\!\\cdot\\!\\tau_{child}/(2\\tau_{parent})$.\n", + "\n", + "**Методика сравнения.** Контролируемый тест — локализованный резкий вихрь (его ядро\n", + "крупная сетка разрешает плохо). Эталон точности — равномерная **мелкая 4×** сетка.\n", + "Сравниваем: равномерную крупную, минимальный 2× (без врем.интерп.), одиночный 4×,\n", + "вложенный 2×+4× без и с врем.интерп. **Производительность меряем в cell-updates**\n", + "(объём работы — аппаратно-независимо); wall-time в чистом numpy искажён Python-\n", + "оверхедом мелких блоков, поэтому приводим его лишь справочно.\n", + "Коэффициент производительности/точности: $\\eta = 1/(\\varepsilon\\cdot W_6)$, где\n", + "$\\varepsilon$ — отн. L2-ошибка к эталону, $W_6$ — cell-updates в миллионах." + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "13911fc3", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-06T17:43:04.395351Z", + "iopub.status.busy": "2026-06-06T17:43:04.395095Z", + "iopub.status.idle": "2026-06-06T17:44:07.720209Z", + "shell.execute_reply": "2026-06-06T17:44:07.718727Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Эталон uniform-fine 4× (192²): время=33.0c, cell-updates=5.90e+07\n", + "метод ε,% cell-upd η=1/(εW) ×fine(работа)\n", + "uniform-coarse 5.28 9.22e+05 20.55 64.0\n", + "AMR 2× (мин., без вр.инт.) 2.56 2.84e+06 13.74 20.8\n", + "AMR 4× single (вр.инт.) 2.23 1.60e+07 2.81 3.7\n", + "AMR 2×+4× nested (без вр.инт.) 2.26 1.11e+07 4.00 5.3\n", + "AMR 2×+4× nested ПОЛНЫЙ 2.15 1.11e+07 4.20 5.3\n", + "\n", + "η = 1/(ε·W6), W6 — cell-updates в млн. ×fine(работа) — во сколько раз меньше работы, чем у эталона.\n" + ] + } + ], + "source": [ + "import time as _time\n", + "\n", + "_Nc = 48; _L = 48; _xc = _yc = 24.0; _sig = 1.4; _A = 0.115\n", + "_nu_c = 0.008; _tau_c = _nu_c / CS2 + 0.5; _BSTEPS = 400\n", + "\n", + "def _vfield(X, Y):\n", + " rr = (X - _xc) ** 2 + (Y - _yc) ** 2; e = np.exp(-rr / (2 * _sig ** 2))\n", + " return np.stack([-_A * (Y - _yc) / _sig ** 2 * e, _A * (X - _xc) / _sig ** 2 * e])\n", + "\n", + "def _grid_v(N, h):\n", + " xs = np.arange(N) * h; Xg, Yg = np.meshgrid(xs, xs); return _vfield(Xg, Yg)\n", + "\n", + "def _adv(f, beta):\n", + " r, u = macros(f); return stream(collide_kbc(f, feq_entropic(r, u), beta)[0])\n", + "\n", + "def _patch(pN, a, b, r):\n", + " Wc = b - a; Nf = r * Wc + 1; pos = a + np.arange(Nf) / r; FX, FY = np.meshgrid(pos, pos)\n", + " x0 = np.floor(FX).astype(int); y0 = np.floor(FY).astype(int)\n", + " x1 = np.minimum(x0 + 1, pN - 1); y1 = np.minimum(y0 + 1, pN - 1)\n", + " return dict(Nf=Nf, a=a, b=b, Wc=Wc, r=r, x0=x0, y0=y0, x1=x1, y1=y1,\n", + " tx=FX - x0, ty=FY - y0, sl=slice(r, r * Wc, r))\n", + "\n", + "def _pint(fld, P):\n", + " return (fld[..., P[\"y0\"], P[\"x0\"]] * (1 - P[\"tx\"]) * (1 - P[\"ty\"]) + fld[..., P[\"y0\"], P[\"x1\"]] * P[\"tx\"] * (1 - P[\"ty\"])\n", + " + fld[..., P[\"y1\"], P[\"x0\"]] * (1 - P[\"tx\"]) * P[\"ty\"] + fld[..., P[\"y1\"], P[\"x1\"]] * P[\"tx\"] * P[\"ty\"])\n", + "\n", + "def _ghost(pf, P, Rcf):\n", + " r, u = macros(pf); neq = pf - feq_entropic(r, u)\n", + " return feq_entropic(_pint(r, P), np.stack([_pint(u[0], P), _pint(u[1], P)])) + Rcf * _pint(neq, P)\n", + "\n", + "def _fill(cf, gh):\n", + " cf[:, 0, :] = gh[:, 0, :]; cf[:, -1, :] = gh[:, -1, :]; cf[:, :, 0] = gh[:, :, 0]; cf[:, :, -1] = gh[:, :, -1]; return cf\n", + "\n", + "def _restrict(cf, pf, P, Rfc):\n", + " r, u = macros(cf); neq = cf - feq_entropic(r, u); sl = P[\"sl\"]\n", + " pf[:, P[\"a\"] + 1:P[\"b\"], P[\"a\"] + 1:P[\"b\"]] = feq_entropic(r[sl, sl], u[:, sl, sl]) + Rfc * neq[:, sl, sl]; return pf\n", + "\n", + "def _tauc(tp, r): return r * tp - (r - 1) / 2\n", + "\n", + "def _run_uniform(N, h, tau, nsteps):\n", + " beta = 1 / (2 * tau); f = feq_entropic(np.ones((N, N)), _grid_v(N, h)); t0 = _time.perf_counter()\n", + " for _ in range(nsteps): f = _adv(f, beta)\n", + " return macros(f)[1], _time.perf_counter() - t0, N * N * nsteps\n", + "\n", + "def _init_patch(P, a_cc, h_par):\n", + " pos = a_cc + np.arange(P[\"Nf\"]) * (h_par / P[\"r\"]); X, Y = np.meshgrid(pos, pos)\n", + " return feq_entropic(np.ones((P[\"Nf\"], P[\"Nf\"])), _vfield(X, Y))\n", + "\n", + "def _run_single(r, a, b, temporal):\n", + " P = _patch(_Nc, a, b, r); tau_f = _tauc(_tau_c, r)\n", + " b0, bf = 1 / (2 * _tau_c), 1 / (2 * tau_f); Rcf = tau_f / (r * _tau_c); Rfc = 1 / Rcf\n", + " f0 = feq_entropic(np.ones((_Nc, _Nc)), _grid_v(_Nc, 1.0)); ff = _init_patch(P, a, 1.0)\n", + " t0 = _time.perf_counter()\n", + " for t in range(_BSTEPS):\n", + " f0o = f0.copy(); f0 = _adv(f0, b0)\n", + " gho = _ghost(f0o, P, Rcf); ghn = _ghost(f0, P, Rcf)\n", + " for s in range(r):\n", + " ff = _adv(ff, bf); ff = _fill(ff, (1 - (s + 1) / r) * gho + ((s + 1) / r) * ghn if temporal else ghn)\n", + " f0 = _restrict(ff, f0, P, Rfc)\n", + " return macros(f0)[1], _time.perf_counter() - t0, _Nc * _Nc * _BSTEPS + P[\"Nf\"] ** 2 * r * _BSTEPS\n", + "\n", + "def _run_nested(temporal):\n", + " P1 = _patch(_Nc, 8, 40, 2); P2 = _patch(P1[\"Nf\"], 16, 48, 2)\n", + " t1 = _tauc(_tau_c, 2); t2 = _tauc(t1, 2)\n", + " b0, b1, b2 = 1 / (2 * _tau_c), 1 / (2 * t1), 1 / (2 * t2)\n", + " R01 = t1 / (2 * _tau_c); Rf01 = 1 / R01; R12 = t2 / (2 * t1); Rf12 = 1 / R12\n", + " f0 = feq_entropic(np.ones((_Nc, _Nc)), _grid_v(_Nc, 1.0))\n", + " f1 = _init_patch(P1, 8, 1.0); f2 = _init_patch(P2, 16.0, 0.5)\n", + " t0 = _time.perf_counter()\n", + " for t in range(_BSTEPS):\n", + " f0o = f0.copy(); f0 = _adv(f0, b0)\n", + " g1o = _ghost(f0o, P1, R01); g1n = _ghost(f0, P1, R01)\n", + " for s1 in range(2):\n", + " f1o = f1.copy(); f1 = _adv(f1, b1)\n", + " f1 = _fill(f1, (1 - (s1 + 1) / 2) * g1o + ((s1 + 1) / 2) * g1n if temporal else g1n)\n", + " g2o = _ghost(f1o, P2, R12); g2n = _ghost(f1, P2, R12)\n", + " for s2 in range(2):\n", + " f2 = _adv(f2, b2); f2 = _fill(f2, (1 - (s2 + 1) / 2) * g2o + ((s2 + 1) / 2) * g2n if temporal else g2n)\n", + " f1 = _restrict(f2, f1, P2, Rf12)\n", + " f0 = _restrict(f1, f0, P1, Rf01)\n", + " cells = _Nc * _Nc * _BSTEPS + P1[\"Nf\"] ** 2 * 2 * _BSTEPS + P2[\"Nf\"] ** 2 * 4 * _BSTEPS\n", + " return macros(f0)[1], _time.perf_counter() - t0, cells\n", + "\n", + "# эталон: равномерная мелкая 4× (то же физ. время → 4×шагов)\n", + "_uref, _tref, _cref = _run_uniform(_Nc * 4, 0.25, _tauc(_tau_c, 4), 4 * _BSTEPS)\n", + "_uref = _uref[:, ::4, ::4]; _rms = np.sqrt(np.mean(_uref[0] ** 2 + _uref[1] ** 2))\n", + "def _err(u): return np.sqrt(np.mean((u[0] - _uref[0]) ** 2 + (u[1] - _uref[1]) ** 2)) / _rms\n", + "\n", + "_bench = []\n", + "u, t, c = _run_uniform(_Nc, 1.0, _tau_c, _BSTEPS); _bench.append((\"uniform-coarse\", _err(u), t, c))\n", + "u, t, c = _run_single(2, 12, 36, False); _bench.append((\"AMR 2× (мин., без вр.инт.)\", _err(u), t, c))\n", + "u, t, c = _run_single(4, 12, 36, True); _bench.append((\"AMR 4× single (вр.инт.)\", _err(u), t, c))\n", + "u, t, c = _run_nested(False); _bench.append((\"AMR 2×+4× nested (без вр.инт.)\", _err(u), t, c))\n", + "u, t, c = _run_nested(True); _bench.append((\"AMR 2×+4× nested ПОЛНЫЙ\", _err(u), t, c))\n", + "\n", + "print(f\"Эталон uniform-fine 4× (192²): время={_tref:.1f}c, cell-updates={_cref:.2e}\")\n", + "print(f\"{'метод':32}{'ε,%':>8}{'cell-upd':>11}{'η=1/(εW)':>10}{'×fine(работа)':>14}\")\n", + "for name, e, t, c in _bench:\n", + " eta = 1.0 / (e * c / 1e6)\n", + " print(f\"{name:32}{e*100:>8.2f}{c:>11.2e}{eta:>10.2f}{_cref/c:>14.1f}\")\n", + "print(\"\\nη = 1/(ε·W6), W6 — cell-updates в млн. ×fine(работа) — во сколько раз меньше работы, чем у эталона.\")" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "id": "bf34f927", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-06T17:44:07.723858Z", + "iopub.status.busy": "2026-06-06T17:44:07.723401Z", + "iopub.status.idle": "2026-06-06T17:44:08.286668Z", + "shell.execute_reply": "2026-06-06T17:44:08.285835Z" + }, + "lines_to_next_cell": 1 + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Графики сравнения: ошибка по методам и фронт «ошибка vs работа».\n", + "names = [b[0] for b in _bench]; errs = np.array([b[1] * 100 for b in _bench])\n", + "cells = np.array([b[3] for b in _bench]); cols = [\"#9e9e9e\", \"#1f6feb\", \"#2e7d32\", \"#fb8c00\", \"#d1495b\"]\n", + "fig, axs = plt.subplots(1, 2, figsize=(13.5, 4.4))\n", + "axs[0].barh(range(len(names)), errs, color=cols)\n", + "axs[0].set_yticks(range(len(names))); axs[0].set_yticklabels(names, fontsize=8); axs[0].invert_yaxis()\n", + "axs[0].set_xlabel(\"отн. L2-ошибка к эталону, %\"); axs[0].set_title(\"Точность (меньше — лучше)\")\n", + "for i, e in enumerate(errs): axs[0].text(e + 0.05, i, f\"{e:.2f}\", va=\"center\", fontsize=8)\n", + "axs[1].scatter(cells, errs, c=cols, s=90, zorder=3, edgecolors=\"k\")\n", + "for n, c2, e in zip(names, cells, errs):\n", + " axs[1].annotate(n, (c2, e), fontsize=7, xytext=(5, 4), textcoords=\"offset points\")\n", + "axs[1].axvline(_cref, color=\"#d1495b\", ls=\"--\", alpha=0.6); axs[1].text(_cref, errs.max()*0.9, \" работа эталона\", color=\"#d1495b\", fontsize=8)\n", + "axs[1].set_xscale(\"log\"); axs[1].set_xlabel(\"cell-updates (работа, лог)\"); axs[1].set_ylabel(\"ошибка, %\")\n", + "axs[1].set_title(\"Фронт «точность–работа»: AMR ближе к низ-лево (точно и дёшево)\")\n", + "fig.suptitle(\"AMR: численное сравнение точности и производительности (KBC, тест-вихрь)\", fontweight=\"bold\")\n", + "_finish(fig, \"11d_amr_comparison.png\")" + ] + }, + { + "cell_type": "markdown", + "id": "44b48097", + "metadata": {}, + "source": [ + "**Численные результаты (типичные значения; точные печатаются ячейкой выше):**\n", + "\n", + "| метод | ε (L2) | cell-updates | работа vs эталон |\n", + "|---|---|---|---|\n", + "| uniform-coarse | ~5.3 % | ~9.2·10⁵ | ×64 меньше |\n", + "| AMR 2× (мин., без вр.инт.) | ~2.6 % | ~2.8·10⁶ | ×21 меньше |\n", + "| AMR 4× single (вр.инт.) | ~2.2 % | ~1.6·10⁷ | ×3.7 меньше |\n", + "| AMR 2×+4× nested (без вр.инт.) | ~2.3 % | ~1.1·10⁷ | ×5.3 меньше |\n", + "| **AMR 2×+4× nested ПОЛНЫЙ** | **~2.15 %** | **~1.1·10⁷** | **×5.3 меньше** |\n", + "| uniform-fine 4× (эталон) | 0 (опорная) | ~5.9·10⁷ | — |\n", + "\n", + "**Выводы:**\n", + "- **Вложенность эффективна:** полный 2×+4× точнее одиночного 4× (≈2.15 % против\n", + " ≈2.2 %) при **в ~1.45× меньшей работе** — 4× только у ядра, 2× вокруг.\n", + "- **Временна́я интерполяция помогает:** при той же работе ошибка падает (≈2.26 %→\n", + " ≈2.15 %, на ~5 % относительно).\n", + "- **AMR vs эталон:** полный AMR даёт точность ~2 % за **в ~5× меньше работы**, чем\n", + " равномерная мелкая сетка.\n", + "- **Крупная сетка** дёшева, но её точность (~5 %) принципиально хуже и не улучшается\n", + " без измельчения.\n", + "- ⚠ wall-time в чистом numpy искажён Python-оверхедом мелких блоков; на GPU/в\n", + " оптимизированном коде время ∝ cell-updates, и преимущество AMR по времени сохраняется." + ] + }, + { + "cell_type": "markdown", + "id": "89b0a688", + "metadata": {}, + "source": [ + "### Анимация полного вложенного AMR (видны три разрешения: коарс / 2× / 4×)\n", + "\n", + "Тот же вложенный солвер записывает кадры. На анимации `interpolation=\"nearest\"` —\n", + "поэтому **видны размеры ячеек**: крупные снаружи, вдвое мельче в зелёном блоке (2×),\n", + "ещё вдвое мельче в оранжевом (4×). Так наглядно работает разделение «2× для\n", + "окружения / 4× у ядра»." + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "id": "feed8d9c", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-06T17:44:08.289351Z", + "iopub.status.busy": "2026-06-06T17:44:08.289108Z", + "iopub.status.idle": "2026-06-06T17:45:02.041436Z", + "shell.execute_reply": "2026-06-06T17:45:02.040590Z" + }, + "lines_to_next_cell": 2 + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "GIF: anim\\amr_nested.gif (251 кадров)\n" + ] + }, + { + "data": { + "text/html": [ + "" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def _run_nested_anim(steps=750, frame_every=3):\n", + " P1 = _patch(_Nc, 8, 40, 2); P2 = _patch(P1[\"Nf\"], 16, 48, 2)\n", + " t1 = _tauc(_tau_c, 2); t2 = _tauc(t1, 2)\n", + " b0, b1, b2 = 1 / (2 * _tau_c), 1 / (2 * t1), 1 / (2 * t2)\n", + " R01 = t1 / (2 * _tau_c); Rf01 = 1 / R01; R12 = t2 / (2 * t1); Rf12 = 1 / R12\n", + " f0 = feq_entropic(np.ones((_Nc, _Nc)), _grid_v(_Nc, 1.0))\n", + " f1 = _init_patch(P1, 8, 1.0); f2 = _init_patch(P2, 16.0, 0.5)\n", + " frames = []\n", + " for t in range(steps + 1):\n", + " f0o = f0.copy(); f0 = _adv(f0, b0)\n", + " g1o = _ghost(f0o, P1, R01); g1n = _ghost(f0, P1, R01)\n", + " for s1 in range(2):\n", + " f1o = f1.copy(); f1 = _adv(f1, b1); f1 = _fill(f1, (1 - (s1 + 1) / 2) * g1o + ((s1 + 1) / 2) * g1n)\n", + " g2o = _ghost(f1o, P2, R12); g2n = _ghost(f1, P2, R12)\n", + " for s2 in range(2):\n", + " f2 = _adv(f2, b2); f2 = _fill(f2, (1 - (s2 + 1) / 2) * g2o + ((s2 + 1) / 2) * g2n)\n", + " f1 = _restrict(f2, f1, P2, Rf12)\n", + " f0 = _restrict(f1, f0, P1, Rf01)\n", + " if t % frame_every == 0:\n", + " frames.append((t, macros(f0)[1], macros(f1)[1], macros(f2)[1]))\n", + " return frames\n", + "\n", + "_naf = _run_nested_anim()\n", + "_vmaxN = np.nanpercentile(np.abs(vorticity(_naf[0][1])), 99.0)\n", + "_cN = plt.get_cmap(\"RdBu_r\").copy(); _cN.set_bad(\"#1b1b1b\")\n", + "\n", + "def _draw_nested(fig, i):\n", + " t, u0, u1, u2 = _naf[i]\n", + " ax = fig.add_subplot(111)\n", + " ax.imshow(vorticity(u0), origin=\"lower\", cmap=_cN, vmin=-_vmaxN, vmax=_vmaxN,\n", + " extent=(0, _Nc, 0, _Nc), interpolation=\"nearest\") # коарс: крупные ячейки\n", + " ax.imshow(vorticity(u1)[1:-1, 1:-1], origin=\"lower\", cmap=_cN, vmin=-_vmaxN, vmax=_vmaxN,\n", + " extent=(8.5, 39.5, 8.5, 39.5), interpolation=\"nearest\") # 2×: вдвое мельче\n", + " ax.imshow(vorticity(u2)[1:-1, 1:-1], origin=\"lower\", cmap=_cN, vmin=-_vmaxN, vmax=_vmaxN,\n", + " extent=(16.25, 31.75, 16.25, 31.75), interpolation=\"nearest\") # 4×: ещё вдвое мельче\n", + " ax.add_patch(mpatches.Rectangle((8, 8), 32, 32, fill=False, edgecolor=\"#7CFC00\", lw=2.5))\n", + " ax.add_patch(mpatches.Rectangle((16, 16), 16, 16, fill=False, edgecolor=\"#ff8a00\", lw=2.5))\n", + " ax.text(8.3, 40.4, \"2× блок\", color=\"#7CFC00\", fontsize=9, weight=\"bold\")\n", + " ax.text(16.3, 32.4, \"4× блок\", color=\"#ff8a00\", fontsize=9, weight=\"bold\")\n", + " ax.set_title(f\"Полный вложенный AMR: коарс + 2× + 4× (видны размеры ячеек) · t={t}\", fontsize=10)\n", + " ax.set_xticks([]); ax.set_yticks([]); fig.tight_layout()\n", + "\n", + "show_gif(render_gif(len(_naf), _draw_nested, \"amr_nested.gif\", (6.2, 6.2), fps=24), width=620)" + ] + }, + { + "cell_type": "markdown", + "id": "98096343", + "metadata": {}, + "source": [ + "## 10. Сопутствующие технологии для полной симуляции\n", + "\n", + "KBC задаёт только **оператор столкновения**. Полный решатель требует ещё ряда\n", + "компонентов.\n", + "\n", + "### 10.1 Граничные условия\n", + "- **Bounce-back (отскок)** — стенка без проскальзывания (no-slip): входящая\n", + " популяция отражается, $f_{\\bar i}=f_i$. Первый порядок (стенка на полпути между\n", + " узлами). Для **движущейся** стенки добавляется импульс\n", + " $-2 w_i\\rho\\,(\\mathbf c_i\\cdot\\mathbf u_w)/c_s^2$ (использован в каверне).\n", + "- **Zou–He** — заданные скорость/давление на входе/выходе: недостающие популяции\n", + " восстанавливаются из условий на $\\rho,\\mathbf u$ и «bounce-back неравновесной\n", + " части». Второй порядок.\n", + "- **Grad / регуляризованные** — реконструкция неравновесной части через тензор\n", + " напряжений $\\Pi^{neq}$; устойчивее при больших градиентах (рекомендуются с\n", + " энтропийными моделями).\n", + "- **Интерполированный bounce-back (Bouzidi, Yu–Mei–Luo–Shyy)** — для кривых\n", + " стенок: используется доля стенки $q\\in[0,1]$ из signed-distance field (SDF),\n", + " две ветви $q\\!\\ge\\!0.5$ и $q\\!<\\!0.5$.\n", + "- **Sponge / absorbing-слой** — у границ плавно подмешивается целевое равновесие,\n", + " чтобы гасить отражения волн (использовался в прежней реализации на 6 гранях).\n", + "\n", + "### 10.2 Объёмные силы (Guo)\n", + "Схема Guo et al. (2002): к столкновению добавляется\n", + "$F_i = \\bigl(1-\\tfrac{\\beta}{...}\\bigr)w_i\\Bigl[\\tfrac{\\mathbf c_i-\\mathbf u}{c_s^2}\n", + "+\\tfrac{(\\mathbf c_i\\cdot\\mathbf u)}{c_s^4}\\mathbf c_i\\Bigr]\\cdot\\mathbf F$, а\n", + "скорость берётся со сдвигом $\\mathbf u\\to\\mathbf u+\\tfrac{\\mathbf F}{2\\rho}$.\n", + "Даёт второй порядок и точное сохранение импульса.\n", + "\n", + "### 10.3 Турбулентность: implicit LES vs Smagorinsky\n", + "- **KBC — implicit LES**: адаптивный $\\gamma$ добавляет диссипацию высших мод\n", + " ровно там, где растут неразрешённые масштабы — параметр-free.\n", + "- **Smagorinsky (явная LES)**: вихревая вязкость $\\nu_t=(C_s\\Delta)^2|S|$,\n", + " $|S|=\\sqrt{2 S_{\\alpha\\beta}S_{\\alpha\\beta}}$ из неравновесного тензора\n", + " напряжений; эффективное $\\tau_{\\mathrm{eff}}=3(\\nu+\\nu_t)+\\tfrac12$. $C_s\\!\\approx\\!0.1$–$0.17$.\n", + " Иногда комбинируют с KBC у стенок.\n", + "\n", + "### 10.4 Единицы и обезразмеривание (lu/ts ↔ СИ)\n", + "Выбираем масштабы $\\Delta x$ (м/lu), $\\Delta t$ (с/ts), $\\rho_0$ (кг/м³). Тогда\n", + "$$ \\nu_{\\text{СИ}} = \\nu_{\\text{lu}}\\,\\frac{\\Delta x^2}{\\Delta t},\\quad\n", + " \\mathbf u_{\\text{СИ}} = \\mathbf u_{\\text{lu}}\\,\\frac{\\Delta x}{\\Delta t},\\quad\n", + " p_{\\text{СИ}} = c_s^2\\rho_{\\text{lu}}\\,\\rho_0\\frac{\\Delta x^2}{\\Delta t^2}. $$\n", + "В решёточных единицах $\\Delta x=\\Delta t=1$ (узел и шаг — за единицу), поэтому\n", + "скорости и вязкости — безразмерные «решёточные». Ограничение сжимаемости:\n", + "$\\mathrm{Ma}=|\\mathbf u|/c_s\\lesssim 0.1$–$0.3$ (ошибка $\\propto\\mathrm{Ma}^2$);\n", + "отсюда Mach-лимитер шага $\\Delta t \\le \\mathrm{Ma}\\,c_s\\,\\Delta x/|\\mathbf u|$.\n", + "\n", + "### 10.5 Решётки, инициализация, измельчение сетки\n", + "- **Решётки**: D2Q9 (2D), **D3Q27** (3D, полная изотропия\n", + " 4-го порядка и галилеева инвариантность — предпочтительна для KBC/турбулентности).\n", + "- **Инициализация**: задать $f=f^{eq}(\\rho,\\mathbf u)$; для согласованности с\n", + " градиентами — добавить неравновесную часть из $\\Pi^{neq}$ (схема Mei).\n", + "- **Измельчение сетки**: многосеточные блоки с пространственно-временной\n", + " интерполяцией; KBC устойчив к смене разрешения (нет явных подсеточных констант)." + ] + }, + { + "cell_type": "markdown", + "id": "f4970cf7", + "metadata": {}, + "source": [ + "## 11. Перенос на D3Q27 и связь с целевой реализацией\n", + "\n", + "Вся математика KBC переносится на 3D **без изменений по сути**: меняются\n", + "решётка (27 скоростей, веса $8/27,\\,2/27,\\,1/54,\\,1/216$), число моментов\n", + "(моментный базис 27×27) и состав сдвиговой части $s$ (девиаторный тензор\n", + "напряжений 3D — 5 независимых компонент). Формула $\\gamma$ и оператор\n", + "$f\\leftarrow f-\\beta(2\\Delta s+\\gamma\\Delta h)$ идентичны." + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "id": "62145381", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-06T17:45:02.044023Z", + "iopub.status.busy": "2026-06-06T17:45:02.043839Z", + "iopub.status.idle": "2026-06-06T17:45:02.347425Z", + "shell.execute_reply": "2026-06-06T17:45:02.346598Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "D3Q27: Σw=1 и Σw c c = c_s² I — OK; число направлений: 27\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# D3Q27: скорости и веса.\n", + "C3 = np.array([[x, y, z] for x in (-1, 0, 1) for y in (-1, 0, 1) for z in (-1, 0, 1)], dtype=float)\n", + "nz = (C3 != 0).sum(1)\n", + "W3 = np.select([nz == 0, nz == 1, nz == 2, nz == 3], [8/27, 2/27, 1/54, 1/216])\n", + "assert np.isclose(W3.sum(), 1.0)\n", + "assert np.allclose((W3[:, None, None] * C3[:, :, None] * C3[:, None, :]).sum(0), CS2 * np.eye(3))\n", + "print(\"D3Q27: Σw=1 и Σw c c = c_s² I — OK; число направлений:\", len(C3))\n", + "\n", + "fig = plt.figure(figsize=(6.4, 5.6))\n", + "ax = fig.add_subplot(111, projection=\"3d\")\n", + "tier3 = {8/27: (\"#d1495b\", \"покой\"), 2/27: (\"#2e7d32\", \"оси (×6)\"),\n", + " 1/54: (\"#1f6feb\", \"рёбра (×12)\"), 1/216: (\"#9c27b0\", \"углы (×8)\")}\n", + "for wv, (col, lab) in tier3.items():\n", + " m = np.isclose(W3, wv)\n", + " ax.scatter(C3[m, 0], C3[m, 1], C3[m, 2], s=70 + 5000 * wv, color=col, label=f\"{lab}, w={wv:.4f}\",\n", + " depthshade=True, edgecolors=\"k\", linewidths=0.4)\n", + "ax.set_xlabel(\"$c_x$\"); ax.set_ylabel(\"$c_y$\"); ax.set_zlabel(\"$c_z$\")\n", + "ax.set_title(\"Решётка D3Q27 (цель реализации)\")\n", + "ax.legend(loc=\"upper left\", fontsize=7, bbox_to_anchor=(0.0, 1.0))\n", + "_finish(fig, \"11_d3q27.png\")" + ] + }, + { + "cell_type": "markdown", + "id": "ab492199", + "metadata": {}, + "source": [ + "### Чем «настоящий KBC» отличается от прежнего подхода\n", + "\n", + "Прежняя реализация (GPU-решатель) фактически использовала **полиномиальное**\n", + "равновесие + **TRT** (две скорости релаксации) + **α-лимитер положительности**\n", + "(ELBM-типа, по симметричной части) + явный **Smagorinsky**. Это устойчивая и\n", + "рабочая схема, но **не** KBC. Переход к настоящему KBC:\n", + "\n", + "| Аспект | Настоящий KBC | Прежний подход (TRT + α) |\n", + "|---|---|---|\n", + "| Равновесие | энтропийное product-form | полиномиальное $O(u^2)$ |\n", + "| Столкновение | энтропийный MRT, $k/s/h$ | TRT (симм./антисимм.) |\n", + "| Стабилизация | $\\gamma$ из энтропии (высшие моды) | α-лимитер положительности (симм. часть) |\n", + "| H-теорема | встроена в вывод $\\gamma$ | контролируется отдельно (диагностика) |\n", + "| Турбулентность | implicit LES (параметр-free) | явный Smagorinsky |\n", + "| Решётка | D3Q27 | D3Q27 (совпадает) |\n", + "\n", + "**Дорожная карта реализации на GPU**: (1) энтропийное $f^{eq}$ (product-form);\n", + "(2) моментные проекторы $P_s,P_h$ для D3Q27 (предвычислить матрицы);\n", + "(3) per-node $\\gamma$ по формуле; (4) коллизия $f-\\beta(2\\Delta s+\\gamma\\Delta h)$;\n", + "(5) опционально — комбинировать с пристеночным Smagorinsky." + ] + }, + { + "cell_type": "markdown", + "id": "3cc19201", + "metadata": {}, + "source": [ + "## 12. Формулы под сверку с оригиналом (⚠) и литература\n", + "\n", + "**Под сверку с первоисточниками** (доступ к части PDF был ограничен — проверить\n", + "коэффициенты по оригиналам):\n", + "1. **Энтропийное равновесие** product-form: префактор $(2-\\sqrt{1+3u_\\alpha^2})$ и\n", + " основание $\\frac{2u_\\alpha+\\sqrt{1+3u_\\alpha^2}}{1-u_\\alpha}$ — сверить вид и\n", + " область применимости (Ansumali–Karlin; Chikatamarla–Karlin).\n", + " *Здесь проверено численно: даёт $\\rho,\\rho\\mathbf u$ точно.*\n", + "2. **Формула $\\gamma$** $=\\tfrac1\\beta-(2-\\tfrac1\\beta)\\tfrac{\\langle\\Delta s|\\Delta h\\rangle}{\\langle\\Delta h|\\Delta h\\rangle}$\n", + " и порядок разложения $\\Delta H$, из которого она получена (Bösch et al. 2015).\n", + " *Здесь проверено: предел $\\gamma=2$ совпадает с BGK.*\n", + "3. **Назначение моментов** в $s$ vs $h$ для вариантов KBC-N1…N4 (D2Q9/D3Q27) —\n", + " сверить точный состав по таблицам оригинала.\n", + "4. **Множитель 2** перед $\\Delta s$ и связь $\\beta=1/(2\\tau)$ — сверить нормировку.\n", + "\n", + "**Литература (первоисточники):**\n", + "- I. V. Karlin, F. Bösch, S. S. Chikatamarla, *Gibbs' principle for the\n", + " lattice-kinetic theory of fluid dynamics*, **Phys. Rev. E 90**, 031302(R) (2014).\n", + "- F. Bösch, S. S. Chikatamarla, I. V. Karlin, *Entropic multirelaxation lattice\n", + " Boltzmann models for turbulent flows*, **Phys. Rev. E 92**, 043309 (2015).\n", + "- S. S. Chikatamarla, I. V. Karlin, *Entropy and Galilean invariance of lattice\n", + " Boltzmann theories*, **Phys. Rev. Lett.** (2006) — энтропийное равновесие.\n", + "- B. Dorschner, S. S. Chikatamarla, I. V. Karlin и др. — применения KBC\n", + " (каналы, обтекание тел), измельчение сетки, подвижные границы.\n", + "- Z. Guo, C. Zheng, B. Shi, *Discrete lattice effects on the forcing term in the\n", + " lattice Boltzmann method*, **Phys. Rev. E 65**, 046308 (2002) — форсинг.\n", + "- U. Ghia, K. N. Ghia, C. T. Shin (1982) — эталон каверны (валидация)." + ] + }, + { + "cell_type": "markdown", + "id": "8e77072f", + "metadata": {}, + "source": [ + "## 13. Итоги\n", + "\n", + "- **KBC** = энтропийный MRT-LBM: сохраняющиеся моды не трогаем, сдвиг релаксируем\n", + " фиксированным $2\\beta$ (задаёт вязкость), высшие моды — адаптивным $\\gamma$ из\n", + " условия неувеличения энтропии. При $\\gamma=2$ — это в точности BGK.\n", + "- **Зачем**: безусловная нелинейная устойчивость и параметр-free implicit LES —\n", + " считает турбулентность на грубых сетках там, где BGK разрушается\n", + " (продемонстрировано на сдвиговом слое).\n", + "- **Проверено численно**: точность равновесия и разложения (до $10^{-15}$),\n", + " правильная вязкость (TGV, ошибка $<0.1\\%$), устойчивость (сдвиговый слой),\n", + " разумное совпадение с эталоном Ghia (каверна).\n", + "- **Дальше**: перенос на D3Q27 на GPU (Vulkan), сверка коэффициентов с\n", + " оригинальными статьями, при необходимости — комбинация с Smagorinsky и\n", + " точными ГУ (Grad/Zou–He, Bouzidi для кривых стенок)." + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "id": "b8decfbf", + "metadata": { + "execution": { + "iopub.execute_input": "2026-06-06T17:45:02.349653Z", + "iopub.status.busy": "2026-06-06T17:45:02.349463Z", + "iopub.status.idle": "2026-06-06T17:45:02.353001Z", + "shell.execute_reply": "2026-06-06T17:45:02.352209Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "=== Все самопроверки и валидации пройдены ===\n" + ] + } + ], + "source": [ + "print(\"\\n=== Все самопроверки и валидации пройдены ===\")" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.14.3" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/docs/theory/_legacy/kbc_lbm.py b/docs/theory/_legacy/kbc_lbm.py new file mode 100644 index 0000000..b9d68e5 --- /dev/null +++ b/docs/theory/_legacy/kbc_lbm.py @@ -0,0 +1,1643 @@ +# --- +# jupyter: +# jupytext: +# text_representation: +# extension: .py +# format_name: percent +# format_version: '1.3' +# kernelspec: +# display_name: Python 3 +# language: python +# name: python3 +# --- + +# %% [markdown] +# # Метод KBC (энтропийный Lattice Boltzmann): математика, физика и рабочий разбор +# +# **Karlin–Bösch–Chikatamarla (KBC)** — энтропийная multi-relaxation-time (MRT) +# формулировка решёточного метода Больцмана (Lattice Boltzmann Method, **LBM**), +# которая обеспечивает **безусловную нелинейную устойчивость** при больших числах +# Рейнольдса без явной модели подсеточной турбулентности (она работает как +# *implicit LES*). +# +# Этот ноутбук — подготовка к реализации: мы разбираем метод «на бумаге», +# **выводим** ключевые формулы, **численно их самопроверяем** и строим рабочий +# 2D-солвер (решётка D2Q9) с валидацией. В конце — перенос на целевую решётку +# D3Q27 и сравнение с подходом «полиномиальное равновесие + TRT + α-лимитер + +# Smagorinsky», который применялся ранее (это и есть «что менять для перехода к +# настоящему KBC»). +# +# > **О источниках.** Формулы по возможности взяты из оригинальных статей +# > (Karlin, Bösch, Chikatamarla, *Phys. Rev. E* **90**, 031302(R), 2014; +# > Bösch, Chikatamarla, Karlin, *Phys. Rev. E* **92**, 043309, 2015; Guo et al., +# > *Phys. Rev. E* **65**, 046308, 2002). Где доступ был только к вторичным +# > источникам, формула помечена **⚠ сверить с оригиналом**, а в конце собран +# > список таких мест. Главный страж корректности здесь — **численная +# > самопроверка** каждой формулы. + +# %% [markdown] +# ## Сводная таблица обозначений +# +# Везде используются **решёточные единицы** (lattice units): шаг сетки +# $\Delta x = 1$ (lu — *lattice unit*) и шаг по времени $\Delta t = 1$ (ts — *time +# step*). Переход к СИ описан в разделе «Единицы и обезразмеривание». +# +# | Символ | Название | Физический смысл | Единицы (lu/ts) | Единицы (СИ) | Диапазон | +# |---|---|---|---|---|---| +# | $f_i$ | популяция | плотность частиц со скоростью $\mathbf c_i$ | $f_i$ безразм. (доля $\rho$) | кг·с³/м⁶ | $f_i>0$ | +# | $\mathbf c_i$ | дискретная скорость | направление переноса $i$ | lu/ts | м/с | компоненты $\in\{-1,0,1\}$ | +# | $w_i$ | вес квадратуры | вес направления, $\sum_i w_i=1$ | безразм. | безразм. | $\{4/9,1/9,1/36\}$ (D2Q9) | +# | $c_s$ | скорость звука решётки | $c_s^2=1/3$ для D2Q9/D3Q27 | lu/ts | м/с | $c_s=1/\sqrt3$ | +# | $\rho$ | плотность | $\rho=\sum_i f_i$ | безразм. (опорная 1) | кг/м³ | $\approx 1$ | +# | $\mathbf u$ | скорость | $\rho\mathbf u=\sum_i \mathbf c_i f_i$ | lu/ts | м/с | $\lvert\mathbf u\rvert\ll c_s$ | +# | $\mathbf j$ | импульс | $\mathbf j=\rho\mathbf u$ | — | — | — | +# | $\tau$ | время релаксации | задаёт вязкость | ts | с | $\tau>1/2$ | +# | $\nu$ | кинематич. вязкость | $\nu=c_s^2(\tau-\tfrac12)$ | lu²/ts | м²/с | $>0$ | +# | $\beta$ | параметр сдвиговой релаксации | $\beta=1/(2\tau)$ | безразм. | — | $0<\beta<1$ | +# | $\gamma$ | **энтропийный стабилизатор** | релаксация высших мод | безразм. | — | $\approx 2$ | +# | $f_i^{\mathrm{eq}}$ | равновесие | максимум энтропии при связях $\rho,\mathbf u$ | как $f_i$ | — | $>0$ | +# | $k_i,s_i,h_i$ | части разложения | кинематич./сдвиг/высшие моды | как $f_i$ | — | — | +# | $\Delta s_i,\Delta h_i$ | неравновесные части | $s_i-s_i^{eq}$, $h_i-h_i^{eq}$ | как $f_i$ | — | малы | +# | $H$ | H-функция (энтропия) | $H=\sum_i f_i\ln(f_i/w_i)$ | безразм. | — | убывает | +# | $\langle X|Y\rangle$ | энтропийное скал. произв. | $\sum_i X_iY_i/f_i^{eq}$ | — | — | — | +# | $\mathrm{Ma}$ | число Маха | $\mathrm{Ma}=\lvert\mathbf u\rvert/c_s$ | безразм. | — | $\lesssim 0.3$ | +# | $\mathrm{Re}$ | число Рейнольдса | $\mathrm{Re}=UL/\nu$ | безразм. | — | задача | +# | $S_{\alpha\beta}$ | тензор скоростей деформации | $\tfrac12(\partial_\alpha u_\beta+\partial_\beta u_\alpha)$ | 1/ts | 1/с | — | +# | $\nu_t$ | вихревая вязкость (LES) | $\nu_t=(C_s\Delta)^2\lvert S\rvert$ | lu²/ts | м²/с | $\ge 0$ | +# | $C_s$ | константа Смагоринского | — | безразм. | — | $0.1$–$0.17$ | +# | $q$ | доля стенки | положение стенки между узлами | безразм. | — | $[0,1]$ | + +# %% [markdown] +# ## 0. Стиль графиков и общие настройки +# +# Подключаем библиотеки и задаём единый «симпатичный» стиль matplotlib. Код +# написан так, чтобы файл работал **и как ноутбук** (графики встраиваются), **и +# как обычный скрипт** `python kbc_lbm.py` (графики сохраняются в `figures/` для +# валидации физики). + +# %% +import numpy as np +import matplotlib + +# Определяем, выполняемся ли мы внутри Jupyter. В скрипте используем неинтерактивный +# бэкенд Agg и сохраняем PNG; в ноутбуке полагаемся на inline-вывод nbconvert. +try: + get_ipython() # есть только в IPython/Jupyter + IN_NOTEBOOK = True +except NameError: + IN_NOTEBOOK = False +if not IN_NOTEBOOK: + matplotlib.use("Agg") + # Консоль Windows может быть в cp1251 — выводим в UTF-8, чтобы кириллица и + # греческие символы в print() не роняли скрипт (в ноутбуке это не нужно). + import sys + try: + sys.stdout.reconfigure(encoding="utf-8") + except Exception: + pass + +import os +import matplotlib.pyplot as plt + +FIGDIR = os.path.join(os.path.dirname(os.path.abspath(__file__)) if "__file__" in globals() else ".", "figures") +os.makedirs(FIGDIR, exist_ok=True) + +plt.rcParams.update({ + "figure.dpi": 110, + "savefig.dpi": 120, + "font.size": 11, + "axes.titlesize": 13, + "axes.titleweight": "bold", + "axes.grid": True, + "grid.alpha": 0.25, + "axes.axisbelow": True, + "figure.facecolor": "white", + "axes.facecolor": "#fbfbfd", +}) + +def _finish(fig, name): + """Сохранить фигуру в figures/ (для скрипта) и показать (в ноутбуке).""" + fig.savefig(os.path.join(FIGDIR, name), bbox_inches="tight") + if IN_NOTEBOOK: + plt.show() # гарантированный inline-вывод при nbconvert + else: + plt.close(fig) + +print("matplotlib", matplotlib.__version__, "| numpy", np.__version__, "| notebook:", IN_NOTEBOOK) + + +# %% [markdown] +# ## 1. Основы LBM и решётка D2Q9 +# +# Решёточный метод Больцмана отслеживает **популяции** $f_i(\mathbf x, t)$ — +# плотность фиктивных частиц, движущихся в узле $\mathbf x$ со скоростью +# $\mathbf c_i$. Динамика — чередование **переноса** (streaming) и **столкновения** +# (collision): +# $$ f_i(\mathbf x + \mathbf c_i\,\Delta t,\; t+\Delta t) = f_i(\mathbf x,t) + \Omega_i, $$ +# где $\Omega_i$ — оператор столкновения. +# +# **Решётка D2Q9** (2D, 9 скоростей): покоящаяся частица, 4 «осевые» и 4 +# «диагональные». Скорость звука $c_s^2 = 1/3$. Веса $w_i$ выбраны так, чтобы +# квадратура точно интегрировала моменты максвеллиана до нужного порядка +# (изотропия 4-го порядка): $w_0=4/9$, осевые $1/9$, диагональные $1/36$, +# $\sum_i w_i = 1$. +# +# **Макроскопические моменты:** +# $$ \rho=\sum_i f_i,\qquad \rho\mathbf u=\sum_i \mathbf c_i f_i. $$ + +# %% +# --- Решётка D2Q9 ----------------------------------------------------------- +# Порядок направлений: 0 — покой; 1..4 — оси (+x,+y,-x,-y); 5..8 — диагонали. +C = np.array([[0, 0], [1, 0], [0, 1], [-1, 0], [0, -1], + [1, 1], [-1, 1], [-1, -1], [1, -1]], dtype=float) # c_i = (c_ix, c_iy) +W = np.array([4/9, 1/9, 1/9, 1/9, 1/9, 1/36, 1/36, 1/36, 1/36]) # веса w_i +CS2 = 1.0 / 3.0 # c_s^2 +Q = 9 +CX, CY = C[:, 0], C[:, 1] +OPP = np.array([0, 3, 4, 1, 2, 7, 8, 5, 6]) # индекс противоположного c_i + +# Самопроверка решёточных тождеств (нужны для корректной гидродинамики): +assert np.isclose(W.sum(), 1.0) # сумма весов = 1 +assert np.allclose((W[:, None] * C).sum(0), 0.0) # sum_i w_i c_i = 0 +assert np.allclose((W[:, None, None] * C[:, :, None] * C[:, None, :]).sum(0), + CS2 * np.eye(2)) # sum_i w_i c_ia c_ib = c_s^2 δ_ab +assert np.all(C[OPP] == -C) # c_{opp(i)} = -c_i +print("Решётка D2Q9: тождества весов и изотропии 2-го порядка — OK") + + +# %% +def make_grid(field_shape): + """Удобный конструктор массива популяций формы (9, Ny, Nx).""" + return np.zeros((Q,) + field_shape) + + +def macros(f): + """Плотность rho (Ny,Nx) и скорость u (2,Ny,Nx) из популяций f (9,Ny,Nx).""" + rho = f.sum(axis=0) + jx = (CX[:, None, None] * f).sum(axis=0) + jy = (CY[:, None, None] * f).sum(axis=0) + u = np.stack([jx / rho, jy / rho]) + return rho, u + + +# %% [markdown] +# ### Рисунок: стенсиль D2Q9 +# +# Стрелки — направления $\mathbf c_i$, цвет/толщина — вес $w_i$ (центральный узел +# имеет наибольший вес $4/9$, диагонали — наименьший $1/36$). + +# %% +fig, ax = plt.subplots(figsize=(5.2, 5.2)) +tier_color = {4/9: "#d1495b", 1/9: "#2e7d32", 1/36: "#1f6feb"} +for i in range(Q): + col = tier_color[W[i]] + if i == 0: + ax.plot(0, 0, "o", ms=18, color=col, zorder=3) + ax.annotate(f"$w_0={W[i]:.3f}$", (0, 0), textcoords="offset points", + xytext=(8, 8), fontsize=9) + else: + ax.annotate("", xy=(CX[i], CY[i]), xytext=(0, 0), + arrowprops=dict(arrowstyle="-|>", lw=1.5 + 40 * W[i], color=col)) + ax.annotate(f"$c_{{{i}}}$", (CX[i], CY[i]), textcoords="offset points", + xytext=(6 * np.sign(CX[i] + 0.1), 6 * np.sign(CY[i] + 0.1)), fontsize=9) +ax.set_xlim(-1.6, 1.6); ax.set_ylim(-1.6, 1.6); ax.set_aspect("equal") +ax.set_title("Решётка D2Q9: дискретные скорости $\\mathbf{c}_i$ и веса $w_i$") +ax.set_xlabel("$c_x$ [lu/ts]"); ax.set_ylabel("$c_y$ [lu/ts]") +from matplotlib.lines import Line2D +ax.legend(handles=[Line2D([0], [0], color=c, lw=3, label=f"$w={k:.4f}$") + for k, c in tier_color.items()], loc="upper right", fontsize=8) +_finish(fig, "01_stencil_d2q9.png") + + +# %% [markdown] +# ## 2. Равновесие: полиномиальное и энтропийное +# +# **Полиномиальное равновесие** (разложение максвеллиана по Эрмиту до $O(u^2)$), +# стандарт для BGK: +# $$ f_i^{\mathrm{eq,poly}} = w_i\,\rho\left[1 + \frac{\mathbf c_i\cdot\mathbf u}{c_s^2} +# + \frac{(\mathbf c_i\cdot\mathbf u)^2}{2c_s^4} - \frac{\mathbf u^2}{2c_s^2}\right]. $$ +# Коэффициенты при $c_s^2=1/3$: $1/c_s^2=3$, $1/(2c_s^4)=4.5$, $1/(2c_s^2)=1.5$. +# +# **Энтропийное равновесие** (Ansumali–Karlin): точный максимум дискретной +# H-функции при связях $\sum f^{eq}=\rho$, $\sum \mathbf c f^{eq}=\rho\mathbf u$. +# Для D2Q9/D3Q27 имеет **замкнутую факторизованную форму** ⚠ (сверить с +# оригиналом): +# $$ f_i^{\mathrm{eq}} = \rho\,w_i\prod_{\alpha\in\{x,y\}} +# \underbrace{\left(2-\sqrt{1+3u_\alpha^2}\right)}_{\text{префактор}} +# \left(\frac{2u_\alpha+\sqrt{1+3u_\alpha^2}}{1-u_\alpha}\right)^{c_{i\alpha}}. $$ +# Здесь $3 = 1/c_s^2$. Энтропийная форма **точно** воспроизводит $\rho$ и +# $\rho\mathbf u$ (проверим ниже) и, в отличие от полинома, гарантирует +# положительность и H-теорему. + +# %% +def feq_poly(rho, u): + """Полиномиальное равновесие O(u^2). rho:(Ny,Nx), u:(2,Ny,Nx) -> (9,Ny,Nx).""" + cu = CX[:, None, None] * u[0] + CY[:, None, None] * u[1] # c_i · u + usq = u[0] ** 2 + u[1] ** 2 + return W[:, None, None] * rho * (1 + cu / CS2 + cu ** 2 / (2 * CS2 ** 2) - usq / (2 * CS2)) + + +def feq_entropic(rho, u): + """Энтропийное равновесие (product-form). Клип скорости для численной безопасности.""" + ux = np.clip(u[0], -0.95, 0.95) + uy = np.clip(u[1], -0.95, 0.95) + sx = np.sqrt(1 + 3 * ux ** 2) + sy = np.sqrt(1 + 3 * uy ** 2) + prefx, prefy = 2 - sx, 2 - sy # префактор по каждому измерению + Bx = (2 * ux + sx) / (1 - ux) # основание степени по x + By = (2 * uy + sy) / (1 - uy) + base = rho * prefx * prefy # (Ny,Nx) + Bxp = Bx[None] ** CX[:, None, None] # (9,Ny,Nx): B_x^{c_ix} + Byp = By[None] ** CY[:, None, None] # (9,Ny,Nx): B_y^{c_iy} + return W[:, None, None] * base[None] * Bxp * Byp + + +# %% [markdown] +# ### Самопроверка равновесий +# +# Проверяем, что **энтропийное** равновесие точно даёт нужные нулевой и первый +# моменты ($\rho$, $\rho\mathbf u$), а второй момент при малом $\mathrm{Ma}$ близок +# к $\rho(c_s^2\delta_{\alpha\beta}+u_\alpha u_\beta)$ (тензор давления Навье–Стокса). + +# %% +rng = np.random.default_rng(0) +rho_t = np.ones((1, 1)) * (1.0 + 0.1 * rng.standard_normal((1, 1))) +u_t = np.stack([0.06 * rng.standard_normal((1, 1)), 0.06 * rng.standard_normal((1, 1))]) +fe = feq_entropic(rho_t, u_t) +rho_m, u_m = macros(fe) +Pxx = (CX[:, None, None] ** 2 * fe).sum(0) +err_rho = abs(rho_m - rho_t).max() +err_u = abs(u_m - u_t).max() +err_P = abs(Pxx - rho_t * (CS2 + u_t[0] ** 2)).max() +print(f"Энтропийное равновесие: |Σf-ρ|={err_rho:.2e}, |Σcf-ρu|={err_u:.2e} (точно),") +print(f" |Σc_x²f - ρ(c_s²+u_x²)|={err_P:.2e} (мало при малом Ma)") +assert err_rho < 1e-12 and err_u < 1e-12 +print("Моменты равновесия — OK") + + +# %% [markdown] +# ## 3. Разложение популяций $f = k + s + h$ через моментные проекторы +# +# Сердце KBC — разбиение каждого 9-вектора популяций на три части по **моментным +# подпространствам**: +# - $k_i$ — **кинематическая** часть, несёт только сохраняющиеся моменты +# ($\rho$, $j_x$, $j_y$); +# - $s_i$ — **сдвиговая** часть, несёт девиаторный тензор напряжений +# ($N=\Pi_{xx}-\Pi_{yy}$ и $\Pi_{xy}$); +# - $h_i$ — **высшие** («ghost») моды: след 2-го момента (объёмная вязкость), +# 3-й и 4-й моменты. +# +# Строим базис из 9 независимых мономов-моментов $\phi^{(a)}_i$ и матрицу +# $M_{ai}=\phi^{(a)}(\mathbf c_i)$, тогда $m = M f$ — вектор моментов. Проектор на +# группу моментов $G$: $\;P_G = M^{-1} D_G M$, где $D_G$ — диагональная маска +# (единицы на моментах из $G$). По построению $P_k+P_s+P_h = I$, поэтому +# $k+s+h=f$ **точно**. Назначение моментов в $s$ vs $h$ задаёт *вариант* KBC +# (ниже — KBC-N1: в $s$ только девиаторный стресс). + +# %% +def moment_matrix(): + """Строки — мономы-моменты, столбцы — направления. m = M @ f.""" + M = np.zeros((Q, Q)) + M[0] = 1.0 # ρ + M[1] = CX # j_x + M[2] = CY # j_y + M[3] = 3 * (CX ** 2 + CY ** 2) - 2 # след 2-го момента (энергия), центрированный + M[4] = CX ** 2 - CY ** 2 # N — разность нормальных напряжений + M[5] = CX * CY # Π_xy — сдвиговое напряжение + M[6] = CX ** 2 * CY # 3-й момент + M[7] = CX * CY ** 2 # 3-й момент + M[8] = CX ** 2 * CY ** 2 # 4-й момент + return M + +M = moment_matrix() +Minv = np.linalg.inv(M) # существует: 9 мономов независимы на D2Q9 + +K_MOMENTS = [0, 1, 2] # сохраняющиеся: ρ, j_x, j_y -> k +S_MOMENTS = [4, 5] # девиаторный стресс: N, Π_xy -> s (вариант KBC-N1) +H_MOMENTS = [3, 6, 7, 8] # след + 3-й + 4-й моменты -> h + +def projector(moment_idx): + D = np.zeros((Q, Q)) + D[moment_idx, moment_idx] = 1.0 + return Minv @ D @ M + +P_k, P_s, P_h = projector(K_MOMENTS), projector(S_MOMENTS), projector(H_MOMENTS) + +# Самопроверка: полнота (P_k+P_s+P_h=I) и что k несёт ровно сохраняющиеся моменты. +assert np.allclose(P_k + P_s + P_h, np.eye(Q)) +ftest = rng.random((Q, 3, 4)) +k = np.einsum("ij,jab->iab", P_k, ftest) +s = np.einsum("ij,jab->iab", P_s, ftest) +h = np.einsum("ij,jab->iab", P_h, ftest) +assert np.allclose(k + s + h, ftest) # разложение полное +# у части k моменты N, Π и высшие — нулевые (несёт только ρ, j_x, j_y): +mk = np.einsum("ai,ijl->ajl", M, k) # моменты части k +assert np.allclose(mk[S_MOMENTS], 0.0) and np.allclose(mk[H_MOMENTS], 0.0) +print("Разложение k+s+h=f: макс. невязка =", abs(k + s + h - ftest).max()) +print("Проекторы P_k+P_s+P_h=I и состав части k — OK") + + +# %% [markdown] +# ## 4. Оператор столкновений KBC и стабилизатор $\gamma$ +# +# Поскольку $f$ и $f^{eq}$ имеют **одинаковые** сохраняющиеся моменты, неравновесие +# $\,f-f^{eq}\,$ не содержит кинематической части: $\Delta k = 0$, значит +# $f-f^{eq}=\Delta s+\Delta h$, где $\Delta s = P_s(f-f^{eq})$, +# $\Delta h = P_h(f-f^{eq})$. +# +# **Столкновение KBC:** +# $$ f_i^{\text{после}} = f_i - \beta\,\bigl(2\,\Delta s_i + \gamma\,\Delta h_i\bigr). $$ +# Множитель **2** перед $\Delta s$ фиксирует сдвиговую вязкость через +# $\beta=1/(2\tau)$; высшие моды релаксируются отдельным $\gamma$. +# +# **Стабилизатор $\gamma$** выбирается локально из условия неувеличения дискретной +# энтропии ($\Delta H = 0$ во 2-м порядке). Результат — **замкнутая формула** +# ⚠ (сверить с оригиналом): +# $$ \gamma = \frac{1}{\beta} - \Bigl(2-\frac{1}{\beta}\Bigr) +# \frac{\langle \Delta s\,|\,\Delta h\rangle}{\langle \Delta h\,|\,\Delta h\rangle}, +# \qquad \langle X|Y\rangle = \sum_i \frac{X_i Y_i}{f_i^{eq}}. $$ +# При $\gamma=2$: $2\Delta s+2\Delta h = 2(f-f^{eq})$, и KBC **сводится к BGK** +# с $\omega=2\beta$: $f^{\text{после}}=f-2\beta(f-f^{eq})$. Адаптивный $\gamma$ +# добавляет/убавляет диссипацию высших мод там, где это нужно для устойчивости. + +# %% +def collide_kbc(f, feq, beta, gamma_fixed=None): + """KBC-столкновение. Возвращает (f_после, поле gamma).""" + dfneq = f - feq + ds = np.einsum("ij,jab->iab", P_s, dfneq) # Δs + dh = dfneq - ds # Δh = (f-feq) - Δs, т.к. Δk=0 + if gamma_fixed is not None: + gamma = np.full(f.shape[1:], float(gamma_fixed)) + else: + inv = 1.0 / feq + num = (ds * dh * inv).sum(0) # ⟨Δs|Δh⟩ + den = (dh * dh * inv).sum(0) # ⟨Δh|Δh⟩ + with np.errstate(divide="ignore", invalid="ignore"): + gamma = np.where(den > 1e-14, + 1.0 / beta - (2.0 - 1.0 / beta) * num / den, + 2.0) # у равновесия (Δh→0) берём предел BGK + fpost = f - beta * (2.0 * ds + gamma[None] * dh) + return fpost, gamma + + +def collide_bgk(f, feq, beta): + """Классический BGK: f - ω(f-feq), ω=2β.""" + return f - 2.0 * beta * (f - feq) + + +# %% [markdown] +# ### Самопроверка: предел $\gamma=2$ совпадает с BGK +# При $\gamma=2$ оператор KBC обязан в точности равняться $f-2\beta(f-f^{eq})$. + +# %% +rho0 = np.ones((6, 7)) +u0 = np.stack([0.05 * rng.standard_normal((6, 7)), 0.05 * rng.standard_normal((6, 7))]) +feq0 = feq_entropic(rho0, u0) +f0 = feq0 + 0.01 * rng.standard_normal((Q, 6, 7)) # слегка неравновесное состояние +f0 *= rho0 / f0.sum(0) # сохранить ρ +beta0 = 0.7 +fk2, _ = collide_kbc(f0, feq_entropic(*macros(f0)), beta0, gamma_fixed=2.0) +fbgk = collide_bgk(f0, feq_entropic(*macros(f0)), beta0) +diff = abs(fk2 - fbgk).max() +# diff — машинный ноль (масштаб |f|·eps ≈ 1e-18); важно лишь, что он ≪ порога 1e-12. +print(f"max|KBC(γ=2) - BGK| = {diff:.1e} → машинный ноль (порог assert 1e-12), операторы совпадают") +assert diff < 1e-12 +print("Предел γ=2 → BGK — OK") + + +# %% [markdown] +# ## 4b. Популярно: что делает каждая формула (математика + физика) +# +# Здесь каждая формула KBC объясняется «на пальцах»: что это математически, какая за +# этим физика потока, и как это считается на каждом шаге. +# +# --- +# **Популяции $f_i(\mathbf x,t)$ и шаг «перенос + столкновение».** +# *Математика:* в каждом узле сетки храним 9 чисел — «сколько газа летит» по каждому из +# 9 направлений $\mathbf c_i$. *Физика:* как 9 встречных потоков на перекрёстке. +# *Как считается:* за шаг потоки сначала **разъезжаются** в соседние узлы (перенос, +# `np.roll`), затем в каждом узле **перемешиваются** (столкновение). Перенос точный и +# дешёвый; вся «физика жидкости» сидит в столкновении. +# +# --- +# **Моменты $\rho=\sum_i f_i$, $\rho\mathbf u=\sum_i \mathbf c_i f_i$.** +# *Математика:* сумма всех потоков = плотность; взвешенная по направлениям = импульс. +# *Физика:* «сколько вещества» и «куда оно в среднем движется». *Как считается:* два +# суммирования по 9 числам — мгновенно. Отсюда привычные $\rho$ и скорость $\mathbf u$. +# +# --- +# **Равновесие $f_i^{\mathrm{eq}}(\rho,\mathbf u)$.** +# *Математика:* распределение по направлениям, максимизирующее энтропию при заданных +# $\rho,\mathbf u$. *Физика:* «к чему стремится газ, если оставить в покое» — локальный +# максвелловский «штиль». *Как считается:* по замкнутой формуле из $\rho,\mathbf u$. +# Столкновение всегда **тянет** $f$ к $f^{eq}$ — это и есть вязкое стремление к равновесию. +# +# --- +# **H-функция $H=\sum_i f_i\ln(f_i/w_i)$.** +# *Математика:* дискретный аналог энтропии. *Физика:* мера беспорядка/необратимости; по +# второму началу не должна самопроизвольно убывать. *Как считается:* одно суммирование. +# В KBC $H$ — **физический компас устойчивости**: из условия «энтропия не падает» +# выводится стабилизатор $\gamma$. +# +# --- +# **Разложение $f = k + s + h$.** +# *Математика:* проекция 9-вектора на три группы моментов. *Физика:* три «слоя» движения: +# - $k$ — **перенос массы и импульса** (поток как целое); +# - $s$ — **вязкий сдвиг** (трение слоёв друг о друга — задаёт вязкость); +# - $h$ — **мелкая «рябь»** высших мод (мелкомасштабные флуктуации, где копится +# неустойчивость на грубой сетке). +# +# *Как считается:* умножение на заранее посчитанные проекторы $P_s,P_h$. Идея KBC: +# релаксировать эти слои **с разной скоростью**. +# +# --- +# **Столкновение $f \leftarrow f - \beta\,(2\,\Delta s + \gamma\,\Delta h)$.** +# *Математика:* $\Delta s,\Delta h$ — отклонения сдвига и ряби от равновесия. *Физика:* +# **вязкий сдвиг** гасим фиксированным темпом $2\beta$ (он задаёт вязкость и Re); **рябь** — +# отдельным темпом $\gamma\beta$, ровно чтобы не нарушить энтропию. *Как считается:* две +# линейные комбинации 9-векторов на узел. Множитель **2** перед $\Delta s$ воспроизводит +# правильную вязкость; при $\gamma=2$ всё сворачивается в обычный BGK. +# +# --- +# **Стабилизатор $\gamma = \dfrac{1}{\beta} - \Bigl(2-\dfrac{1}{\beta}\Bigr) +# \dfrac{\langle \Delta s|\Delta h\rangle}{\langle \Delta h|\Delta h\rangle}$.** +# *Математика:* единственное $\gamma$, при котором изменение энтропии за шаг равно нулю +# (во 2-м порядке). *Физика:* **локальный термостат потока** в реальном времени — в каждой +# точке на каждом шаге подкручивает, насколько гасить «рябь», чтобы энтропия не росла. В +# спокойных зонах $\gamma\approx 2$ (как BGK); у резких градиентов (кромки тел, вихри) +# $\gamma$ отклоняется и добавляет ровно столько диссипации, сколько нужно, **не давая +# симуляции взорваться**. Это «implicit LES» — встроенная, без подгоночных констант, +# модель мелкомасштабной турбулентности. *Как считается:* два скалярных произведения на +# узел → одно число $\gamma$. +# +# --- +# **Энтропийное скалярное произведение $\langle X|Y\rangle=\sum_i X_iY_i/f_i^{eq}$.** +# *Математика:* взвешенное (на $1/f^{eq}$) скалярное произведение — кривизна энтропии у +# равновесия. *Физика:* измеряет, насколько «рябь» $\Delta h$ выровнена со сдвигом +# $\Delta s$; по этому решается, сколько диссипации добавить. *Как считается:* поэлементное +# произведение и сумма по 9 направлениям. +# +# --- +# **Вязкость $\nu = c_s^2\bigl(\tfrac{1}{2\beta}-\tfrac12\bigr)$, $\beta=1/(2\tau)$.** +# *Математика:* связь темпа релаксации сдвига с вязкостью. *Физика:* чем медленнее гасится +# сдвиг (меньше $\beta$), тем «гуще» жидкость; через $\nu$ задаётся $\mathrm{Re}=UL/\nu$. +# *Как считается:* один раз при настройке (выбрали $\nu$ под нужный Re → получили $\beta$). + + +# %% [markdown] +# ## 5. Перенос (streaming) и связь вязкости с $\beta$ +# +# Перенос — сдвиг каждой популяции на её вектор $\mathbf c_i$ (здесь — периодически +# через `np.roll`). Вязкость: $\nu = c_s^2\bigl(\tfrac{1}{2\beta}-\tfrac12\bigr)$, +# то есть $\tau=\nu/c_s^2+\tfrac12$, $\beta=1/(2\tau)$. Число Рейнольдса +# $\mathrm{Re}=UL/\nu$; число Маха $\mathrm{Ma}=U/c_s$ держим $\lesssim 0.1$. + +# %% +def stream(f): + """Периодический перенос популяций на c_i. f:(9,Ny,Nx).""" + fs = np.empty_like(f) + for i in range(Q): + fs[i] = np.roll(f[i], shift=(int(CY[i]), int(CX[i])), axis=(0, 1)) + return fs + + +def nu_to_beta(nu): + tau = nu / CS2 + 0.5 + return 1.0 / (2.0 * tau) + + +def H_function(f): + """Дискретная H-функция (энтропия) H = Σ f_i ln(f_i/w_i).""" + fp = np.maximum(f, 1e-300) + return (fp * np.log(fp / W[:, None, None])).sum(0) + + +print("Пример: ν=0.01 → β =", round(nu_to_beta(0.01), 4), ", τ =", round(0.01 / CS2 + 0.5, 4)) + + +# %% [markdown] +# ## 6. Алгоритм одного шага KBC +# +# ``` +# для каждого узла: +# 1) макро-моменты: rho = sum f_i, rho*u = sum c_i f_i +# 2) равновесие: f_i^eq (энтропийное product-form) +# 3) неравновесие: Ds = P_s (f - f^eq), Dh = (f - f^eq) - Ds +# 4) стабилизатор: gamma = 1/beta - (2 - 1/beta) / +# 5) столкновение: f <- f - beta (2 Ds + gamma Dh) +# 6) перенос: f_i(x + c_i) <- f_i(x) +# 7) граничные условия (bounce-back / Zou-He / sponge) +# ``` + +# %% +fig, ax = plt.subplots(figsize=(4.3, 6.2)) +ax.set_axis_off() +steps_txt = [ + ("Макро-моменты\n$\\rho=\\sum f_i,\\ \\rho\\mathbf{u}=\\sum \\mathbf{c}_i f_i$", "#e8f0fe"), + ("Равновесие $f_i^{eq}$\n(энтропийное)", "#e6f4ea"), + ("Неравновесие\n$\\Delta s=P_s(f-f^{eq}),\\ \\Delta h=(f-f^{eq})-\\Delta s$", "#fff4e5"), + ("Стабилизатор $\\gamma$\n$=1/\\beta-(2-1/\\beta)\\frac{\\langle\\Delta s|\\Delta h\\rangle}{\\langle\\Delta h|\\Delta h\\rangle}$", "#fde7ef"), + ("Столкновение\n$f\\leftarrow f-\\beta(2\\Delta s+\\gamma\\Delta h)$", "#f3e8fd"), + ("Перенос\n$f_i(\\mathbf{x}+\\mathbf{c}_i)\\leftarrow f_i(\\mathbf{x})$", "#e8f0fe"), + ("Граничные условия", "#eceff1"), +] +y = 0.95 +for txt, col in steps_txt: + ax.add_patch(plt.Rectangle((0.05, y - 0.1), 0.9, 0.085, transform=ax.transAxes, + facecolor=col, edgecolor="#555", lw=1.2)) + ax.text(0.5, y - 0.057, txt, transform=ax.transAxes, ha="center", va="center", fontsize=8.5) + if y > 0.2: + ax.annotate("", xy=(0.5, y - 0.118), xytext=(0.5, y - 0.1), xycoords="axes fraction", + arrowprops=dict(arrowstyle="-|>", color="#555")) + y -= 0.13 +ax.set_title("Шаг KBC") +_finish(fig, "06_algorithm_flow.png") + + +# %% [markdown] +# ## 7. Демо-1: вихрь Тейлора–Грина (валидация вязкости и H-теоремы) +# +# Точное решение несжимаемого Навье–Стокса в периодической области: +# $$ u_x=-U_0\cos(k x)\sin(k y),\quad u_y=U_0\sin(k x)\cos(k y),\quad k=2\pi/N. $$ +# Кинетическая энергия затухает как $E(t)=E_0\,e^{-4\nu k^2 t}$. Прогоняем KBC и +# **измеряем** $\nu$ по наклону $\ln E(t)$ — он должен совпасть с заданным $\nu$. + +# %% +def run_tgv(N=96, U0=0.04, nu=0.0125, steps=10000, rec=50, n_snap=10, frame_every=42): + k = 2 * np.pi / N + xs = np.arange(N) + X, Yc = np.meshgrid(xs, xs) # X — индекс x (ось 1), Yc — индекс y (ось 0) + ux = -U0 * np.cos(k * X) * np.sin(k * Yc) + uy = U0 * np.sin(k * X) * np.cos(k * Yc) + rho = np.ones((N, N)) + f = feq_entropic(rho, np.stack([ux, uy])) + beta = nu_to_beta(nu) + # моменты времени для n_snap снимков поля скорости через равные интервалы + snap_at = sorted(set(int(round(v)) for v in np.linspace(0, steps, n_snap))) + snaps, frames, ts, KE, Hs = [], [], [], [], [] + for t in range(steps + 1): + rho, u = macros(f) + f, _ = collide_kbc(f, feq_entropic(rho, u), beta) + f = stream(f) + need = (t in snap_at) or (t % rec == 0) or (t % frame_every == 0) + if need: + _, uu = macros(f) + if t in snap_at: + snaps.append((t, uu.copy())) # снимки для статической панели + if t % frame_every == 0: + frames.append((t, uu.copy())) # кадры для анимации + if t % rec == 0: + ts.append(t) + KE.append(0.5 * np.mean(uu[0] ** 2 + uu[1] ** 2)) + Hs.append(H_function(f).mean()) + return dict(N=N, k=k, nu=nu, U0=U0, ts=np.array(ts), KE=np.array(KE), + H=np.array(Hs), u=u, rho=rho, snaps=snaps, frames=frames) + + +tgv = run_tgv() +# Измеряем ν по наклону ln(KE): slope = -4 ν k^2 +mask = tgv["KE"] > 0 +slope = np.polyfit(tgv["ts"][mask], np.log(tgv["KE"][mask]), 1)[0] +nu_meas = -slope / (4 * tgv["k"] ** 2) +rel_err = abs(nu_meas - tgv["nu"]) / tgv["nu"] +print(f"TGV: nu_zadano={tgv['nu']:.5f}, nu_izmereno={nu_meas:.5f}, otn.oshibka={rel_err*100:.2f}%") +assert rel_err < 0.06, "TGV: измеренная вязкость отклонилась слишком сильно" +print("Валидация TGV (вязкость по затуханию энергии) — OK") + + +# %% +def vorticity(u): + duy_dx = (np.roll(u[1], -1, 1) - np.roll(u[1], 1, 1)) * 0.5 + dux_dy = (np.roll(u[0], -1, 0) - np.roll(u[0], 1, 0)) * 0.5 + return duy_dx - dux_dy + + +fig, axs = plt.subplots(1, 3, figsize=(13.5, 4.0)) +om = vorticity(tgv["u"]) +im = axs[0].imshow(om, origin="lower", cmap="RdBu_r") +axs[0].set_title("Завихренность $\\omega$ (TGV, срез)") +axs[0].set_xlabel("$x$ [lu]"); axs[0].set_ylabel("$y$ [lu]") +plt.colorbar(im, ax=axs[0], fraction=0.046) + +axs[1].semilogy(tgv["ts"], tgv["KE"], "o", ms=3, label="KBC (измерено)") +axs[1].semilogy(tgv["ts"], tgv["KE"][0] * np.exp(-4 * tgv["nu"] * tgv["k"] ** 2 * tgv["ts"]), + "-", color="#d1495b", label="$E_0 e^{-4\\nu k^2 t}$ (аналитика)") +axs[1].set_title("Затухание кин. энергии"); axs[1].set_xlabel("$t$ [ts]") +axs[1].set_ylabel("$E(t)$"); axs[1].legend() + +axs[2].plot(tgv["ts"], tgv["H"], color="#2e7d32") +axs[2].set_title("H-функция (энтропия) во времени") +axs[2].set_xlabel("$t$ [ts]"); axs[2].set_ylabel("$\\langle H\\rangle$") +fig.suptitle("Демо-1: вихрь Тейлора–Грина (KBC, D2Q9)", y=1.04, fontweight="bold") +_finish(fig, "07_taylor_green.png") + + +# %% [markdown] +# ### Распад вихря: 10 срезов через равные интервалы времени +# +# Поле завихренности $\omega=\partial_x u_y-\partial_y u_x$ в 10 моментов времени, +# равномерно распределённых от $t=0$ до конца прогона. **Шкала цвета единая для всех +# панелей** (фиксирована по начальной завихренности $\pm|\omega|_{\max}(0)$) — поэтому +# наглядно видно именно *затухание*: пространственная структура (4 противоположно +# вращающихся вихря) сохраняется, а амплитуда экспоненциально гаснет. В заголовке +# каждой панели — шаг $t$ и доля кинетической энергии $E/E_0$. + +# %% +snaps = tgv["snaps"] +om0 = np.abs(vorticity(snaps[0][1])).max() # масштаб цвета по t=0 +KE0 = 0.5 * np.mean(snaps[0][1][0] ** 2 + snaps[0][1][1] ** 2) # начальная энергия + +fig, axs = plt.subplots(2, 5, figsize=(15, 6.3), constrained_layout=True) +im = None +for ax, (tt, uu) in zip(axs.ravel(), snaps): + im = ax.imshow(vorticity(uu), origin="lower", cmap="RdBu_r", vmin=-om0, vmax=om0) + KEf = 0.5 * np.mean(uu[0] ** 2 + uu[1] ** 2) / KE0 + ax.set_title(f"t={tt} · $E/E_0$={KEf:.2f}", fontsize=10) + ax.set_xticks([]); ax.set_yticks([]) +fig.colorbar(im, ax=axs, fraction=0.025, pad=0.01, label="завихренность $\\omega$ [1/ts]") +fig.suptitle("Распад вихря Тейлора–Грина: завихренность на равных интервалах времени " + "(единая шкала цвета)", fontweight="bold") +_finish(fig, "07b_tgv_decay_slices.png") + + +# %% [markdown] +# ## 8. Демо-2: устойчивость — двойной сдвиговый слой (BGK против KBC) +# +# Классический тест Minion–Brown: тонкие сдвиговые слои на **недоразрешённой** +# сетке. Стандартный BGK при малой вязкости разрушается (отрицательные +# популяции, NaN), а KBC за счёт адаптивного $\gamma$ остаётся устойчивым и даёт +# гладкие свёрнутые вихри — это и есть «implicit LES». + +# %% +def init_shear(N, U0=0.04, delta=0.05, kappa=80.0): + xs = np.arange(N) / N + X, Yc = np.meshgrid(xs, xs) + ux = np.where(Yc <= 0.5, U0 * np.tanh(kappa * (Yc - 0.25)), + U0 * np.tanh(kappa * (0.75 - Yc))) + uy = delta * U0 * np.sin(2 * np.pi * (X + 0.25)) + return np.stack([ux, uy]) + + +def run_shear(scheme, N=128, U0=0.04, nu=1.7e-4, steps=8000, rec=100, frame_every=33): + u0 = init_shear(N, U0=U0) + rho = np.ones((N, N)) + beta = nu_to_beta(nu) + feq0 = feq_entropic if scheme == "kbc" else feq_poly + f = feq0(rho, u0) + ts, umax, frames = [], [], [] + blew_up_at = None + last_u, last_g = u0, np.full((N, N), 2.0) + for t in range(steps + 1): + rho, u = macros(f) + if not np.all(np.isfinite(u)) or np.abs(u).max() > 0.5: + blew_up_at = t + break + if t % frame_every == 0: + frames.append((t, u.copy())) # кадры (только до разрушения) + if scheme == "kbc": + f, g = collide_kbc(f, feq_entropic(rho, u), beta) + last_g = g + else: + f = collide_bgk(f, feq_poly(rho, u), beta) + f = stream(f) + last_u = u + if t % rec == 0: + ts.append(t); umax.append(np.abs(u).max()) + return dict(scheme=scheme, ts=np.array(ts), umax=np.array(umax), frames=frames, + u=last_u, gamma=last_g, blew_up_at=blew_up_at, N=N, U0=U0, nu=nu) + + +Re_shear = 0.04 * 128 / 1.7e-4 +print(f"Sdvigovyj sloj: Re ~ {Re_shear:.0f}, beta ~ {nu_to_beta(1.7e-4):.4f}") +res_bgk = run_shear("bgk") +res_kbc = run_shear("kbc") +print("BGK:", ("raz=" + str(res_bgk["blew_up_at"])) if res_bgk["blew_up_at"] else "ustojchiv") +print("KBC:", ("raz=" + str(res_kbc["blew_up_at"])) if res_kbc["blew_up_at"] else "ustojchiv") +assert res_kbc["blew_up_at"] is None, "KBC должен оставаться устойчивым" +print("Демонстрация устойчивости BGK vs KBC — OK") + + +# %% +fig, axs = plt.subplots(1, 3, figsize=(13.5, 4.0)) +om_k = vorticity(res_kbc["u"]) +im0 = axs[0].imshow(om_k, origin="lower", cmap="RdBu_r") +axs[0].set_title("KBC: завихренность (устойчиво)") +axs[0].set_xlabel("$x$ [lu]"); axs[0].set_ylabel("$y$ [lu]") +plt.colorbar(im0, ax=axs[0], fraction=0.046) + +im1 = axs[1].imshow(res_kbc["gamma"] - 2.0, origin="lower", cmap="magma") +axs[1].set_title("Поле стабилизатора $\\gamma-2$") +axs[1].set_xlabel("$x$ [lu]"); axs[1].set_ylabel("$y$ [lu]") +plt.colorbar(im1, ax=axs[1], fraction=0.046) + +axs[2].plot(res_kbc["ts"], res_kbc["umax"], color="#2e7d32", label="KBC") +axs[2].plot(res_bgk["ts"], res_bgk["umax"], color="#d1495b", label="BGK") +if res_bgk["blew_up_at"]: + axs[2].axvline(res_bgk["blew_up_at"], color="#d1495b", ls="--", alpha=0.6) +axs[2].set_title("$\\max|\\mathbf{u}|$ во времени") +axs[2].set_xlabel("$t$ [ts]"); axs[2].set_ylabel("$\\max|\\mathbf{u}|$ [lu/ts]"); axs[2].legend() +fig.suptitle(f"Демо-2: сдвиговый слой, Re~{Re_shear:.0f} (BGK разрушается, KBC держит)", + y=1.04, fontweight="bold") +_finish(fig, "08_shear_stability.png") + + +# %% [markdown] +# ## 9. Демо-3: каверна с движущейся крышкой против эталона Ghia (Re=1000) +# +# Квадратная каверна, верхняя стенка движется со скоростью $U$. На неподвижных +# стенках — **bounce-back** (отскок), на крышке — bounce-back с поправкой импульса +# подвижной стенки $-2 w_i \rho\,(\mathbf c_i\cdot\mathbf u_w)/c_s^2$. Сравниваем +# профили скорости по центральным линиям с данными **Ghia, Ghia & Shin (1982)**. +# Здесь сетка намеренно грубая (для быстрого прогона), а bounce-back — первого +# порядка, поэтому совпадение **качественное**; оно улучшается измельчением сетки, +# числом шагов и переходом к ГУ второго порядка (Zou–He / Grad на крышке). + +# %% +UP = [2, 5, 6] # c_iy = +1 (вверх) +DOWN = [4, 7, 8] # c_iy = -1 (вниз) +RIGHT = [1, 5, 8] # c_ix = +1 +LEFT = [3, 6, 7] # c_ix = -1 + + +def run_cavity(N=110, Re=1000.0, U=0.05, steps=14000, tol=1e-7, check=500, frame_every=58): + nu = U * N / Re + beta = nu_to_beta(nu) + rho = np.ones((N, N)) + u = np.zeros((2, N, N)) + f = feq_entropic(rho, u) + uw = np.array([U, 0.0]) + prev = None + frames = [] + t = 0 + for t in range(steps): + rho, u = macros(f) + if t % frame_every == 0: + frames.append((t, u.copy())) # кадры становления течения + fcol, _ = collide_kbc(f, feq_entropic(rho, u), beta) + f = stream(fcol) + # bounce-back: на каждой стенке неизвестны направления, входящие в область. + for i in UP: # низ (y=0) + f[i, 0, :] = fcol[OPP[i], 0, :] + for i in RIGHT: # лево (x=0) + f[i, :, 0] = fcol[OPP[i], :, 0] + for i in LEFT: # право (x=N-1) + f[i, :, -1] = fcol[OPP[i], :, -1] + for i in DOWN: # верх (крышка) + поправка подвижной стенки + io = OPP[i] # io ударяет в крышку (идёт вверх) + corr = 2.0 * W[io] * (CX[io] * uw[0] + CY[io] * uw[1]) / CS2 + f[i, -1, :] = fcol[io, -1, :] - corr + if t % check == 0 and t > 0: + cur = u.copy() + if prev is not None and np.abs(cur - prev).max() < tol: + break + prev = cur + rho, u = macros(f) + return dict(N=N, Re=Re, U=U, u=u, steps=t, frames=frames) + + +cav = run_cavity() +print(f"Kaverna: Re={cav['Re']:.0f}, N={cav['N']}, ostanovleno na shage {cav['steps']}") + +# Эталон Ghia, Ghia & Shin (1982), Re=1000. +ghia_y = np.array([0.0000, 0.0547, 0.0625, 0.0703, 0.1016, 0.1719, 0.2813, 0.4531, + 0.5000, 0.6172, 0.7344, 0.8516, 0.9531, 0.9609, 0.9688, 0.9766, 1.0000]) +ghia_u = np.array([0.0000, -0.18109, -0.20196, -0.22220, -0.29730, -0.38289, -0.27805, + -0.10648, -0.06080, 0.05702, 0.18719, 0.33304, 0.46604, 0.51117, + 0.57492, 0.65928, 1.0000]) +ghia_x = np.array([0.0000, 0.0625, 0.0703, 0.0781, 0.0938, 0.1563, 0.2266, 0.2344, + 0.5000, 0.8047, 0.8594, 0.9063, 0.9453, 0.9531, 0.9609, 0.9688, 1.0000]) +ghia_v = np.array([0.0000, 0.27485, 0.29012, 0.30353, 0.32627, 0.37095, 0.33075, 0.32235, + 0.02526, -0.31966, -0.42665, -0.51550, -0.39188, -0.33714, -0.27669, + -0.21388, 0.0000]) + +Ncav = cav["N"] +yc = (np.arange(Ncav) + 0.5) / Ncav +xc = (np.arange(Ncav) + 0.5) / Ncav +u_centerline = cav["u"][0, :, Ncav // 2] / cav["U"] # u_x(y) на вертикали x=0.5 +v_centerline = cav["u"][1, Ncav // 2, :] / cav["U"] # u_y(x) на горизонтали y=0.5 + +fig, axs = plt.subplots(1, 3, figsize=(14, 4.4)) +spd = np.sqrt(cav["u"][0] ** 2 + cav["u"][1] ** 2) / cav["U"] +axs[0].imshow(spd, origin="lower", cmap="viridis", extent=[0, 1, 0, 1]) +sx = np.linspace(0, 1, Ncav) +axs[0].streamplot(sx, sx, cav["u"][0], cav["u"][1], density=1.1, color="white", linewidth=0.6) +axs[0].set_title("Линии тока и $|\\mathbf{u}|/U$"); axs[0].set_xlabel("$x/L$"); axs[0].set_ylabel("$y/L$") + +axs[1].plot(u_centerline, yc, "-", color="#1f6feb", label="KBC") +axs[1].plot(ghia_u, ghia_y, "o", ms=5, mfc="none", color="#d1495b", label="Ghia 1982") +axs[1].set_title("$u_x/U$ по вертикали $x=0.5$"); axs[1].set_xlabel("$u_x/U$") +axs[1].set_ylabel("$y/L$"); axs[1].legend() + +axs[2].plot(xc, v_centerline, "-", color="#1f6feb", label="KBC") +axs[2].plot(ghia_x, ghia_v, "o", ms=5, mfc="none", color="#d1495b", label="Ghia 1982") +axs[2].set_title("$u_y/U$ по горизонтали $y=0.5$"); axs[2].set_xlabel("$x/L$") +axs[2].set_ylabel("$u_y/U$"); axs[2].legend() +fig.suptitle("Демо-3: каверна с движущейся крышкой, Re=1000 (KBC vs Ghia)", + y=1.04, fontweight="bold") +_finish(fig, "09_cavity_ghia.png") + +u_interp = np.interp(ghia_y, yc, u_centerline) +rms = np.sqrt(np.mean((u_interp - ghia_u) ** 2)) +print(f"Kaverna: RMS-otklonenie u_x ot Ghia ~ {rms:.3f} (gruboe BB -> dopustimo)") + + +# %% [markdown] +# ## 9b. Анимации: зацикленное воспроизведение тестов (видео) +# +# Для каждого теста собираем **зацикленный GIF** (бесконечный `loop`) из кадров, +# записанных во время прогона: вихрь Тейлора–Грина (затухание), сдвиговый слой +# (BGK против KBC бок о бок — видно момент разрушения BGK) и становление течения в +# каверне. Файлы сохраняются в `anim/` (самостоятельные «видео»), а ниже встроены +# в ноутбук и проигрываются циклически. Скорость воспроизведения — `fps` кадров/с +# (физическое время между кадрами постоянно). + +# %% +import io as _io +from PIL import Image +from IPython.display import HTML, display + +ANIMDIR = os.path.join(os.path.dirname(os.path.abspath(__file__)) if "__file__" in globals() else ".", "anim") +os.makedirs(ANIMDIR, exist_ok=True) + + +def render_gif(n_frames, draw_fn, name, figsize, fps=18, dpi=80): + """Отрисовать n_frames кадров (draw_fn(fig, i)) и сохранить зацикленный GIF.""" + path = os.path.join(ANIMDIR, name) + fig = plt.figure(figsize=figsize, dpi=dpi) + pil = [] + for i in range(n_frames): + fig.clf() + draw_fn(fig, i) + buf = _io.BytesIO() + fig.savefig(buf, format="png") # фикс. размер кадра (figsize×dpi) + buf.seek(0) + pil.append(Image.open(buf).convert("RGB").convert("P", palette=Image.ADAPTIVE)) + plt.close(fig) + pil[0].save(path, save_all=True, append_images=pil[1:], + duration=int(1000 / fps), loop=0, optimize=True) # loop=0 → бесконечно + print("GIF:", os.path.relpath(path), f"({n_frames} кадров)") + return path + + +def show_gif(path, width=460): + """Встроить GIF в ноутбук (ссылкой на файл — авто-цикл в браузере/Jupyter).""" + if IN_NOTEBOOK: + display(HTML(f'')) + + +# %% [markdown] +# ### Видео 1 — затухание вихря Тейлора–Грина + +# %% +_tgv_fr = tgv["frames"] +_om0 = np.abs(vorticity(_tgv_fr[0][1])).max() +_KE0 = 0.5 * np.mean(_tgv_fr[0][1][0] ** 2 + _tgv_fr[0][1][1] ** 2) + +def _draw_tgv(fig, i): + t, u = _tgv_fr[i] + ax = fig.add_subplot(111) + ax.imshow(vorticity(u), origin="lower", cmap="RdBu_r", vmin=-_om0, vmax=_om0) + ke = 0.5 * np.mean(u[0] ** 2 + u[1] ** 2) / _KE0 + ax.set_title(f"Тейлор–Грин · t={t} · $E/E_0$={ke:.2f}", fontsize=10) + ax.set_xticks([]); ax.set_yticks([]) + fig.tight_layout() + +show_gif(render_gif(len(_tgv_fr), _draw_tgv, "tgv_decay.gif", (4.6, 4.4), fps=24)) + +# %% [markdown] +# ### Видео 2 — сдвиговый слой: BGK (слева) против KBC (справа) +# BGK замирает на последнем устойчивом кадре с пометкой «разрушился», KBC +# продолжает гладко сворачивать вихри. + +# %% +_kf, _bf = res_kbc["frames"], res_bgk["frames"] +_om0s = np.percentile(np.abs(vorticity(_kf[len(_kf) // 2][1])), 99.5) + +def _draw_shear(fig, i): + ax1 = fig.add_subplot(1, 2, 1) + ax2 = fig.add_subplot(1, 2, 2) + dead = i >= len(_bf) + tb, ub = _bf[min(i, len(_bf) - 1)] + ax1.imshow(vorticity(ub), origin="lower", cmap="RdBu_r", vmin=-_om0s, vmax=_om0s) + ax1.set_title("BGK — разрушился" if dead else f"BGK · t={tb}", + color="red" if dead else "black", fontsize=10) + tk, uk = _kf[i] + ax2.imshow(vorticity(uk), origin="lower", cmap="RdBu_r", vmin=-_om0s, vmax=_om0s) + ax2.set_title(f"KBC · t={tk}", fontsize=10) + for a in (ax1, ax2): + a.set_xticks([]); a.set_yticks([]) + fig.tight_layout() + +show_gif(render_gif(len(_kf), _draw_shear, "shear_bgk_vs_kbc.gif", (8.4, 4.3), fps=24), width=720) + +# %% [markdown] +# ### Видео 3 — становление течения в каверне (Re=1000) + +# %% +_cf = cav["frames"] +_vmax = max(np.sqrt(u[0] ** 2 + u[1] ** 2).max() for _, u in _cf) / cav["U"] + +def _draw_cav(fig, i): + t, u = _cf[i] + ax = fig.add_subplot(111) + sp = np.sqrt(u[0] ** 2 + u[1] ** 2) / cav["U"] + ax.imshow(sp, origin="lower", cmap="viridis", vmin=0, vmax=_vmax, extent=[0, 1, 0, 1]) + ax.set_title(f"Каверна Re=1000 · t={t} · $|\\mathbf{{u}}|/U$", fontsize=10) + ax.set_xlabel("$x/L$"); ax.set_ylabel("$y/L$") + fig.tight_layout() + +show_gif(render_gif(len(_cf), _draw_cav, "cavity_transient.gif", (4.9, 4.5), fps=24)) + + +# %% [markdown] +# ## Демо-4: обтекание твёрдых тел разной формы (2D) +# +# Канал с втоком слева (Дирихле + плавный разгон), нуль-градиентным оттоком справа и +# стенками сверху/снизу. Тело задаётся маской и отражает популяции (**bounce-back**). +# За плохо обтекаемыми телами при Re≈150 формируется **вихревая дорожка Кармана** — +# поочерёдный срыв вихрей; KBC держит течение устойчивым на грубой сетке. Тела: цилиндр, +# квадрат, треугольник, профиль (под углом атаки). Ниже — анимация всех четырёх (≈10 c), +# статический срез завихренности и колебания скорости в следе (мерило частоты срыва). + +# %% +def smoothstep(x): + x = min(max(x, 0.0), 1.0) + return x * x * (3.0 - 2.0 * x) + + +def solid_mask(Nx, Ny, shape, cx, cy, D): + Y, X = np.mgrid[0:Ny, 0:Nx] + if shape == "circle": + m = (X - cx) ** 2 + (Y - cy) ** 2 <= (D / 2) ** 2 + elif shape == "square": + m = (np.abs(X - cx) <= D / 2) & (np.abs(Y - cy) <= D / 2) + elif shape == "triangle": # вершиной против потока + tt = (X - (cx - D / 2)) / D + m = (tt >= 0) & (tt <= 1) & (np.abs(Y - cy) <= tt * (D / 2)) + elif shape == "airfoil": # наклонный эллипс (угол атаки 18°) + aoa = np.deg2rad(18.0); a = D * 0.95; b = D * 0.26 + xr = (X - cx) * np.cos(aoa) + (Y - cy) * np.sin(aoa) + yr = -(X - cx) * np.sin(aoa) + (Y - cy) * np.cos(aoa) + m = (xr / a) ** 2 + (yr / b) ** 2 <= 1 + else: + m = np.zeros((Ny, Nx), bool) + m[0, :] = True; m[-1, :] = True # стенки канала (верх/низ) + return m + + +def run_obstacle(shape, Nx=150, Ny=72, D=14, U=0.06, Re=150.0, steps=9600, + ramp=1000, frame_every=40): + cx, cy = Nx // 4, Ny // 2 + solid = solid_mask(Nx, Ny, shape, cx, cy, D) + beta = nu_to_beta(U * D / Re) + f = feq_entropic(np.ones((Ny, Nx)), np.zeros((2, Ny, Nx))) + frames, probe = [], [] + px, py = cx + 3 * D, cy # зонд в следе + ones_col = np.ones((Ny, 1)) + for t in range(steps + 1): + rho, u = macros(f) + fcol, _ = collide_kbc(f, feq_entropic(rho, u), beta) + for i in range(Q): + fcol[i, solid] = f[OPP[i], solid] # bounce-back (тело + стенки) + f = stream(fcol) + Uin = U * smoothstep(t / ramp) # плавный разгон входа + uin = np.zeros((2, Ny, 1)); uin[0, :, 0] = Uin + f[:, 1:-1, 0] = feq_entropic(ones_col, uin)[:, 1:-1, 0] # вток (Дирихле) + f[:, 1:-1, -1] = f[:, 1:-1, -2] # отток (нуль-градиент) + if t % frame_every == 0: + _, uu = macros(f) + frames.append((t, uu.copy())) + probe.append(uu[1, py, px]) + return dict(shape=shape, solid=solid, frames=frames, probe=np.array(probe), + Nx=Nx, Ny=Ny, U=U, Re=Re, D=D, cx=cx, cy=cy) + + +SHAPES = [("circle", "цилиндр"), ("square", "квадрат"), + ("triangle", "треугольник"), ("airfoil", "профиль")] +obs = {key: run_obstacle(key) for key, _ in SHAPES} +for key, name in SHAPES: + p = obs[key]["probe"]; half = p[len(p) // 2:] + print(f"{name:12}: max|u_y(зонд)|={np.abs(half).max():.4f} (колебания → срыв вихрей)") + + +# %% +# Анимация-монтаж всех четырёх тел (завихренность, тело — тёмное). +_keys = [k for k, _ in SHAPES] +_titles = {k: n for k, n in SHAPES} +_nf = min(len(obs[k]["frames"]) for k in _keys) +_vmax = max(np.percentile(np.abs(vorticity(obs[k]["frames"][_nf // 2][1])), 99.0) for k in _keys) +_ocmap = plt.get_cmap("RdBu_r").copy(); _ocmap.set_bad("#1b1b1b") + +def _draw_obst(fig, i): + for j, k in enumerate(_keys): + ax = fig.add_subplot(2, 2, j + 1) + t, u = obs[k]["frames"][i] + vort = np.where(obs[k]["solid"], np.nan, vorticity(u)) + ax.imshow(vort, origin="lower", cmap=_ocmap, vmin=-_vmax, vmax=_vmax) + ax.set_title(f"{_titles[k]} · t={t}", fontsize=9) + ax.set_xticks([]); ax.set_yticks([]) + fig.suptitle("Обтекание тел (KBC, Re≈150): завихренность", fontsize=11) + fig.tight_layout(rect=(0, 0, 1, 0.96)) + +show_gif(render_gif(_nf, _draw_obst, "obstacle_shapes.gif", (11, 6.2), fps=24), width=780) + +# %% +# Статический срез завихренности в конце прогона + колебания в следе. +fig, axs = plt.subplots(2, 2, figsize=(12, 5.6), constrained_layout=True) +for ax, k in zip(axs.ravel(), _keys): + t, u = obs[k]["frames"][-1] + vort = np.where(obs[k]["solid"], np.nan, vorticity(u)) + ax.imshow(vort, origin="lower", cmap=_ocmap, vmin=-_vmax, vmax=_vmax) + ax.set_title(f"{_titles[k]} (t={t})", fontsize=10) + ax.set_xticks([]); ax.set_yticks([]) +fig.suptitle("Обтекание тел: поле завихренности в конце прогона", fontweight="bold") +_finish(fig, "10_obstacle_shapes.png") + +fig, ax = plt.subplots(figsize=(9.5, 3.4)) +for k in _keys: + ax.plot(np.arange(len(obs[k]["probe"])), obs[k]["probe"], label=_titles[k]) +ax.set_title("Поперечная скорость в следе (зонд за телом): колебания = срыв вихрей") +ax.set_xlabel("кадр"); ax.set_ylabel("$u_y$ в зонде [lu/ts]"); ax.legend(fontsize=8, ncol=4) +_finish(fig, "10b_obstacle_probe.png") + + +# %% [markdown] +# ## KBC на сетках с измельчением у границ (grid refinement) +# +# **Может ли KBC работать с неоднородным разрешением?** Да — но важно, *как именно*: +# +# 1. **Чистый LBM живёт на РАВНОМЕРНОЙ решётке.** Перенос $f_i(\mathbf x+\mathbf c_i)$ +# требует, чтобы сосед был ровно на расстоянии $\mathbf c_i$ — шаг сетки постоянен. +# Поэтому одна «кривая» неравномерная сетка для классического LBM не подходит. +# 2. **Неоднородное разрешение делают блочным измельчением (multi-block / AMR):** область +# делят на вложенные РАВНОМЕРНЫЕ блоки разного шага — крупный вдали, мелкий у тел и в +# следе. На стыке блоков поля **интерполируют** и **перемасштабируют**: при переходе на +# вдвое более мелкий блок $\Delta x\!\to\!\Delta x/2$, $\Delta t\!\to\!\Delta t/2$ +# (акустическое масштабирование, $c_s$ сохраняется), время релаксации меняется как +# $\tau_f = 2\tau_c - \tfrac12$ (вязкость $\nu$ постоянна), а неравновесная часть +# $f^{neq}$ масштабируется множителем отношения шагов. ⚠ детали сверить с оригиналом. +# 3. **KBC полностью совместим с измельчением.** Это локальный оператор столкновения: на +# каждом блоке своё $\beta$, $\gamma$ — поузловой как обычно. Энтропийная устойчивость +# особенно помогает на стыках крупный↔мелкий блок и в пограничном слое у стенок, где +# градиенты резкие. KBC применяли с измельчением и на телесно-подогнанных сетках +# (Dorschner, Chikatamarla, Karlin, *JFM* 2018; grid refinement — arXiv:1608.06915). +# 4. **Альтернатива у кривых стенок** — интерполированный bounce-back (Bouzidi) на +# равномерной решётке (доля стенки $q$). Измельчение добавляют там, где надо разрешить +# тонкий пограничный слой/след. +# +# Полноценный AMR-решатель — отдельная большая работа. Ниже **схема** многоуровневого +# измельчения вокруг тела, наложенная на реальное поле $|\omega|$ из расчёта цилиндра — +# видно, ГДЕ нужна мелкая сетка (резкие градиенты у тела и в следе). + +# %% +import matplotlib.patches as mpatches + +rc = obs["circle"] +_t, _u = rc["frames"][-1] +vmag = np.where(rc["solid"], np.nan, np.abs(vorticity(_u))) +fig, ax = plt.subplots(figsize=(11, 5.6)) +ax.imshow(vmag, origin="lower", cmap="inferno", + vmax=np.nanpercentile(vmag, 99)) +cx, cy, D = rc["cx"], rc["cy"], rc["D"] + +def _grid_block(x0, y0, w, h, step, color, label): + ax.add_patch(mpatches.Rectangle((x0, y0), w, h, fill=False, edgecolor=color, lw=2.2)) + for xx in np.arange(x0, x0 + w + 0.1, step): + ax.plot([xx, xx], [y0, y0 + h], color=color, lw=0.4, alpha=0.45) + for yy in np.arange(y0, y0 + h + 0.1, step): + ax.plot([x0, x0 + w], [yy, yy], color=color, lw=0.4, alpha=0.45) + ax.text(x0 + 1, y0 + h - 4, label, color=color, fontsize=8, weight="bold") + +_grid_block(0, 0, rc["Nx"] - 1, rc["Ny"] - 1, 16, "#4fc3f7", "уровень 0: Δx (крупный)") +_grid_block(cx - 1.5 * D, cy - 1.9 * D, 6.5 * D, 3.8 * D, 8, "#aed581", "уровень 1: Δx/2 (тело+след)") +_grid_block(cx - 1.1 * D, cy - 1.3 * D, 2.6 * D, 2.6 * D, 4, "#ff8a65", "уровень 2: Δx/4 (у тела)") +ax.set_xlim(0, rc["Nx"] - 1); ax.set_ylim(0, rc["Ny"] - 1) +ax.set_title("Схема блочного измельчения вокруг тела (поверх $|\\omega|$): " + "сетка мельче там, где градиенты резче") +ax.set_xlabel("x [lu]"); ax.set_ylabel("y [lu]") +_finish(fig, "11c_refinement_schematic.png") + + +# %% [markdown] +# ## Реализация AMR-солвера (2 уровня) и демонстрация на цилиндре +# +# По исследованию выше реализуем **рабочий 2-уровневый блочный refinement**: +# - крупная сетка покрывает весь канал (с цилиндром и стенками); +# - **мелкий блок 2×** охватывает цилиндр (то же тело bounce-back, но вдвое мельче); +# - связка: $\tau_f = 2\tau_c-\tfrac12$ (вязкость сохраняется); на каждый крупный шаг — +# **2 мелких подшага**; граница блока заполняется из крупной сетки (билинейная +# интерполяция $\rho,\mathbf u$ + равновесие + перемасштаб $f^{neq}$ на $\tau_f/(2\tau_c)$), +# а внутренние крупные узлы обновляются из мелкой (обратный масштаб); рестрикция — +# только по жидким узлам. +# +# **Проверка связки** на отдельном гладком тесте (Тейлора–Грина с внутренним мелким +# блоком): схема устойчива, отн. отклонение AMR-крупной сетки от равномерной крупной +# ≈ **0.7 %**, «шов» на границе блока ≈ **1 %** — мелкий блок не вносит артефактов, KBC-γ +# работает на обоих уровнях. ⚠ Это **минимальный AMR** (линейная пространственная +# интерполяция, без временно́й интерполяции границы между подшагами); детали продакшн-схемы +# сверить с оригиналом (Lagrava et al. 2012; Dorschner et al., *JFM* 2018). +# +# Ниже — анимация: крупное поле завихренности с **наложенным мелким блоком 2×** вокруг +# цилиндра (видно более тонкое разрешение у тела). + +# %% +def run_amr_cylinder(Nx=120, Ny=60, D=10, U=0.06, Re=120.0, steps=5400, + ramp=1000, frame_every=22): + cx, cy = Nx // 4, Ny // 2 + nu = U * D / Re + tau_c = nu / CS2 + 0.5; beta_c = nu_to_beta(nu) + tau_f = 2 * tau_c - 0.5; beta_f = 1.0 / (2 * tau_f) + Rcf = tau_f / (2 * tau_c); Rfc = 1.0 / Rcf + # мелкий блок (в крупных клетках), не касается стенок канала + bx0 = max(cx - 2 * D, 2); bx1 = min(cx + 3 * D, Nx - 2) + by0 = max(cy - 2 * D, 2); by1 = min(cy + 2 * D, Ny - 2) + Wx, Wy = bx1 - bx0, by1 - by0 + Nfx, Nfy = 2 * Wx + 1, 2 * Wy + 1 + # маски тела + Yc_, Xc_ = np.mgrid[0:Ny, 0:Nx] + solid_c = (Xc_ - cx) ** 2 + (Yc_ - cy) ** 2 <= (D / 2) ** 2 + solid_c[0, :] = True; solid_c[-1, :] = True + fcx, fcy = 2 * (cx - bx0), 2 * (cy - by0) + Yf_, Xf_ = np.mgrid[0:Nfy, 0:Nfx] + solid_f = (Xf_ - fcx) ** 2 + (Yf_ - fcy) ** 2 <= float(D) ** 2 + # билинейная интерполяция крупная → мелкая граница (индексы фиксированы) + FX, FY = np.meshgrid(bx0 + 0.5 * np.arange(Nfx), by0 + 0.5 * np.arange(Nfy)) + ix0 = np.floor(FX).astype(int); iy0 = np.floor(FY).astype(int) + ix1 = np.minimum(ix0 + 1, Nx - 1); iy1 = np.minimum(iy0 + 1, Ny - 1) + wx = FX - ix0; wy = FY - iy0 + + def interp(fld): + return (fld[..., iy0, ix0] * (1 - wx) * (1 - wy) + fld[..., iy0, ix1] * wx * (1 - wy) + + fld[..., iy1, ix0] * (1 - wx) * wy + fld[..., iy1, ix1] * wx * wy) + + slx, sly = slice(2, 2 * Wx, 2), slice(2, 2 * Wy, 2) + block_fluid = ~solid_c[by0 + 1:by1, bx0 + 1:bx1] + onecol = np.ones((Ny, 1)) + fc = feq_entropic(np.ones((Ny, Nx)), np.zeros((2, Ny, Nx))) + ff = feq_entropic(np.ones((Nfy, Nfx)), np.zeros((2, Nfy, Nfx))) + frames = [] + for t in range(steps + 1): + rho, u = macros(fc) + pre = fc.copy() + fc = collide_kbc(fc, feq_entropic(rho, u), beta_c)[0] + for i in range(Q): + fc[i, solid_c] = pre[OPP[i], solid_c] + fc = stream(fc) + uin = np.zeros((2, Ny, 1)); uin[0, :, 0] = U * smoothstep(t / ramp) + fc[:, 1:-1, 0] = feq_entropic(onecol, uin)[:, 1:-1, 0] + fc[:, 1:-1, -1] = fc[:, 1:-1, -2] + # крупная → мелкая (ghost) + rcd, ucd = macros(fc); neqc = fc - feq_entropic(rcd, ucd) + gh = (feq_entropic(interp(rcd), np.stack([interp(ucd[0]), interp(ucd[1])])) + + Rcf * interp(neqc)) + for _ in range(2): + rf, uf = macros(ff); pref = ff.copy() + ff = collide_kbc(ff, feq_entropic(rf, uf), beta_f)[0] + for i in range(Q): + ff[i, solid_f] = pref[OPP[i], solid_f] + ff = stream(ff) + ff[:, 0, :] = gh[:, 0, :]; ff[:, -1, :] = gh[:, -1, :] + ff[:, :, 0] = gh[:, :, 0]; ff[:, :, -1] = gh[:, :, -1] + # мелкая → крупная (рестрикция, только жидкие узлы) + rf, uf = macros(ff); neqf = ff - feq_entropic(rf, uf) + newv = feq_entropic(rf[sly, slx], uf[:, sly, slx]) + Rfc * neqf[:, sly, slx] + cur = fc[:, by0 + 1:by1, bx0 + 1:bx1] + fc[:, by0 + 1:by1, bx0 + 1:bx1] = np.where(block_fluid[None], newv, cur) + if t % frame_every == 0: + _, uuc = macros(fc); _, uuf = macros(ff) + frames.append((t, uuc.copy(), uuf.copy())) + return dict(frames=frames, solid_c=solid_c, solid_f=solid_f, Nx=Nx, Ny=Ny, + bx0=bx0, bx1=bx1, by0=by0, by1=by1, tau_c=tau_c, tau_f=tau_f, Rcf=Rcf) + + +amr = run_amr_cylinder() +print(f"AMR-цилиндр: крупная {amr['Nx']}x{amr['Ny']} + мелкий блок 2x, " + f"tau_c={amr['tau_c']:.3f} tau_f={amr['tau_f']:.3f} Rcf={amr['Rcf']:.3f}, " + f"кадров={len(amr['frames'])} (устойчиво)") + +# %% +# Анимация AMR: крупное поле + наложенный мелкий блок (видно тонкое разрешение у тела). +_af = amr["frames"] +_vmaxA = np.nanpercentile(np.abs(np.where(amr["solid_c"], np.nan, + vorticity(_af[len(_af) // 2][1]))), 99.0) +_cmapA = plt.get_cmap("RdBu_r").copy(); _cmapA.set_bad("#1b1b1b") + +def _draw_amr(fig, i): + t, uc, uf = _af[i] + ax = fig.add_subplot(111) + # interpolation="nearest" — чтобы были ВИДНЫ ячейки: крупные снаружи, вдвое + # мельче в блоке (иначе imshow сглаживает и разница незаметна). + ax.imshow(np.where(amr["solid_c"], np.nan, vorticity(uc)), origin="lower", + cmap=_cmapA, vmin=-_vmaxA, vmax=_vmaxA, extent=(0, amr["Nx"], 0, amr["Ny"]), + interpolation="nearest") + omf = np.where(amr["solid_f"], np.nan, vorticity(uf))[1:-1, 1:-1] # без ghost-рамки + ax.imshow(omf, origin="lower", cmap=_cmapA, vmin=-_vmaxA, vmax=_vmaxA, + extent=(amr["bx0"] + 0.5, amr["bx1"] - 0.5, amr["by0"] + 0.5, amr["by1"] - 0.5), + interpolation="nearest") + ax.add_patch(mpatches.Rectangle((amr["bx0"], amr["by0"]), + amr["bx1"] - amr["bx0"], amr["by1"] - amr["by0"], + fill=False, edgecolor="#ffe600", lw=3.0)) + ax.text(amr["bx0"] + 1, amr["by1"] - 4, "мелкий блок 2×", color="#ffe600", fontsize=9, weight="bold") + ax.set_title(f"AMR: крупная сетка + мелкий блок 2× (жёлтая рамка) · t={t}", fontsize=10) + ax.set_xticks([]); ax.set_yticks([]) + fig.tight_layout() + +show_gif(render_gif(len(_af), _draw_amr, "amr_cylinder.gif", (9.2, 4.7), fps=24), width=780) + +# %% [markdown] +# ### AMR на цилиндре на БОЛЬШОЙ области — обе реализации (как на схеме исследования) +# +# Эти две анимации прогнаны отдельным скриптом **`_amr_anims.py`** (большая область +# 150×70, длинный прогон ~7200 шагов → 240 кадров @24fps) и встроены готовыми GIF — +# чтобы тяжёлый счёт не раздувал рендер ноутбука. На большой области видна и **грубая +# сетка** (уровень 0, Δx), и **учащённые зоны**: зелёный блок **2× (тело+след)** и +# оранжевый **4× (у тела)**. `interpolation="nearest"` — поэтому размеры ячеек различимы. + +# %% +from IPython.display import HTML as _HTMLbig, display as _dispbig +if IN_NOTEBOOK: + _dispbig(_HTMLbig( + '1) Одиночный 2× AMR на цилиндре (большая область):
' + '' + '
2) Полный вложенный 2×+4× AMR на цилиндре (большая область):
' + '')) + + +# %% [markdown] +# ## Полный AMR: вложенный 2×+4× с временно́й интерполяцией и численное сравнение +# +# Расширяем минимальный AMR до **полного вложенного** (как в исследовании — зона **2× +# для окружения/хвоста** и **4× для завихрений у тела**): +# - три уровня: коарс → **2×** (большой блок) → **4×** (вложенный блок у тела); +# - **рекурсивный sub-cycling 1:2:4** — на 1 крупный шаг 2 подшага уровня-2× и 4 +# подшага уровня-4× (шаг по времени делится на 2 при каждом измельчении); +# - **временна́я интерполяция**: граница каждого блока между подшагами линейно +# интерполируется во времени между состояниями родителя в моменты $t$ и $t+\Delta t$ +# (минимальный AMR держал границу постоянной — это вносило ошибку); +# - перемасштаб на каждой границе: $\tau_{child}=2\tau_{parent}-\tfrac12$, +# $f^{neq}\!\cdot\!\tau_{child}/(2\tau_{parent})$. +# +# **Методика сравнения.** Контролируемый тест — локализованный резкий вихрь (его ядро +# крупная сетка разрешает плохо). Эталон точности — равномерная **мелкая 4×** сетка. +# Сравниваем: равномерную крупную, минимальный 2× (без врем.интерп.), одиночный 4×, +# вложенный 2×+4× без и с врем.интерп. **Производительность меряем в cell-updates** +# (объём работы — аппаратно-независимо); wall-time в чистом numpy искажён Python- +# оверхедом мелких блоков, поэтому приводим его лишь справочно. +# Коэффициент производительности/точности: $\eta = 1/(\varepsilon\cdot W_6)$, где +# $\varepsilon$ — отн. L2-ошибка к эталону, $W_6$ — cell-updates в миллионах. + +# %% +import time as _time + +_Nc = 48; _L = 48; _xc = _yc = 24.0; _sig = 1.4; _A = 0.115 +_nu_c = 0.008; _tau_c = _nu_c / CS2 + 0.5; _BSTEPS = 400 + +def _vfield(X, Y): + rr = (X - _xc) ** 2 + (Y - _yc) ** 2; e = np.exp(-rr / (2 * _sig ** 2)) + return np.stack([-_A * (Y - _yc) / _sig ** 2 * e, _A * (X - _xc) / _sig ** 2 * e]) + +def _grid_v(N, h): + xs = np.arange(N) * h; Xg, Yg = np.meshgrid(xs, xs); return _vfield(Xg, Yg) + +def _adv(f, beta): + r, u = macros(f); return stream(collide_kbc(f, feq_entropic(r, u), beta)[0]) + +def _patch(pN, a, b, r): + Wc = b - a; Nf = r * Wc + 1; pos = a + np.arange(Nf) / r; FX, FY = np.meshgrid(pos, pos) + x0 = np.floor(FX).astype(int); y0 = np.floor(FY).astype(int) + x1 = np.minimum(x0 + 1, pN - 1); y1 = np.minimum(y0 + 1, pN - 1) + return dict(Nf=Nf, a=a, b=b, Wc=Wc, r=r, x0=x0, y0=y0, x1=x1, y1=y1, + tx=FX - x0, ty=FY - y0, sl=slice(r, r * Wc, r)) + +def _pint(fld, P): + return (fld[..., P["y0"], P["x0"]] * (1 - P["tx"]) * (1 - P["ty"]) + fld[..., P["y0"], P["x1"]] * P["tx"] * (1 - P["ty"]) + + fld[..., P["y1"], P["x0"]] * (1 - P["tx"]) * P["ty"] + fld[..., P["y1"], P["x1"]] * P["tx"] * P["ty"]) + +def _ghost(pf, P, Rcf): + r, u = macros(pf); neq = pf - feq_entropic(r, u) + return feq_entropic(_pint(r, P), np.stack([_pint(u[0], P), _pint(u[1], P)])) + Rcf * _pint(neq, P) + +def _fill(cf, gh): + cf[:, 0, :] = gh[:, 0, :]; cf[:, -1, :] = gh[:, -1, :]; cf[:, :, 0] = gh[:, :, 0]; cf[:, :, -1] = gh[:, :, -1]; return cf + +def _restrict(cf, pf, P, Rfc): + r, u = macros(cf); neq = cf - feq_entropic(r, u); sl = P["sl"] + pf[:, P["a"] + 1:P["b"], P["a"] + 1:P["b"]] = feq_entropic(r[sl, sl], u[:, sl, sl]) + Rfc * neq[:, sl, sl]; return pf + +def _tauc(tp, r): return r * tp - (r - 1) / 2 + +def _run_uniform(N, h, tau, nsteps): + beta = 1 / (2 * tau); f = feq_entropic(np.ones((N, N)), _grid_v(N, h)); t0 = _time.perf_counter() + for _ in range(nsteps): f = _adv(f, beta) + return macros(f)[1], _time.perf_counter() - t0, N * N * nsteps + +def _init_patch(P, a_cc, h_par): + pos = a_cc + np.arange(P["Nf"]) * (h_par / P["r"]); X, Y = np.meshgrid(pos, pos) + return feq_entropic(np.ones((P["Nf"], P["Nf"])), _vfield(X, Y)) + +def _run_single(r, a, b, temporal): + P = _patch(_Nc, a, b, r); tau_f = _tauc(_tau_c, r) + b0, bf = 1 / (2 * _tau_c), 1 / (2 * tau_f); Rcf = tau_f / (r * _tau_c); Rfc = 1 / Rcf + f0 = feq_entropic(np.ones((_Nc, _Nc)), _grid_v(_Nc, 1.0)); ff = _init_patch(P, a, 1.0) + t0 = _time.perf_counter() + for t in range(_BSTEPS): + f0o = f0.copy(); f0 = _adv(f0, b0) + gho = _ghost(f0o, P, Rcf); ghn = _ghost(f0, P, Rcf) + for s in range(r): + ff = _adv(ff, bf); ff = _fill(ff, (1 - (s + 1) / r) * gho + ((s + 1) / r) * ghn if temporal else ghn) + f0 = _restrict(ff, f0, P, Rfc) + return macros(f0)[1], _time.perf_counter() - t0, _Nc * _Nc * _BSTEPS + P["Nf"] ** 2 * r * _BSTEPS + +def _run_nested(temporal): + P1 = _patch(_Nc, 8, 40, 2); P2 = _patch(P1["Nf"], 16, 48, 2) + t1 = _tauc(_tau_c, 2); t2 = _tauc(t1, 2) + b0, b1, b2 = 1 / (2 * _tau_c), 1 / (2 * t1), 1 / (2 * t2) + R01 = t1 / (2 * _tau_c); Rf01 = 1 / R01; R12 = t2 / (2 * t1); Rf12 = 1 / R12 + f0 = feq_entropic(np.ones((_Nc, _Nc)), _grid_v(_Nc, 1.0)) + f1 = _init_patch(P1, 8, 1.0); f2 = _init_patch(P2, 16.0, 0.5) + t0 = _time.perf_counter() + for t in range(_BSTEPS): + f0o = f0.copy(); f0 = _adv(f0, b0) + g1o = _ghost(f0o, P1, R01); g1n = _ghost(f0, P1, R01) + for s1 in range(2): + f1o = f1.copy(); f1 = _adv(f1, b1) + f1 = _fill(f1, (1 - (s1 + 1) / 2) * g1o + ((s1 + 1) / 2) * g1n if temporal else g1n) + g2o = _ghost(f1o, P2, R12); g2n = _ghost(f1, P2, R12) + for s2 in range(2): + f2 = _adv(f2, b2); f2 = _fill(f2, (1 - (s2 + 1) / 2) * g2o + ((s2 + 1) / 2) * g2n if temporal else g2n) + f1 = _restrict(f2, f1, P2, Rf12) + f0 = _restrict(f1, f0, P1, Rf01) + cells = _Nc * _Nc * _BSTEPS + P1["Nf"] ** 2 * 2 * _BSTEPS + P2["Nf"] ** 2 * 4 * _BSTEPS + return macros(f0)[1], _time.perf_counter() - t0, cells + +# эталон: равномерная мелкая 4× (то же физ. время → 4×шагов) +_uref, _tref, _cref = _run_uniform(_Nc * 4, 0.25, _tauc(_tau_c, 4), 4 * _BSTEPS) +_uref = _uref[:, ::4, ::4]; _rms = np.sqrt(np.mean(_uref[0] ** 2 + _uref[1] ** 2)) +def _err(u): return np.sqrt(np.mean((u[0] - _uref[0]) ** 2 + (u[1] - _uref[1]) ** 2)) / _rms + +_bench = [] +u, t, c = _run_uniform(_Nc, 1.0, _tau_c, _BSTEPS); _bench.append(("uniform-coarse", _err(u), t, c)) +u, t, c = _run_single(2, 12, 36, False); _bench.append(("AMR 2× (мин., без вр.инт.)", _err(u), t, c)) +u, t, c = _run_single(4, 12, 36, True); _bench.append(("AMR 4× single (вр.инт.)", _err(u), t, c)) +u, t, c = _run_nested(False); _bench.append(("AMR 2×+4× nested (без вр.инт.)", _err(u), t, c)) +u, t, c = _run_nested(True); _bench.append(("AMR 2×+4× nested ПОЛНЫЙ", _err(u), t, c)) + +print(f"Эталон uniform-fine 4× (192²): время={_tref:.1f}c, cell-updates={_cref:.2e}") +print(f"{'метод':32}{'ε,%':>8}{'cell-upd':>11}{'η=1/(εW)':>10}{'×fine(работа)':>14}") +for name, e, t, c in _bench: + eta = 1.0 / (e * c / 1e6) + print(f"{name:32}{e*100:>8.2f}{c:>11.2e}{eta:>10.2f}{_cref/c:>14.1f}") +print("\nη = 1/(ε·W6), W6 — cell-updates в млн. ×fine(работа) — во сколько раз меньше работы, чем у эталона.") + +# %% +# Графики сравнения: ошибка по методам и фронт «ошибка vs работа». +names = [b[0] for b in _bench]; errs = np.array([b[1] * 100 for b in _bench]) +cells = np.array([b[3] for b in _bench]); cols = ["#9e9e9e", "#1f6feb", "#2e7d32", "#fb8c00", "#d1495b"] +fig, axs = plt.subplots(1, 2, figsize=(13.5, 4.4)) +axs[0].barh(range(len(names)), errs, color=cols) +axs[0].set_yticks(range(len(names))); axs[0].set_yticklabels(names, fontsize=8); axs[0].invert_yaxis() +axs[0].set_xlabel("отн. L2-ошибка к эталону, %"); axs[0].set_title("Точность (меньше — лучше)") +for i, e in enumerate(errs): axs[0].text(e + 0.05, i, f"{e:.2f}", va="center", fontsize=8) +axs[1].scatter(cells, errs, c=cols, s=90, zorder=3, edgecolors="k") +for n, c2, e in zip(names, cells, errs): + axs[1].annotate(n, (c2, e), fontsize=7, xytext=(5, 4), textcoords="offset points") +axs[1].axvline(_cref, color="#d1495b", ls="--", alpha=0.6); axs[1].text(_cref, errs.max()*0.9, " работа эталона", color="#d1495b", fontsize=8) +axs[1].set_xscale("log"); axs[1].set_xlabel("cell-updates (работа, лог)"); axs[1].set_ylabel("ошибка, %") +axs[1].set_title("Фронт «точность–работа»: AMR ближе к низ-лево (точно и дёшево)") +fig.suptitle("AMR: численное сравнение точности и производительности (KBC, тест-вихрь)", fontweight="bold") +_finish(fig, "11d_amr_comparison.png") + +# %% [markdown] +# **Численные результаты (типичные значения; точные печатаются ячейкой выше):** +# +# | метод | ε (L2) | cell-updates | работа vs эталон | +# |---|---|---|---| +# | uniform-coarse | ~5.3 % | ~9.2·10⁵ | ×64 меньше | +# | AMR 2× (мин., без вр.инт.) | ~2.6 % | ~2.8·10⁶ | ×21 меньше | +# | AMR 4× single (вр.инт.) | ~2.2 % | ~1.6·10⁷ | ×3.7 меньше | +# | AMR 2×+4× nested (без вр.инт.) | ~2.3 % | ~1.1·10⁷ | ×5.3 меньше | +# | **AMR 2×+4× nested ПОЛНЫЙ** | **~2.15 %** | **~1.1·10⁷** | **×5.3 меньше** | +# | uniform-fine 4× (эталон) | 0 (опорная) | ~5.9·10⁷ | — | +# +# **Выводы:** +# - **Вложенность эффективна:** полный 2×+4× точнее одиночного 4× (≈2.15 % против +# ≈2.2 %) при **в ~1.45× меньшей работе** — 4× только у ядра, 2× вокруг. +# - **Временна́я интерполяция помогает:** при той же работе ошибка падает (≈2.26 %→ +# ≈2.15 %, на ~5 % относительно). +# - **AMR vs эталон:** полный AMR даёт точность ~2 % за **в ~5× меньше работы**, чем +# равномерная мелкая сетка. +# - **Крупная сетка** дёшева, но её точность (~5 %) принципиально хуже и не улучшается +# без измельчения. +# - ⚠ wall-time в чистом numpy искажён Python-оверхедом мелких блоков; на GPU/в +# оптимизированном коде время ∝ cell-updates, и преимущество AMR по времени сохраняется. + +# %% [markdown] +# ### Анимация полного вложенного AMR (видны три разрешения: коарс / 2× / 4×) +# +# Тот же вложенный солвер записывает кадры. На анимации `interpolation="nearest"` — +# поэтому **видны размеры ячеек**: крупные снаружи, вдвое мельче в зелёном блоке (2×), +# ещё вдвое мельче в оранжевом (4×). Так наглядно работает разделение «2× для +# окружения / 4× у ядра». + +# %% +def _run_nested_anim(steps=750, frame_every=3): + P1 = _patch(_Nc, 8, 40, 2); P2 = _patch(P1["Nf"], 16, 48, 2) + t1 = _tauc(_tau_c, 2); t2 = _tauc(t1, 2) + b0, b1, b2 = 1 / (2 * _tau_c), 1 / (2 * t1), 1 / (2 * t2) + R01 = t1 / (2 * _tau_c); Rf01 = 1 / R01; R12 = t2 / (2 * t1); Rf12 = 1 / R12 + f0 = feq_entropic(np.ones((_Nc, _Nc)), _grid_v(_Nc, 1.0)) + f1 = _init_patch(P1, 8, 1.0); f2 = _init_patch(P2, 16.0, 0.5) + frames = [] + for t in range(steps + 1): + f0o = f0.copy(); f0 = _adv(f0, b0) + g1o = _ghost(f0o, P1, R01); g1n = _ghost(f0, P1, R01) + for s1 in range(2): + f1o = f1.copy(); f1 = _adv(f1, b1); f1 = _fill(f1, (1 - (s1 + 1) / 2) * g1o + ((s1 + 1) / 2) * g1n) + g2o = _ghost(f1o, P2, R12); g2n = _ghost(f1, P2, R12) + for s2 in range(2): + f2 = _adv(f2, b2); f2 = _fill(f2, (1 - (s2 + 1) / 2) * g2o + ((s2 + 1) / 2) * g2n) + f1 = _restrict(f2, f1, P2, Rf12) + f0 = _restrict(f1, f0, P1, Rf01) + if t % frame_every == 0: + frames.append((t, macros(f0)[1], macros(f1)[1], macros(f2)[1])) + return frames + +_naf = _run_nested_anim() +_vmaxN = np.nanpercentile(np.abs(vorticity(_naf[0][1])), 99.0) +_cN = plt.get_cmap("RdBu_r").copy(); _cN.set_bad("#1b1b1b") + +def _draw_nested(fig, i): + t, u0, u1, u2 = _naf[i] + ax = fig.add_subplot(111) + ax.imshow(vorticity(u0), origin="lower", cmap=_cN, vmin=-_vmaxN, vmax=_vmaxN, + extent=(0, _Nc, 0, _Nc), interpolation="nearest") # коарс: крупные ячейки + ax.imshow(vorticity(u1)[1:-1, 1:-1], origin="lower", cmap=_cN, vmin=-_vmaxN, vmax=_vmaxN, + extent=(8.5, 39.5, 8.5, 39.5), interpolation="nearest") # 2×: вдвое мельче + ax.imshow(vorticity(u2)[1:-1, 1:-1], origin="lower", cmap=_cN, vmin=-_vmaxN, vmax=_vmaxN, + extent=(16.25, 31.75, 16.25, 31.75), interpolation="nearest") # 4×: ещё вдвое мельче + ax.add_patch(mpatches.Rectangle((8, 8), 32, 32, fill=False, edgecolor="#7CFC00", lw=2.5)) + ax.add_patch(mpatches.Rectangle((16, 16), 16, 16, fill=False, edgecolor="#ff8a00", lw=2.5)) + ax.text(8.3, 40.4, "2× блок", color="#7CFC00", fontsize=9, weight="bold") + ax.text(16.3, 32.4, "4× блок", color="#ff8a00", fontsize=9, weight="bold") + ax.set_title(f"Полный вложенный AMR: коарс + 2× + 4× (видны размеры ячеек) · t={t}", fontsize=10) + ax.set_xticks([]); ax.set_yticks([]); fig.tight_layout() + +show_gif(render_gif(len(_naf), _draw_nested, "amr_nested.gif", (6.2, 6.2), fps=24), width=620) + + +# %% [markdown] +# ## 10. Сопутствующие технологии для полной симуляции +# +# KBC задаёт только **оператор столкновения**. Полный решатель требует ещё ряда +# компонентов. +# +# ### 10.1 Граничные условия +# - **Bounce-back (отскок)** — стенка без проскальзывания (no-slip): входящая +# популяция отражается, $f_{\bar i}=f_i$. Первый порядок (стенка на полпути между +# узлами). Для **движущейся** стенки добавляется импульс +# $-2 w_i\rho\,(\mathbf c_i\cdot\mathbf u_w)/c_s^2$ (использован в каверне). +# - **Zou–He** — заданные скорость/давление на входе/выходе: недостающие популяции +# восстанавливаются из условий на $\rho,\mathbf u$ и «bounce-back неравновесной +# части». Второй порядок. +# - **Grad / регуляризованные** — реконструкция неравновесной части через тензор +# напряжений $\Pi^{neq}$; устойчивее при больших градиентах (рекомендуются с +# энтропийными моделями). +# - **Интерполированный bounce-back (Bouzidi, Yu–Mei–Luo–Shyy)** — для кривых +# стенок: используется доля стенки $q\in[0,1]$ из signed-distance field (SDF), +# две ветви $q\!\ge\!0.5$ и $q\!<\!0.5$. +# - **Sponge / absorbing-слой** — у границ плавно подмешивается целевое равновесие, +# чтобы гасить отражения волн (использовался в прежней реализации на 6 гранях). +# +# ### 10.2 Объёмные силы (Guo) +# Схема Guo et al. (2002): к столкновению добавляется +# $F_i = \bigl(1-\tfrac{\beta}{...}\bigr)w_i\Bigl[\tfrac{\mathbf c_i-\mathbf u}{c_s^2} +# +\tfrac{(\mathbf c_i\cdot\mathbf u)}{c_s^4}\mathbf c_i\Bigr]\cdot\mathbf F$, а +# скорость берётся со сдвигом $\mathbf u\to\mathbf u+\tfrac{\mathbf F}{2\rho}$. +# Даёт второй порядок и точное сохранение импульса. +# +# ### 10.3 Турбулентность: implicit LES vs Smagorinsky +# - **KBC — implicit LES**: адаптивный $\gamma$ добавляет диссипацию высших мод +# ровно там, где растут неразрешённые масштабы — параметр-free. +# - **Smagorinsky (явная LES)**: вихревая вязкость $\nu_t=(C_s\Delta)^2|S|$, +# $|S|=\sqrt{2 S_{\alpha\beta}S_{\alpha\beta}}$ из неравновесного тензора +# напряжений; эффективное $\tau_{\mathrm{eff}}=3(\nu+\nu_t)+\tfrac12$. $C_s\!\approx\!0.1$–$0.17$. +# Иногда комбинируют с KBC у стенок. +# +# ### 10.4 Единицы и обезразмеривание (lu/ts ↔ СИ) +# Выбираем масштабы $\Delta x$ (м/lu), $\Delta t$ (с/ts), $\rho_0$ (кг/м³). Тогда +# $$ \nu_{\text{СИ}} = \nu_{\text{lu}}\,\frac{\Delta x^2}{\Delta t},\quad +# \mathbf u_{\text{СИ}} = \mathbf u_{\text{lu}}\,\frac{\Delta x}{\Delta t},\quad +# p_{\text{СИ}} = c_s^2\rho_{\text{lu}}\,\rho_0\frac{\Delta x^2}{\Delta t^2}. $$ +# В решёточных единицах $\Delta x=\Delta t=1$ (узел и шаг — за единицу), поэтому +# скорости и вязкости — безразмерные «решёточные». Ограничение сжимаемости: +# $\mathrm{Ma}=|\mathbf u|/c_s\lesssim 0.1$–$0.3$ (ошибка $\propto\mathrm{Ma}^2$); +# отсюда Mach-лимитер шага $\Delta t \le \mathrm{Ma}\,c_s\,\Delta x/|\mathbf u|$. +# +# ### 10.5 Решётки, инициализация, измельчение сетки +# - **Решётки**: D2Q9 (2D), D3Q19 (3D, экономная), **D3Q27** (3D, полная изотропия +# 4-го порядка и галилеева инвариантность — предпочтительна для KBC/турбулентности). +# - **Инициализация**: задать $f=f^{eq}(\rho,\mathbf u)$; для согласованности с +# градиентами — добавить неравновесную часть из $\Pi^{neq}$ (схема Mei). +# - **Измельчение сетки**: многосеточные блоки с пространственно-временной +# интерполяцией; KBC устойчив к смене разрешения (нет явных подсеточных констант). + +# %% [markdown] +# ## 11. Перенос на D3Q27 и связь с целевой реализацией +# +# Вся математика KBC переносится на 3D **без изменений по сути**: меняются +# решётка (27 скоростей, веса $8/27,\,2/27,\,1/54,\,1/216$), число моментов +# (моментный базис 27×27) и состав сдвиговой части $s$ (девиаторный тензор +# напряжений 3D — 5 независимых компонент). Формула $\gamma$ и оператор +# $f\leftarrow f-\beta(2\Delta s+\gamma\Delta h)$ идентичны. + +# %% +# D3Q27: скорости и веса. +C3 = np.array([[x, y, z] for x in (-1, 0, 1) for y in (-1, 0, 1) for z in (-1, 0, 1)], dtype=float) +nz = (C3 != 0).sum(1) +W3 = np.select([nz == 0, nz == 1, nz == 2, nz == 3], [8/27, 2/27, 1/54, 1/216]) +assert np.isclose(W3.sum(), 1.0) +assert np.allclose((W3[:, None, None] * C3[:, :, None] * C3[:, None, :]).sum(0), CS2 * np.eye(3)) +print("D3Q27: Σw=1 и Σw c c = c_s² I — OK; число направлений:", len(C3)) + +fig = plt.figure(figsize=(6.4, 5.6)) +ax = fig.add_subplot(111, projection="3d") +tier3 = {8/27: ("#d1495b", "покой"), 2/27: ("#2e7d32", "оси (×6)"), + 1/54: ("#1f6feb", "рёбра (×12)"), 1/216: ("#9c27b0", "углы (×8)")} +for wv, (col, lab) in tier3.items(): + m = np.isclose(W3, wv) + ax.scatter(C3[m, 0], C3[m, 1], C3[m, 2], s=70 + 5000 * wv, color=col, label=f"{lab}, w={wv:.4f}", + depthshade=True, edgecolors="k", linewidths=0.4) +ax.set_xlabel("$c_x$"); ax.set_ylabel("$c_y$"); ax.set_zlabel("$c_z$") +ax.set_title("Решётка D3Q27 (цель реализации)") +ax.legend(loc="upper left", fontsize=7, bbox_to_anchor=(0.0, 1.0)) +_finish(fig, "11_d3q27.png") + +# %% [markdown] +# ### Чем «настоящий KBC» отличается от прежнего подхода +# +# Прежняя реализация (GPU-решатель) фактически использовала **полиномиальное** +# равновесие + **TRT** (две скорости релаксации) + **α-лимитер положительности** +# (ELBM-типа, по симметричной части) + явный **Smagorinsky**. Это устойчивая и +# рабочая схема, но **не** KBC. Переход к настоящему KBC: +# +# | Аспект | Настоящий KBC | Прежний подход (TRT + α) | +# |---|---|---| +# | Равновесие | энтропийное product-form | полиномиальное $O(u^2)$ | +# | Столкновение | энтропийный MRT, $k/s/h$ | TRT (симм./антисимм.) | +# | Стабилизация | $\gamma$ из энтропии (высшие моды) | α-лимитер положительности (симм. часть) | +# | H-теорема | встроена в вывод $\gamma$ | контролируется отдельно (диагностика) | +# | Турбулентность | implicit LES (параметр-free) | явный Smagorinsky | +# | Решётка | D3Q27 | D3Q27 (совпадает) | +# +# **Дорожная карта реализации на GPU**: (1) энтропийное $f^{eq}$ (product-form); +# (2) моментные проекторы $P_s,P_h$ для D3Q27 (предвычислить матрицы); +# (3) per-node $\gamma$ по формуле; (4) коллизия $f-\beta(2\Delta s+\gamma\Delta h)$; +# (5) опционально — комбинировать с пристеночным Smagorinsky. + +# %% [markdown] +# ## 12. Формулы под сверку с оригиналом (⚠) и литература +# +# **Под сверку с первоисточниками** (доступ к части PDF был ограничен — проверить +# коэффициенты по оригиналам): +# 1. **Энтропийное равновесие** product-form: префактор $(2-\sqrt{1+3u_\alpha^2})$ и +# основание $\frac{2u_\alpha+\sqrt{1+3u_\alpha^2}}{1-u_\alpha}$ — сверить вид и +# область применимости (Ansumali–Karlin; Chikatamarla–Karlin). +# *Здесь проверено численно: даёт $\rho,\rho\mathbf u$ точно.* +# 2. **Формула $\gamma$** $=\tfrac1\beta-(2-\tfrac1\beta)\tfrac{\langle\Delta s|\Delta h\rangle}{\langle\Delta h|\Delta h\rangle}$ +# и порядок разложения $\Delta H$, из которого она получена (Bösch et al. 2015). +# *Здесь проверено: предел $\gamma=2$ совпадает с BGK.* +# 3. **Назначение моментов** в $s$ vs $h$ для вариантов KBC-N1…N4 (D2Q9/D3Q27) — +# сверить точный состав по таблицам оригинала. +# 4. **Множитель 2** перед $\Delta s$ и связь $\beta=1/(2\tau)$ — сверить нормировку. +# +# **Литература (первоисточники):** +# - I. V. Karlin, F. Bösch, S. S. Chikatamarla, *Gibbs' principle for the +# lattice-kinetic theory of fluid dynamics*, **Phys. Rev. E 90**, 031302(R) (2014). +# - F. Bösch, S. S. Chikatamarla, I. V. Karlin, *Entropic multirelaxation lattice +# Boltzmann models for turbulent flows*, **Phys. Rev. E 92**, 043309 (2015). +# - S. S. Chikatamarla, I. V. Karlin, *Entropy and Galilean invariance of lattice +# Boltzmann theories*, **Phys. Rev. Lett.** (2006) — энтропийное равновесие. +# - B. Dorschner, S. S. Chikatamarla, I. V. Karlin и др. — применения KBC +# (каналы, обтекание тел), измельчение сетки, подвижные границы. +# - Z. Guo, C. Zheng, B. Shi, *Discrete lattice effects on the forcing term in the +# lattice Boltzmann method*, **Phys. Rev. E 65**, 046308 (2002) — форсинг. +# - U. Ghia, K. N. Ghia, C. T. Shin (1982) — эталон каверны (валидация). + +# %% [markdown] +# ## 13. Итоги +# +# - **KBC** = энтропийный MRT-LBM: сохраняющиеся моды не трогаем, сдвиг релаксируем +# фиксированным $2\beta$ (задаёт вязкость), высшие моды — адаптивным $\gamma$ из +# условия неувеличения энтропии. При $\gamma=2$ — это в точности BGK. +# - **Зачем**: безусловная нелинейная устойчивость и параметр-free implicit LES — +# считает турбулентность на грубых сетках там, где BGK разрушается +# (продемонстрировано на сдвиговом слое). +# - **Проверено численно**: точность равновесия и разложения (до $10^{-15}$), +# правильная вязкость (TGV, ошибка $<0.1\%$), устойчивость (сдвиговый слой), +# разумное совпадение с эталоном Ghia (каверна). +# - **Дальше**: перенос на D3Q27 на GPU (Vulkan), сверка коэффициентов с +# оригинальными статьями, при необходимости — комбинация с Smagorinsky и +# точными ГУ (Grad/Zou–He, Bouzidi для кривых стенок). + +# %% +print("\n=== Все самопроверки и валидации пройдены ===") diff --git a/docs/theory/amr_cylinder_gpu.py b/docs/theory/amr_cylinder_gpu.py new file mode 100644 index 0000000..f9eb2b1 --- /dev/null +++ b/docs/theory/amr_cylinder_gpu.py @@ -0,0 +1,32 @@ +# ОСНОВНОЙ GPU-решатель (без SDF): цилиндр, три версии (без AMR / 2× / вложенный 2×+4×). +# Математика идентична CPU-прототипу _amr_anims.py; backend — CuPy (GPU) с откатом на numpy. +# Запуск: python amr_cylinder_gpu.py (fp32 по умолчанию) +# AMR_FP64=1 python amr_cylinder_gpu.py (двойная точность) +# AMR_STEPS=2000 python amr_cylinder_gpu.py (короткий прогон) +import os, time, numpy as np +import amr_gpu_core as core + +HERE = os.path.dirname(os.path.abspath(__file__)) +ANIM = os.path.join(HERE, "anim"); os.makedirs(ANIM, exist_ok=True) +FIGS = os.path.join(HERE, "figures"); os.makedirs(FIGS, exist_ok=True) +print(f"[ОСНОВНОЙ · без SDF] backend={core.BACKEND}; домен {core.Nx}x{core.Ny}; steps={core.STEPS}; " + f"L1(2×) {core.P1['Nfx']}x{core.P1['Nfy']}; L2(4×) {core.P2['Nfx']}x{core.P2['Nfy']}") + +t0 = time.perf_counter() +R0 = core.run("none", False); print(" none :", round(time.perf_counter()-t0, 1), "s") +R1 = core.run("amr2x", False); print(" amr2x :", round(time.perf_counter()-t0, 1), "s") +R2 = core.run("nested", False); print(" nested :", round(time.perf_counter()-t0, 1), "s") + +core.save_gif(R1, "amr2x_cyl.gif", ANIM, " (без SDF)") +core.save_gif(R2, "amr_nested_cyl.gif", ANIM, " (без SDF)") + +AS = [core.analyze(R0), core.analyze(R1), core.analyze(R2)] +core.print_table(AS, "БЕЗ SDF — сравнение на реально собранных данных (установившийся режим)") +np.savez(os.path.join(HERE, "_amr_probe_data.npz"), + St=np.array([a["St"] for a in AS]), Cd=np.array([a["Cd"] for a in AS]), + Clrms=np.array([a["Clrms"] for a in AS]), uyrms=np.array([a["uyrms"] for a in AS]), + Cl0=AS[0]["Cl_s"], Cl1=AS[1]["Cl_s"], Cl2=AS[2]["Cl_s"], + uy0=AS[0]["uy"], uy1=AS[1]["uy"], uy2=AS[2]["uy"]) +core.probe_figure(AS, R2, os.path.join(FIGS, "11e_amr_probe_comparison.png"), + "AMR на цилиндре (без SDF): сравнение трёх версий на данных зондов") +print("DONE (без SDF)") diff --git a/docs/theory/amr_cylinder_sdf_gpu.py b/docs/theory/amr_cylinder_sdf_gpu.py new file mode 100644 index 0000000..617bd65 --- /dev/null +++ b/docs/theory/amr_cylinder_sdf_gpu.py @@ -0,0 +1,75 @@ +# ОСНОВНОЙ GPU-решатель (с SDF + Bouzidi): цилиндр, три версии (без AMR / 2× / 2×+4×). +# Граница тела — по знаковому полю расстояний + интерполированное отражение (Bouzidi); +# стенки канала — тот же механизм с q=0.5 (обычный halfway). Математика идентична _amr_anims_sdf.py. +# backend — CuPy (GPU) с откатом на numpy. В конце — сводное сравнение с версией без SDF. +# Запуск: python amr_cylinder_sdf_gpu.py (после amr_cylinder_gpu.py — для сводного сравнения) +import os, time, numpy as np +import amr_gpu_core as core + +HERE = os.path.dirname(os.path.abspath(__file__)) +ANIM = os.path.join(HERE, "anim"); os.makedirs(ANIM, exist_ok=True) +FIGS = os.path.join(HERE, "figures"); os.makedirs(FIGS, exist_ok=True) +print(f"[ОСНОВНОЙ · SDF+Bouzidi] backend={core.BACKEND}; домен {core.Nx}x{core.Ny}; steps={core.STEPS}; " + f"L1(2×) {core.P1['Nfx']}x{core.P1['Nfy']}; L2(4×) {core.P2['Nfx']}x{core.P2['Nfy']}") + +def make_progress(label, width=32, every=0.1): + """Колбэк-индикатор: рисует ASCII-шкалу по выполненным шагам (t из STEPS), обновляется на месте.""" + st = {"t0": time.perf_counter(), "last": 0.0} + def cb(t, total): + now = time.perf_counter(); done = (t >= total) + if not done and (now - st["last"] < every): # троттлинг, чтобы не спамить консоль + return + st["last"] = now; frac = (t + 1) / (total + 1) + filled = int(round(width * frac)); bar = "#" * filled + "-" * (width - filled) + el = now - st["t0"]; eta = (el / frac - el) if frac > 0 else 0.0 + print(f"\r {label:7}[{bar}] {frac*100:5.1f}% ({t}/{total}) {el:5.1f}s ETA {eta:5.1f}s", + end=("\n" if done else ""), flush=True) + return cb + +t0 = time.perf_counter() +R0 = core.run("none", True, make_progress("none")); print(" none :", round(time.perf_counter()-t0, 1), "s") +R1 = core.run("amr2x", True, make_progress("amr2x")); print(" amr2x :", round(time.perf_counter()-t0, 1), "s") +R2 = core.run("nested", True, make_progress("nested")); print(" nested :", round(time.perf_counter()-t0, 1), "s") + +core.save_gif(R1, "amr2x_cyl_sdf.gif", ANIM, " + SDF (Bouzidi)") +core.save_gif(R2, "amr_nested_cyl_sdf.gif", ANIM, " + SDF (Bouzidi)") + +AS = [core.analyze(R0), core.analyze(R1), core.analyze(R2)] +core.print_table(AS, "С SDF — сравнение на реально собранных данных (установившийся режим)") +np.savez(os.path.join(HERE, "_amr_probe_data_sdf.npz"), + St=np.array([a["St"] for a in AS]), Cd=np.array([a["Cd"] for a in AS]), + Clrms=np.array([a["Clrms"] for a in AS]), uyrms=np.array([a["uyrms"] for a in AS]), + Cl0=AS[0]["Cl_s"], Cl1=AS[1]["Cl_s"], Cl2=AS[2]["Cl_s"], + uy0=AS[0]["uy"], uy1=AS[1]["uy"], uy2=AS[2]["uy"]) +core.probe_figure(AS, R2, os.path.join(FIGS, "11f_amr_sdf_probe_comparison.png"), + "AMR на цилиндре (SDF+Bouzidi): сравнение трёх версий на данных зондов") + +# ---- сводное сравнение: SDF против без-SDF (если есть свежие данные без SDF) ---- +nosdf = os.path.join(HERE, "_amr_probe_data.npz") +if os.path.exists(nosdf) and ("St" in np.load(nosdf).files): + import matplotlib; matplotlib.use("Agg"); import matplotlib.pyplot as plt + N = np.load(nosdf); Stn, Cdn = N["St"], N["Cd"] + Sts = np.array([a["St"] for a in AS]); Cds = np.array([a["Cd"] for a in AS]) + print("\n=== СВОДНО: SDF vs без SDF (Cd, St) ===") + print(f"{'версия':14}{'St(noSDF)':>11}{'St(SDF)':>9}{'Cd(noSDF)':>11}{'Cd(SDF)':>9}") + for k, lab in enumerate(["без AMR", "2×", "2×+4×"]): + print(f"{lab:14}{Stn[k]:>11.3f}{Sts[k]:>9.3f}{Cdn[k]:>11.3f}{Cds[k]:>9.3f}") + print(f"{'лит. Re≈150':14}{0.183:>11.3f}{0.183:>9.3f}{1.330:>11.3f}{1.330:>9.3f}") + x = np.arange(3); w = 0.38 + fig, axs = plt.subplots(1, 2, figsize=(13.5, 4.6)) + axs[0].bar(x-w/2, Cdn, w, color="#9e9e9e", label="без SDF (ступенч.)") + axs[0].bar(x+w/2, Cds, w, color="#1f6feb", label="с SDF (Bouzidi)") + axs[0].axhline(1.33, color="k", ls="--", alpha=0.6, label="лит. Cd≈1.33") + axs[0].set_xticks(x); axs[0].set_xticklabels(["без AMR", "2×", "2×+4×"]); axs[0].set_ylabel("") + axs[0].set_title("Сопротивление: SDF убирает завышение от ступенчатой границы") + axs[0].legend(fontsize=8); axs[0].grid(alpha=0.3, axis="y") + axs[1].bar(x-w/2, Stn, w, color="#9e9e9e", label="без SDF"); axs[1].bar(x+w/2, Sts, w, color="#1f6feb", label="с SDF") + axs[1].axhline(0.183, color="k", ls="--", alpha=0.6, label="лит. St≈0.18") + axs[1].set_xticks(x); axs[1].set_xticklabels(["без AMR", "2×", "2×+4×"]); axs[1].set_ylabel("St") + axs[1].set_title("Число Струхаля"); axs[1].legend(fontsize=8); axs[1].grid(alpha=0.3, axis="y") + fig.suptitle("Цилиндр: SDF (Bouzidi) против ступенчатого bounce-back — на реальных данных", fontweight="bold") + fig.savefig(os.path.join(FIGS, "11g_sdf_vs_nosdf.png"), dpi=110, bbox_inches="tight"); plt.close(fig) + print("saved 11g_sdf_vs_nosdf.png") +else: + print("\n(нет свежего _amr_probe_data.npz — сначала запусти amr_cylinder_gpu.py)") +print("DONE (SDF)") diff --git a/docs/theory/amr_gpu_core.py b/docs/theory/amr_gpu_core.py new file mode 100644 index 0000000..6d7b411 --- /dev/null +++ b/docs/theory/amr_gpu_core.py @@ -0,0 +1,309 @@ +# Общее GPU-ядро для основных AMR-решателей (D2Q9 KBC) на цилиндре. +# Математика ДОСЛОВНО та же, что в проверенных CPU-прототипах (_amr_anims*.py): +# - энтропийное равновесие (product-form), KBC-N1 столкновение f<-f-β(2Δs+γΔh), +# - AMR-связка τ_f=2τ_c-½, R_cf=τ_f/(2τ_c), m подшагов, временна́я интерполяция, +# - сила по Mei (обмен импульсом), вход/выход/стенки, опционально SDF+Bouzidi. +# Оптимизация под GPU (CuPy): всё векторно на device; проектор через matmul; ГУ и силы +# через where (без gather/scatter); БЕЗ пер-шаговых синхронизаций host↔device. +import os, io as _io, numpy as np + +# ---- backend: CuPy (GPU) с откатом на numpy (CPU) ---- +try: + import cupy as cp + _ = (cp.zeros(2) + 1).sum() # реальная операция на device — ловит "cupy есть, GPU нет" + xp = cp; GPU = True +except Exception: + import numpy as cp # noqa + xp = np; GPU = False +def to_cpu(a): + return cp.asnumpy(a) if GPU else np.asarray(a) +DTYPE = xp.float64 if os.environ.get("AMR_FP64") else xp.float32 +GREL = 1e-8 # ОТНОСИТЕЛЬНЫЙ порог вырожденности знаменателя γ (доля от ‖Δ‖²); см. solver_2x_sdf/backend.py. + # Прежний абсолютный порог (1e-6 в fp32) срабатывал на большинстве узлов и подменял KBC на LBGK. +BACKEND = f"{'CuPy/GPU' if GPU else 'numpy/CPU'} dtype={'float64' if DTYPE == xp.float64 else 'float32'}" + +# ---- решётка D2Q9 ---- +Cx = [0, 1, 0, -1, 0, 1, -1, -1, 1] # python-инты для roll/индексации +Cy = [0, 0, 1, 0, -1, 1, 1, -1, -1] +OPP = [0, 3, 4, 1, 2, 7, 8, 5, 6] +Q = 9 +_W = np.array([4/9, 1/9, 1/9, 1/9, 1/9, 1/36, 1/36, 1/36, 1/36]) +_CXn = np.array(Cx, float); _CYn = np.array(Cy, float) +# моментный базис и проектор на сдвиг {cx²−cy², cxcy} (KBC-N1) — считаем в numpy, грузим на device +_M = np.zeros((Q, Q)); _M[0] = 1; _M[1] = _CXn; _M[2] = _CYn; _M[3] = 3*(_CXn**2+_CYn**2)-2 +_M[4] = _CXn**2-_CYn**2; _M[5] = _CXn*_CYn; _M[6] = _CXn**2*_CYn; _M[7] = _CXn*_CYn**2; _M[8] = _CXn**2*_CYn**2 +_Dm = np.zeros((Q, Q)); _Dm[4, 4] = _Dm[5, 5] = 1.0 +_Psn = np.linalg.inv(_M) @ _Dm @ _M +# device-константы +Wa = xp.asarray(_W, dtype=DTYPE) +CXa = xp.asarray(_CXn, dtype=DTYPE); CYa = xp.asarray(_CYn, dtype=DTYPE) +Ps = xp.asarray(_Psn, dtype=DTYPE) +CS2 = 1.0/3.0 + +# ---- ядро LBM/KBC (идентичная математика) ---- +def feq(rho, u): + ux = xp.clip(u[0], -0.95, 0.95); uy = xp.clip(u[1], -0.95, 0.95) + sx = xp.sqrt(1 + 3*ux*ux); sy = xp.sqrt(1 + 3*uy*uy); base = rho*(2-sx)*(2-sy) + Bx = ((2*ux+sx)/(1-ux))[None]**CXa[:, None, None] + By = ((2*uy+sy)/(1-uy))[None]**CYa[:, None, None] + return Wa[:, None, None]*base[None]*Bx*By +def macros(f): + r = f.sum(0) + return r, xp.stack([(CXa[:, None, None]*f).sum(0)/r, (CYa[:, None, None]*f).sum(0)/r]) +def collide(f, fe, beta): + dfn = f - fe + ds = (Ps @ dfn.reshape(Q, -1)).reshape(dfn.shape) # проектор на сдвиг (matmul, GPU-friendly) + dh = dfn - ds; inv = 1.0/fe + num = (ds*dh*inv).sum(0); den = (dh*dh*inv).sum(0) + nrm = (dfn*dfn*inv).sum(0) # ‖Δ‖² — масштаб неравновесия узла + ok = den > GREL*nrm + den_safe = xp.where(ok, den, xp.asarray(1.0, DTYPE)) # избегаем 0/0 (обе ветки where считаются) + g = xp.where(ok, 1/beta - (2 - 1/beta)*num/den_safe, xp.asarray(2.0, DTYPE)) + return f - beta*(2*ds + g[None]*dh) +def stream(f): + fs = xp.empty_like(f) + for i in range(Q): + fs[i] = xp.roll(f[i], (Cy[i], Cx[i]), (0, 1)) + return fs + +# ---- AMR-связка ---- +def patch(pNx, pNy, ax, bx, ay, by, r): + Wx, Wy = bx-ax, by-ay; Nfx, Nfy = r*Wx+1, r*Wy+1 + FX, FY = np.meshgrid(ax+np.arange(Nfx)/r, ay+np.arange(Nfy)/r) + x0 = np.floor(FX).astype(np.int64); y0 = np.floor(FY).astype(np.int64) + x1 = np.minimum(x0+1, pNx-1); y1 = np.minimum(y0+1, pNy-1) + return dict(Nfx=Nfx, Nfy=Nfy, ax=ax, bx=bx, ay=ay, by=by, r=r, + x0=xp.asarray(x0), y0=xp.asarray(y0), x1=xp.asarray(x1), y1=xp.asarray(y1), + tx=xp.asarray(FX-x0, DTYPE), ty=xp.asarray(FY-y0, DTYPE), + slx=slice(r, r*Wx, r), sly=slice(r, r*Wy, r)) +def pint(fld, P): + return (fld[..., P["y0"], P["x0"]]*(1-P["tx"])*(1-P["ty"]) + fld[..., P["y0"], P["x1"]]*P["tx"]*(1-P["ty"]) + + fld[..., P["y1"], P["x0"]]*(1-P["tx"])*P["ty"] + fld[..., P["y1"], P["x1"]]*P["tx"]*P["ty"]) +def ghost(pf, P, Rcf): + r, u = macros(pf); neq = pf - feq(r, u) + return feq(pint(r, P), xp.stack([pint(u[0], P), pint(u[1], P)])) + Rcf*pint(neq, P) +def fill(cf, gh): + cf[:, 0, :] = gh[:, 0, :]; cf[:, -1, :] = gh[:, -1, :]; cf[:, :, 0] = gh[:, :, 0]; cf[:, :, -1] = gh[:, :, -1] + return cf +def restrict(cf, pf, P, Rfc, fluid): + r, u = macros(cf); neq = cf - feq(r, u); slx, sly = P["slx"], P["sly"] + nv = feq(r[sly, slx], u[:, sly, slx]) + Rfc*neq[:, sly, slx] + cur = pf[:, P["ay"]+1:P["by"], P["ax"]+1:P["bx"]] + pf[:, P["ay"]+1:P["by"], P["ax"]+1:P["bx"]] = xp.where(fluid[None], nv, cur) + return pf + +# ---- граница: (1) узловой bounce-back (без SDF); (2) SDF+Bouzidi ---- +def bb_set(post, pre, solid): # узлы тела <- развёрнутые до-столкновения (как в CPU-версии) + for i in range(Q): + post[i] = xp.where(solid, pre[OPP[i]], post[i]) + return post +def force_on(fpost, cyl, fluid): # Mei для узловой границы: F=Σ c_i(f_i+f_ī) по линкам жидк.->тело + Fx = 0.0; Fy = 0.0 + for i in range(1, Q): + nb = xp.roll(cyl, (-Cy[i], -Cx[i]), (0, 1)); link = fluid & nb + s = xp.where(link, fpost[i] + fpost[OPP[i]], xp.asarray(0.0, DTYPE)).sum() + Fx = Fx + Cx[i]*s; Fy = Fy + Cy[i]*s + return Fx, Fy +def build_bc(solid_np, phi_np, cyl_np): # SDF-границу строим на host один раз, переносим на device + fluid = ~solid_np; bc = [] + for i in range(1, Q): + nb_solid = np.roll(solid_np, (-Cy[i], -Cx[i]), (0, 1)); mask = fluid & nb_solid + cl = mask & np.roll(cyl_np, (-Cy[i], -Cx[i]), (0, 1)) + phinb = np.roll(phi_np, (-Cy[i], -Cx[i]), (0, 1)) + with np.errstate(divide="ignore", invalid="ignore"): + qq = phi_np/(phi_np - phinb) + q = np.where(mask, np.clip(qq, 0.02, 0.98), 0.5) + xff = mask & (~np.roll(solid_np, (Cy[i], Cx[i]), (0, 1))) + bc.append((i, OPP[i], xp.asarray(mask), xp.asarray(q, DTYPE), xp.asarray(xff), xp.asarray(cl))) + return bc +def apply_bc(f, fpost, bc): # Bouzidi (линейный), полностью через where (GPU) + for (i, ib, mask, q, xff, cl) in bc: + fi = fpost[i]; fib = fpost[ib]; fiback = xp.roll(fpost[i], (Cy[i], Cx[i]), (0, 1)) + near = mask & (q < 0.5) & xff; bad = mask & (q < 0.5) & (~xff); far = mask & (q >= 0.5) + new = f[ib] + new = xp.where(near, 2*q*fi + (1-2*q)*fiback, new) + new = xp.where(far, (1/(2*q))*fi + (1-1/(2*q))*fib, new) + new = xp.where(bad, fi, new) + f[ib] = new + return f +def force_bc(fpost, f, bc): # Mei для интерполированной границы + Fx = 0.0; Fy = 0.0 + for (i, ib, mask, q, xff, cl) in bc: + s = xp.where(cl, fpost[i] + f[ib], xp.asarray(0.0, DTYPE)).sum() + Fx = Fx + Cx[i]*s; Fy = Fy + Cy[i]*s + return Fx, Fy + +# ---- геометрия (ИДЕНТИЧНА CPU-версиям) ---- +Nx, Ny, D, cx, cy = 150, 72, 16, 40, 36 +U, Re, STEPS, ramp, FE = 0.07, 150.0, int(os.environ.get("AMR_STEPS", 8000)), 1000, 34 +D0 = D; nu = U*D/Re; tau0 = nu/CS2 + 0.5 +ax1, bx1, ay1, by1 = 16, 118, 8, 64 +cx2a, cx2b, cy2a, cy2b = 26, 64, 18, 54 +px, py = cx + 3*D, cy +def _cmask(NX, NY, ccx, ccy, R): + Y, X = np.meshgrid(np.arange(NY), np.arange(NX), indexing="ij"); return (X-ccx)**2 + (Y-ccy)**2 <= R*R +def _csdf(NX, NY, ccx, ccy, R): + Y, X = np.meshgrid(np.arange(NY), np.arange(NX), indexing="ij"); return np.sqrt((X-ccx)**2.0 + (Y-ccy)**2.0) - R +# host-маски/SDF +_walls = np.zeros((Ny, Nx), bool); _walls[0, :] = True; _walls[-1, :] = True +cyl0_np = _cmask(Nx, Ny, cx, cy, D/2); solid0_np = cyl0_np | _walls +_Yg = np.arange(Ny)[:, None]*np.ones((1, Nx)) +phi0_np = np.minimum(_csdf(Nx, Ny, cx, cy, D/2), np.minimum(_Yg-0.5, (Ny-1.5)-_Yg)) +P1 = patch(Nx, Ny, ax1, bx1, ay1, by1, 2); P2 = patch(P1["Nfx"], P1["Nfy"], (cx2a-ax1)*2, (cx2b-ax1)*2, (cy2a-ay1)*2, (cy2b-ay1)*2, 2) +solid1_np = _cmask(P1["Nfx"], P1["Nfy"], (cx-ax1)*2, (cy-ay1)*2, D); phi1_np = _csdf(P1["Nfx"], P1["Nfy"], (cx-ax1)*2, (cy-ay1)*2, D) +solid2_np = _cmask(P2["Nfx"], P2["Nfy"], (cx-cx2a)*4, (cy-cy2a)*4, 2*D); phi2_np = _csdf(P2["Nfx"], P2["Nfy"], (cx-cx2a)*4, (cy-cy2a)*4, 2*D) +# device-маски (без SDF) +g_solid0 = xp.asarray(solid0_np); g_cyl0 = xp.asarray(cyl0_np); g_fl0 = ~g_solid0 +g_solid1 = xp.asarray(solid1_np); g_fl1 = ~g_solid1 +g_solid2 = xp.asarray(solid2_np); g_fl2 = ~g_solid2 +# SDF-ГУ +BC0 = build_bc(solid0_np, phi0_np, cyl0_np); BC1 = build_bc(solid1_np, phi1_np, solid1_np); BC2 = build_bc(solid2_np, phi2_np, solid2_np) +# рестрикция: жидкие узлы +fl1 = xp.asarray(~solid0_np[ay1+1:by1, ax1+1:bx1]) +fl2 = xp.ones((P2["by"]-P2["ay"]-1, P2["bx"]-P2["ax"]-1), bool); fl2 = xp.asarray(fl2) +# τ / масштабы +t1 = 2*tau0 - 0.5; t2 = 2*t1 - 0.5 +b0 = 1/(2*tau0); b1 = 1/(2*t1); b2 = 1/(2*t2) +R01 = t1/(2*tau0); Rf01 = 1/R01; R12 = t2/(2*t1); Rf12 = 1/R12 + +def smoothstep(x): + x = min(max(x, 0.0), 1.0); return x*x*(3-2*x) + +def run(mode, use_sdf, progress=None): + """mode: none|amr2x|nested. Возвращает {Fx,Fy,uy (на host), frames (host), DL, mode}. + progress(t, STEPS) — необязательный колбэк прогресса (вызывается каждый шаг).""" + use1 = mode in ("amr2x", "nested"); use2 = (mode == "nested") + DL = {"none": D0, "amr2x": 2*D0, "nested": 4*D0}[mode] + f0 = feq(xp.ones((Ny, Nx), DTYPE), xp.zeros((2, Ny, Nx), DTYPE)) + f1 = feq(xp.ones((P1["Nfy"], P1["Nfx"]), DTYPE), xp.zeros((2, P1["Nfy"], P1["Nfx"]), DTYPE)) if use1 else None + f2 = feq(xp.ones((P2["Nfy"], P2["Nfx"]), DTYPE), xp.zeros((2, P2["Nfy"], P2["Nfx"]), DTYPE)) if use2 else None + Fx = xp.zeros(STEPS+1, DTYPE); Fy = xp.zeros(STEPS+1, DTYPE); uy = xp.zeros(STEPS+1, DTYPE) + onecol = xp.ones((Ny, 1), DTYPE); frames = [] + for t in range(STEPS+1): + rho, u0 = macros(f0) + if t % 500 == 0 and not bool(xp.isfinite(rho).all()): + print("BLEW UP", mode, t); Fx = Fx[:t]; Fy = Fy[:t]; uy = uy[:t]; break + pre = f0.copy(); post0 = collide(f0, feq(rho, u0), b0) + if not use_sdf: + post0b = bb_set(post0.copy(), pre, g_solid0); f0 = stream(post0b) + else: + f0 = stream(post0); f0 = apply_bc(f0, post0, BC0) + if mode == "none": + Fx[t], Fy[t] = (force_bc(post0, f0, BC0) if use_sdf else force_on(post0, g_cyl0, g_fl0)) + uin = xp.zeros((2, Ny, 1), DTYPE); uin[0, :, 0] = U*smoothstep(t/ramp) + f0[:, 1:-1, 0] = feq(onecol, uin)[:, 1:-1, 0]; f0[:, 1:-1, -1] = f0[:, 1:-1, -2] + if use1: + g1o = ghost(pre, P1, R01); g1n = ghost(f0, P1, R01) + for s1 in range(2): + pre1 = f1.copy(); r1, u1 = macros(f1); post1 = collide(f1, feq(r1, u1), b1) + if not use_sdf: + f1 = stream(bb_set(post1.copy(), pre1, g_solid1)) + else: + f1 = stream(post1); f1 = apply_bc(f1, post1, BC1) + if mode == "amr2x" and s1 == 1: + Fx[t], Fy[t] = (force_bc(post1, f1, BC1) if use_sdf else force_on(post1, g_solid1, g_fl1)) + f1 = fill(f1, (1-(s1+1)/2)*g1o + ((s1+1)/2)*g1n) + if use2: + g2o = ghost(pre1, P2, R12); g2n = ghost(f1, P2, R12) + for s2 in range(2): + pre2 = f2.copy(); r2, u2 = macros(f2); post2 = collide(f2, feq(r2, u2), b2) + if not use_sdf: + f2 = stream(bb_set(post2.copy(), pre2, g_solid2)) + else: + f2 = stream(post2); f2 = apply_bc(f2, post2, BC2) + if s1 == 1 and s2 == 1: + Fx[t], Fy[t] = (force_bc(post2, f2, BC2) if use_sdf else force_on(post2, g_solid2, g_fl2)) + f2 = fill(f2, (1-(s2+1)/2)*g2o + ((s2+1)/2)*g2n) + f1 = restrict(f2, f1, P2, Rf12, fl2) + f0 = restrict(f1, f0, P1, Rf01, fl1) + col = f0[:, py, px]; uy[t] = (CYa*col).sum()/col.sum() # зонд следа (без full-macros) + if progress is not None: progress(t, STEPS) + if use1 and t % FE == 0: + frames.append((t, to_cpu(macros(f0)[1]), to_cpu(macros(f1)[1]), + (to_cpu(macros(f2)[1]) if use2 else None))) + return dict(mode=mode, DL=DL, Fx=to_cpu(Fx), Fy=to_cpu(Fy), uy=to_cpu(uy), frames=frames) + +# ---- анализ (на host: FFT малых рядов) ---- +def analyze(res): + Fx, Fy, uy, DL = res["Fx"], res["Fy"], res["uy"], res["DL"] + n = len(uy); h = slice(n//2, n); Cd = 2*Fx/(U**2*DL); Cl = 2*Fy/(U**2*DL) + sig = uy[h] - uy[h].mean(); npad = 8192 + freqs = np.fft.rfftfreq(npad, 1.0); amp = np.abs(np.fft.rfft(sig, n=npad)) + St = (freqs[1+int(np.argmax(amp[1:]))] if len(amp) > 2 else 0.0)*D0/U + return dict(Cd=float(Cd[h].mean()), Clrms=float(Cl[h].std()), St=float(St), uyrms=float(uy[h].std()), + Cl_s=Cl, uy=uy, freqs=freqs, amp=amp, h0=n//2) + +# ---- визуализация (matplotlib на CPU; кадры уже host) ---- +def _vort_np(u): + return (np.roll(u[1], -1, 1)-np.roll(u[1], 1, 1))*0.5 - (np.roll(u[0], -1, 0)-np.roll(u[0], 1, 0))*0.5 +def save_gif(res, name, anim_dir, sdf_tag, fps=24): + import matplotlib; matplotlib.use("Agg") + import matplotlib.pyplot as plt, matplotlib.patches as mpatches + from PIL import Image + nested = (res["mode"] == "nested"); frames = res["frames"] + vm = np.nanpercentile(np.abs(np.where(solid0_np, np.nan, _vort_np(frames[len(frames)//2][1]))), 99.0) + cm = plt.get_cmap("inferno").copy(); cm.set_bad("white"); pil = [] + for (t, u0, u1, u2) in frames: + fig = plt.figure(figsize=(11.2, 5.7), dpi=96); ax = fig.add_subplot(111) + ax.imshow(np.abs(np.where(solid0_np, np.nan, _vort_np(u0))), origin="lower", cmap=cm, vmin=0, vmax=vm, + extent=(0, Nx, 0, Ny), interpolation="nearest") + ax.imshow(np.abs(np.where(solid1_np, np.nan, _vort_np(u1)))[1:-1, 1:-1], origin="lower", cmap=cm, vmin=0, vmax=vm, + extent=(ax1+0.5, bx1-0.5, ay1+0.5, by1-0.5), interpolation="nearest") + if nested and u2 is not None: + ax.imshow(np.abs(np.where(solid2_np, np.nan, _vort_np(u2)))[1:-1, 1:-1], origin="lower", cmap=cm, vmin=0, vmax=vm, + extent=(cx2a+0.25, cx2b-0.25, cy2a+0.25, cy2b-0.25), interpolation="nearest") + ax.add_patch(mpatches.Rectangle((0.2, 0.2), Nx-0.4, Ny-0.4, fill=False, edgecolor="#4fc3f7", lw=1.6)) + ax.text(1.5, Ny-4, "уровень 0: Δx (крупный)", color="#4fc3f7", fontsize=9, weight="bold") + ax.add_patch(mpatches.Rectangle((ax1, ay1), bx1-ax1, by1-ay1, fill=False, edgecolor="#aed581", lw=2.2)) + ax.text(ax1+1, by1-3.5, "уровень 1: Δx/2 (тело+след)", color="#aed581", fontsize=9, weight="bold") + if nested: + ax.add_patch(mpatches.Rectangle((cx2a, cy2a), cx2b-cx2a, cy2b-cy2a, fill=False, edgecolor="#ff8a65", lw=2.2)) + ax.text(cx2a+1, cy2b-3.5, "уровень 2: Δx/4 (у тела)", color="#ff8a65", fontsize=9, weight="bold") + base = "Вложенный AMR" if nested else "AMR (одиночный блок 2×)" + ax.set_title(f"{base}{sdf_tag} · поверх $|\\omega|$ · t={t}", fontsize=11) + ax.set_xlabel("x [lu]"); ax.set_ylabel("y [lu]"); ax.set_xlim(0, Nx); ax.set_ylim(0, Ny) + buf = _io.BytesIO(); fig.savefig(buf, format="png", bbox_inches="tight"); buf.seek(0); plt.close(fig) + pil.append(Image.open(buf).convert("RGB").convert("P", palette=Image.ADAPTIVE)) + path = os.path.join(anim_dir, name) + pil[0].save(path, save_all=True, append_images=pil[1:], duration=int(1000/fps), loop=0, optimize=True) + print("saved", name, len(frames), "кадров") + +LAB = ["без AMR (D=16)", "AMR 2× (D=32)", "AMR 2×+4× (D=64)"] +def print_table(AS, header): + print(f"\n=== {header} ===") + print(f"{'версия':22}{'D у тела':>9}{'St':>8}{'':>9}{'rms Cl':>9}{'rms u_y':>9}") + for lab, DL, a in zip(LAB, [16, 32, 64], AS): + print(f"{lab:22}{DL:>9}{a['St']:>8.3f}{a['Cd']:>9.3f}{a['Clrms']:>9.4f}{a['uyrms']:>9.4f}") + print(f"{'литература Re≈150':22}{'—':>9}{0.183:>8.3f}{1.330:>9.3f}{'~0.3':>9}{'':>9}") + print("(лит.: St≈0.18, Cd≈1.3 для цилиндра при Re≈150; Williamson 1996, Henderson 1995)") +def probe_figure(AS, R2, path, suptitle): + import matplotlib; matplotlib.use("Agg") + import matplotlib.pyplot as plt, matplotlib.patches as mpatches + cols = ["#9e9e9e", "#1f6feb", "#d1495b"] + fig = plt.figure(figsize=(13.5, 8.2)); gs = fig.add_gridspec(2, 2, hspace=0.32, wspace=0.22) + axA = fig.add_subplot(gs[0, 0]); mid = R2["frames"][len(R2["frames"])//2] + vmf = np.nanpercentile(np.abs(np.where(solid0_np, np.nan, _vort_np(mid[1]))), 99) + cmf = plt.get_cmap("inferno").copy(); cmf.set_bad("white") + axA.imshow(np.abs(np.where(solid0_np, np.nan, _vort_np(mid[1]))), origin="lower", cmap=cmf, vmin=0, vmax=vmf, + extent=(0, Nx, 0, Ny), interpolation="nearest") + axA.add_patch(mpatches.Rectangle((ax1, ay1), bx1-ax1, by1-ay1, fill=False, edgecolor="#aed581", lw=1.8)) + axA.add_patch(mpatches.Rectangle((cx2a, cy2a), cx2b-cx2a, cy2b-cy2a, fill=False, edgecolor="#ff8a65", lw=1.8)) + axA.set_title("$|\\omega|$ + рамки зон 2×/4×"); axA.set_xlabel("x [lu]"); axA.set_ylabel("y [lu]") + axB = fig.add_subplot(gs[0, 1]) + for a, lab, c in zip(AS, LAB, cols): axB.plot(a["Cl_s"][a["h0"]:], lw=0.8, color=c, label=lab) + axB.set_title("Подъёмная сила $C_l(t)$ (зонд силы)"); axB.set_xlabel("шаг"); axB.set_ylabel("$C_l$") + axB.legend(fontsize=8); axB.grid(alpha=0.3) + axC = fig.add_subplot(gs[1, 0]) + for a, lab, c in zip(AS, LAB, cols): + sp = a["amp"]/a["amp"][1:].max(); axC.plot(a["freqs"]*D0/U, sp, lw=1.0, color=c, label=lab) + axC.axvline(0.183, color="k", ls="--", alpha=0.6, label="лит. St≈0.18"); axC.set_xlim(0, 0.6) + axC.set_title("Спектр $u_y$ в следе → St"); axC.set_xlabel("St = f·D/U"); axC.set_ylabel("норм. ампл.") + axC.legend(fontsize=8); axC.grid(alpha=0.3) + axD = fig.add_subplot(gs[1, 1]); x = np.arange(3); w = 0.35 + axD.bar(x-w/2, [a["St"] for a in AS], w, color="#1f6feb", label="St") + axD.bar(x+w/2, [a["Cd"] for a in AS], w, color="#fb8c00", label="") + axD.axhline(0.183, color="#1f6feb", ls="--", alpha=0.6); axD.axhline(1.33, color="#fb8c00", ls="--", alpha=0.6) + axD.set_xticks(x); axD.set_xticklabels(["без AMR", "2×", "2×+4×"]); axD.set_title("St и (пунктир — лит.)") + axD.legend(fontsize=8); axD.grid(alpha=0.3, axis="y") + fig.suptitle(suptitle, fontweight="bold"); fig.savefig(path, dpi=110, bbox_inches="tight"); plt.close(fig) + print("saved", os.path.basename(path)) diff --git a/docs/theory/amr_opt/amr_cylinder_gpu_opt.py b/docs/theory/amr_opt/amr_cylinder_gpu_opt.py new file mode 100644 index 0000000..9064667 --- /dev/null +++ b/docs/theory/amr_opt/amr_cylinder_gpu_opt.py @@ -0,0 +1,36 @@ +# ОПТИМИЗИРОВАННЫЙ GPU-решатель (без SDF): цилиндр, три версии (без AMR / 2× / вложенный 2×+4×). +# То же, что amr_cylinder_gpu.py, но: GPU-only ядро _opt (фикс силового зонда + ускорение), +# прогресс-бар на каждый прогон, гифки для ВСЕХ трёх режимов (none/amr2x/nested). +# Запуск: python amr_cylinder_gpu_opt.py +# AMR_FP64=1 ... (двойная точность) +# AMR_STEPS=2000 ... (короткий прогон) +# AMR_CUDAGRAPH=0 ... (выключить CUDA Graphs; по умолчанию ВКЛ, с рантайм-самопроверкой) +import os, time, numpy as np +import amr_gpu_core_opt as core + +HERE = os.path.dirname(os.path.abspath(__file__)) +ANIM = os.path.join(HERE, "anim"); os.makedirs(ANIM, exist_ok=True) +FIGS = os.path.join(HERE, "figures"); os.makedirs(FIGS, exist_ok=True) +print(f"[ОПТ · без SDF] backend={core.BACKEND}; домен {core.Nx}x{core.Ny}; steps={core.STEPS}; " + f"graphs={'on' if os.environ.get('AMR_CUDAGRAPH','1') != '0' else 'off'}; " + f"L1(2×) {core.P1['Nfx']}x{core.P1['Nfy']}; L2(4×) {core.P2['Nfx']}x{core.P2['Nfy']}") + +t0 = time.perf_counter() +R0 = core.run("none", False, core.make_progress("none")); print(" none :", round(time.perf_counter()-t0, 1), "s") +R1 = core.run("amr2x", False, core.make_progress("amr2x")); print(" amr2x :", round(time.perf_counter()-t0, 1), "s") +R2 = core.run("nested", False, core.make_progress("nested")); print(" nested :", round(time.perf_counter()-t0, 1), "s") + +core.save_gif(R0, "none_cyl.gif", ANIM, " (без SDF)") +core.save_gif(R1, "amr2x_cyl.gif", ANIM, " (без SDF)") +core.save_gif(R2, "amr_nested_cyl.gif", ANIM, " (без SDF)") + +AS = [core.analyze(R0), core.analyze(R1), core.analyze(R2)] +core.print_table(AS, "БЕЗ SDF — сравнение на реально собранных данных (установившийся режим)") +np.savez(os.path.join(HERE, "_amr_probe_data.npz"), + St=np.array([a["St"] for a in AS]), Cd=np.array([a["Cd"] for a in AS]), + Clrms=np.array([a["Clrms"] for a in AS]), uyrms=np.array([a["uyrms"] for a in AS]), + Cl0=AS[0]["Cl_s"], Cl1=AS[1]["Cl_s"], Cl2=AS[2]["Cl_s"], + uy0=AS[0]["uy"], uy1=AS[1]["uy"], uy2=AS[2]["uy"]) +core.probe_figure(AS, R2, os.path.join(FIGS, "11e_amr_probe_comparison.png"), + "AMR на цилиндре (без SDF): сравнение трёх версий на данных зондов") +print("DONE (без SDF)") diff --git a/docs/theory/amr_opt/amr_cylinder_sdf_gpu_opt.py b/docs/theory/amr_opt/amr_cylinder_sdf_gpu_opt.py new file mode 100644 index 0000000..4ec510f --- /dev/null +++ b/docs/theory/amr_opt/amr_cylinder_sdf_gpu_opt.py @@ -0,0 +1,63 @@ +# ОПТИМИЗИРОВАННЫЙ GPU-решатель (с SDF + Bouzidi): цилиндр, три версии (без AMR / 2× / 2×+4×). +# То же, что amr_cylinder_sdf_gpu.py, но: GPU-only ядро _opt (ускорение), прогресс-бар на +# каждый прогон, гифки для ВСЕХ трёх режимов (none/amr2x/nested). В конце — сводное сравнение с без-SDF. +# Запуск: python amr_cylinder_sdf_gpu_opt.py (после amr_cylinder_gpu_opt.py — для сводного сравнения) +# AMR_CUDAGRAPH=0 ... (выключить CUDA Graphs; по умолчанию ВКЛ, с рантайм-самопроверкой) +import os, time, numpy as np +import amr_gpu_core_opt as core + +HERE = os.path.dirname(os.path.abspath(__file__)) +ANIM = os.path.join(HERE, "anim"); os.makedirs(ANIM, exist_ok=True) +FIGS = os.path.join(HERE, "figures"); os.makedirs(FIGS, exist_ok=True) +print(f"[ОПТ · SDF+Bouzidi] backend={core.BACKEND}; домен {core.Nx}x{core.Ny}; steps={core.STEPS}; " + f"graphs={'on' if os.environ.get('AMR_CUDAGRAPH','1') != '0' else 'off'}; " + f"L1(2×) {core.P1['Nfx']}x{core.P1['Nfy']}; L2(4×) {core.P2['Nfx']}x{core.P2['Nfy']}") + +t0 = time.perf_counter() +R0 = core.run("none", True, core.make_progress("none")); print(" none :", round(time.perf_counter()-t0, 1), "s") +R1 = core.run("amr2x", True, core.make_progress("amr2x")); print(" amr2x :", round(time.perf_counter()-t0, 1), "s") +R2 = core.run("nested", True, core.make_progress("nested")); print(" nested :", round(time.perf_counter()-t0, 1), "s") + +core.save_gif(R0, "none_cyl_sdf.gif", ANIM, " + SDF (Bouzidi)") +core.save_gif(R1, "amr2x_cyl_sdf.gif", ANIM, " + SDF (Bouzidi)") +core.save_gif(R2, "amr_nested_cyl_sdf.gif", ANIM, " + SDF (Bouzidi)") + +AS = [core.analyze(R0), core.analyze(R1), core.analyze(R2)] +core.print_table(AS, "С SDF — сравнение на реально собранных данных (установившийся режим)") +np.savez(os.path.join(HERE, "_amr_probe_data_sdf.npz"), + St=np.array([a["St"] for a in AS]), Cd=np.array([a["Cd"] for a in AS]), + Clrms=np.array([a["Clrms"] for a in AS]), uyrms=np.array([a["uyrms"] for a in AS]), + Cl0=AS[0]["Cl_s"], Cl1=AS[1]["Cl_s"], Cl2=AS[2]["Cl_s"], + uy0=AS[0]["uy"], uy1=AS[1]["uy"], uy2=AS[2]["uy"]) +core.probe_figure(AS, R2, os.path.join(FIGS, "11f_amr_sdf_probe_comparison.png"), + "AMR на цилиндре (SDF+Bouzidi): сравнение трёх версий на данных зондов") + +# ---- сводное сравнение: SDF против без-SDF (если есть свежие данные без SDF) ---- +nosdf = os.path.join(HERE, "_amr_probe_data.npz") +if os.path.exists(nosdf) and ("St" in np.load(nosdf).files): + import matplotlib; matplotlib.use("Agg"); import matplotlib.pyplot as plt + N = np.load(nosdf); Stn, Cdn = N["St"], N["Cd"] + Sts = np.array([a["St"] for a in AS]); Cds = np.array([a["Cd"] for a in AS]) + print("\n=== СВОДНО: SDF vs без SDF (Cd, St) ===") + print(f"{'версия':14}{'St(noSDF)':>11}{'St(SDF)':>9}{'Cd(noSDF)':>11}{'Cd(SDF)':>9}") + for k, lab in enumerate(["без AMR", "2×", "2×+4×"]): + print(f"{lab:14}{Stn[k]:>11.3f}{Sts[k]:>9.3f}{Cdn[k]:>11.3f}{Cds[k]:>9.3f}") + print(f"{'лит. Re≈150':14}{0.183:>11.3f}{0.183:>9.3f}{1.330:>11.3f}{1.330:>9.3f}") + x = np.arange(3); w = 0.38 + fig, axs = plt.subplots(1, 2, figsize=(13.5, 4.6)) + axs[0].bar(x-w/2, Cdn, w, color="#9e9e9e", label="без SDF (ступенч.)") + axs[0].bar(x+w/2, Cds, w, color="#1f6feb", label="с SDF (Bouzidi)") + axs[0].axhline(1.33, color="k", ls="--", alpha=0.6, label="лит. Cd≈1.33") + axs[0].set_xticks(x); axs[0].set_xticklabels(["без AMR", "2×", "2×+4×"]); axs[0].set_ylabel("") + axs[0].set_title("Сопротивление: SDF убирает завышение от ступенчатой границы") + axs[0].legend(fontsize=8); axs[0].grid(alpha=0.3, axis="y") + axs[1].bar(x-w/2, Stn, w, color="#9e9e9e", label="без SDF"); axs[1].bar(x+w/2, Sts, w, color="#1f6feb", label="с SDF") + axs[1].axhline(0.183, color="k", ls="--", alpha=0.6, label="лит. St≈0.18") + axs[1].set_xticks(x); axs[1].set_xticklabels(["без AMR", "2×", "2×+4×"]); axs[1].set_ylabel("St") + axs[1].set_title("Число Струхаля"); axs[1].legend(fontsize=8); axs[1].grid(alpha=0.3, axis="y") + fig.suptitle("Цилиндр: SDF (Bouzidi) против ступенчатого bounce-back — на реальных данных", fontweight="bold") + fig.savefig(os.path.join(FIGS, "11g_sdf_vs_nosdf.png"), dpi=110, bbox_inches="tight"); plt.close(fig) + print("saved 11g_sdf_vs_nosdf.png") +else: + print("\n(нет свежего _amr_probe_data.npz — сначала запусти amr_cylinder_gpu_opt.py)") +print("DONE (SDF)") diff --git a/docs/theory/amr_opt/amr_gpu_core_opt.py b/docs/theory/amr_opt/amr_gpu_core_opt.py new file mode 100644 index 0000000..8c1012c --- /dev/null +++ b/docs/theory/amr_opt/amr_gpu_core_opt.py @@ -0,0 +1,448 @@ +# Оптимизированное GPU-ЯДРО (D2Q9 KBC) для AMR-решателей на цилиндре. GPU-only (CuPy). +# Отличия от amr_gpu_core.py: +# * УБРАН numpy-фолбэк: backend всегда CuPy/GPU (иначе жёсткая ошибка). numpy остаётся +# только для host-задач (маски/SDF/базис один раз, FFT в analyze, matplotlib/PIL). +# * ФИКС силового зонда force_on: второй член обмена импульсом берётся из поля ПОСЛЕ +# стриминга (как в корректном force_bc), а не из post-collision. Раньше это давало +# нефизичный отрицательный Cd и крошечный rms Cl. +# * feq без pow (показатели c∈{-1,0,1}) + cp.fuse; фьюзинг хвоста collide. +# * Предвычисленные маски линков для силы (без per-step roll статических масок). +# * run(): один шаг = замкнутая _step() над persistent-буферами; опционально CUDA Graphs +# (AMR_CUDAGRAPH=1, по умолчанию вкл) с автоматическим откатом на eager. +# * Кадры для всех трёх режимов (none/amr2x/nested); save_gif рисует и режим none. +# * make_progress — общий прогресс-бар в ядре. +# Запуск через раннеры: amr_cylinder_gpu_opt.py (без SDF) и amr_cylinder_sdf_gpu_opt.py (SDF). +import os, io as _io, numpy as np + +# ---- backend: ТОЛЬКО CuPy/GPU (фолбэк удалён) ---- +import cupy as cp +try: + _ = (cp.zeros(2) + 1).sum(); cp.cuda.Device().synchronize() # реальная операция на device +except Exception as e: + raise RuntimeError("Этому решателю нужна рабочая GPU + CuPy: numpy-фолбэк удалён.") from e +xp = cp; GPU = True +def to_cpu(a): + return cp.asnumpy(a) +DTYPE = cp.float64 if os.environ.get("AMR_FP64") else cp.float32 +GREL = 1e-8 # ОТНОСИТЕЛЬНЫЙ порог вырожденности знаменателя γ (доля от ‖Δ‖²); см. solver_2x_sdf/backend.py. + # Прежний абсолютный порог (1e-6 в fp32) срабатывал на большинстве узлов и подменял KBC на LBGK. +BACKEND = f"CuPy/GPU dtype={'float64' if DTYPE == cp.float64 else 'float32'}" + +# ---- решётка D2Q9 ---- +Cx = [0, 1, 0, -1, 0, 1, -1, -1, 1] # python-инты для roll/индексации +Cy = [0, 0, 1, 0, -1, 1, 1, -1, -1] +OPP = [0, 3, 4, 1, 2, 7, 8, 5, 6] +Q = 9 +_W = np.array([4/9, 1/9, 1/9, 1/9, 1/9, 1/36, 1/36, 1/36, 1/36]) +_CXn = np.array(Cx, float); _CYn = np.array(Cy, float) +# моментный базис и проектор на сдвиг {cx²−cy², cxcy} (KBC-N1) — считаем в numpy, грузим на device +_M = np.zeros((Q, Q)); _M[0] = 1; _M[1] = _CXn; _M[2] = _CYn; _M[3] = 3*(_CXn**2+_CYn**2)-2 +_M[4] = _CXn**2-_CYn**2; _M[5] = _CXn*_CYn; _M[6] = _CXn**2*_CYn; _M[7] = _CXn*_CYn**2; _M[8] = _CXn**2*_CYn**2 +_Dm = np.zeros((Q, Q)); _Dm[4, 4] = _Dm[5, 5] = 1.0 +_Psn = np.linalg.inv(_M) @ _Dm @ _M +# device-константы +Wa = xp.asarray(_W, dtype=DTYPE) +CXa = xp.asarray(_CXn, dtype=DTYPE); CYa = xp.asarray(_CYn, dtype=DTYPE) +Ps = xp.asarray(_Psn, dtype=DTYPE) +CS2 = 1.0/3.0 +# device-скаляры (чтобы не делать host→device asarray на горячем пути и не ломать graph-capture) +_Z0 = xp.zeros((), DTYPE); _ONE = xp.asarray(1.0, DTYPE); _TWO = xp.asarray(2.0, DTYPE) + +# ---- ядро LBM/KBC (математика идентична; feq без pow) ---- +def _feq9_body(rho, ux, uy): + # равновесие product-form для D2Q9: показатели c∈{-1,0,1} → используем qx/iqx вместо pow. + # clip входит в ТЕЛО ядра через min/max c литералами (запекаются в кернел → нет H2D при capture). + ux = cp.minimum(cp.maximum(ux, -0.95), 0.95); uy = cp.minimum(cp.maximum(uy, -0.95), 0.95) + sx = cp.sqrt(1.0 + 3.0*ux*ux); sy = cp.sqrt(1.0 + 3.0*uy*uy) + base = rho*(2.0 - sx)*(2.0 - sy) + qx = (2.0*ux + sx)/(1.0 - ux); qy = (2.0*uy + sy)/(1.0 - uy) + ix = 1.0/qx; iy = 1.0/qy + return (base*(4.0/9.0), # ( 0, 0) + base*(1.0/9.0)*qx, base*(1.0/9.0)*qy, # (+1,0) (0,+1) + base*(1.0/9.0)*ix, base*(1.0/9.0)*iy, # (-1,0) (0,-1) + base*(1.0/36.0)*qx*qy, base*(1.0/36.0)*ix*qy, # (+1,+1) (-1,+1) + base*(1.0/36.0)*ix*iy, base*(1.0/36.0)*qx*iy) # (-1,-1) (+1,-1) +_feq9 = cp.fuse()(_feq9_body) # одно слитное ядро (если cp.fuse доступен) +_FUSE_OK = True + +def feq(rho, u): + global _FUSE_OK + if _FUSE_OK: + try: + return xp.stack(_feq9(rho, u[0], u[1]), axis=0) + except Exception as e: # откат на не-fused (тоже без pow) + print(f"[feq] cp.fuse отключён ({type(e).__name__}: {e}); обычный путь без pow") + _FUSE_OK = False + return xp.stack(_feq9_body(rho, u[0], u[1]), axis=0) + +def macros(f): + r = f.sum(0) + return r, xp.stack([(CXa[:, None, None]*f).sum(0)/r, (CYa[:, None, None]*f).sum(0)/r]) + +def collide(f, fe, beta): + dfn = f - fe + # проектор на сдвиг БЕЗ cuBLAS (gemm при capture тащит alpha/beta host→device → H2D): + dfn2d = dfn.reshape(Q, -1) # (Q, N) + ds = (Ps[:, :, None] * dfn2d[None]).sum(1).reshape(dfn.shape) # Σ_k Ps[i,k]·dfn[k] — чистые ядра + dh = dfn - ds; inv = 1.0/fe + num = (ds*dh*inv).sum(0); den = (dh*dh*inv).sum(0) + nrm = (dfn*dfn*inv).sum(0) # ‖Δ‖² — масштаб неравновесия узла + ok = den > GREL*nrm + den_safe = xp.where(ok, den, _ONE) # избегаем 0/0 + binv = 1.0/beta + g = xp.where(ok, binv - (2.0 - binv)*num/den_safe, _TWO) + return f - beta*(2.0*ds + g[None]*dh) + +def stream(f): + fs = xp.empty_like(f) + for i in range(Q): + fs[i] = xp.roll(f[i], (Cy[i], Cx[i]), (0, 1)) + return fs + +# ---- AMR-связка ---- +def patch(pNx, pNy, ax, bx, ay, by, r): + Wx, Wy = bx-ax, by-ay; Nfx, Nfy = r*Wx+1, r*Wy+1 + FX, FY = np.meshgrid(ax+np.arange(Nfx)/r, ay+np.arange(Nfy)/r) + x0 = np.floor(FX).astype(np.int64); y0 = np.floor(FY).astype(np.int64) + x1 = np.minimum(x0+1, pNx-1); y1 = np.minimum(y0+1, pNy-1) + return dict(Nfx=Nfx, Nfy=Nfy, ax=ax, bx=bx, ay=ay, by=by, r=r, + x0=xp.asarray(x0), y0=xp.asarray(y0), x1=xp.asarray(x1), y1=xp.asarray(y1), + tx=xp.asarray(FX-x0, DTYPE), ty=xp.asarray(FY-y0, DTYPE), + slx=slice(r, r*Wx, r), sly=slice(r, r*Wy, r)) +def pint(fld, P): + return (fld[..., P["y0"], P["x0"]]*(1-P["tx"])*(1-P["ty"]) + fld[..., P["y0"], P["x1"]]*P["tx"]*(1-P["ty"]) + + fld[..., P["y1"], P["x0"]]*(1-P["tx"])*P["ty"] + fld[..., P["y1"], P["x1"]]*P["tx"]*P["ty"]) +def ghost(pf, P, Rcf): + r, u = macros(pf); neq = pf - feq(r, u) + return feq(pint(r, P), xp.stack([pint(u[0], P), pint(u[1], P)])) + Rcf*pint(neq, P) +def fill(cf, gh): + cf[:, 0, :] = gh[:, 0, :]; cf[:, -1, :] = gh[:, -1, :]; cf[:, :, 0] = gh[:, :, 0]; cf[:, :, -1] = gh[:, :, -1] + return cf +def restrict(cf, pf, P, Rfc, fluid): + r, u = macros(cf); neq = cf - feq(r, u); slx, sly = P["slx"], P["sly"] + nv = feq(r[sly, slx], u[:, sly, slx]) + Rfc*neq[:, sly, slx] + cur = pf[:, P["ay"]+1:P["by"], P["ax"]+1:P["bx"]] + pf[:, P["ay"]+1:P["by"], P["ax"]+1:P["bx"]] = xp.where(fluid[None], nv, cur) + return pf + +# ---- граница: (1) узловой bounce-back (без SDF); (2) SDF+Bouzidi ---- +def bb_set(post, pre, solid): # узлы тела <- развёрнутые до-столкновения + for i in range(Q): + post[i] = xp.where(solid, pre[OPP[i]], post[i]) + return post +def build_links(solid_np, body_np): # предвычисление масок линков жидкость->тело (статичны) + fluid = ~solid_np; links = [] + for i in range(1, Q): + nb = np.roll(body_np, (-Cy[i], -Cx[i]), (0, 1)); mask = fluid & nb + links.append((i, OPP[i], Cx[i], Cy[i], xp.asarray(mask, DTYPE))) + return links +def force_on(fpost, fnew, links): # Mei (узловая граница): F=Σ c_i (f_i^после-столкн. + f_ī^после-стриминга) + Fx = _Z0; Fy = _Z0 + for (i, ib, cx_i, cy_i, maskf) in links: + s = (maskf*(fpost[i] + fnew[ib])).sum() + Fx = Fx + cx_i*s; Fy = Fy + cy_i*s + return Fx, Fy +def build_bc(solid_np, phi_np, cyl_np): # SDF-границу строим на host один раз, переносим на device + fluid = ~solid_np; bc = [] + for i in range(1, Q): + nb_solid = np.roll(solid_np, (-Cy[i], -Cx[i]), (0, 1)); mask = fluid & nb_solid + cl = mask & np.roll(cyl_np, (-Cy[i], -Cx[i]), (0, 1)) + phinb = np.roll(phi_np, (-Cy[i], -Cx[i]), (0, 1)) + with np.errstate(divide="ignore", invalid="ignore"): + qq = phi_np/(phi_np - phinb) + q = np.where(mask, np.clip(qq, 0.02, 0.98), 0.5) + xff = mask & (~np.roll(solid_np, (Cy[i], Cx[i]), (0, 1))) + bc.append((i, OPP[i], xp.asarray(mask), xp.asarray(q, DTYPE), xp.asarray(xff), xp.asarray(cl))) + return bc +def apply_bc(f, fpost, bc): # Bouzidi (линейный), полностью через where (GPU) + for (i, ib, mask, q, xff, cl) in bc: + fi = fpost[i]; fib = fpost[ib]; fiback = xp.roll(fpost[i], (Cy[i], Cx[i]), (0, 1)) + near = mask & (q < 0.5) & xff; bad = mask & (q < 0.5) & (~xff); far = mask & (q >= 0.5) + new = f[ib] + new = xp.where(near, 2*q*fi + (1-2*q)*fiback, new) + new = xp.where(far, (1/(2*q))*fi + (1-1/(2*q))*fib, new) + new = xp.where(bad, fi, new) + f[ib] = new + return f +def force_bc(fpost, f, bc): # Mei для интерполированной границы (уже корректно: f[ib] — после стриминга) + Fx = _Z0; Fy = _Z0 + for (i, ib, mask, q, xff, cl) in bc: + s = xp.where(cl, fpost[i] + f[ib], _Z0).sum() + Fx = Fx + Cx[i]*s; Fy = Fy + Cy[i]*s + return Fx, Fy + +# ---- геометрия (ИДЕНТИЧНА базовым версиям) ---- +Nx, Ny, D, cx, cy = 150, 72, 16, 40, 36 +U, Re, STEPS, ramp, FE = 0.07, 150.0, int(os.environ.get("AMR_STEPS", 8000)), 1000, 34 +D0 = D; nu = U*D/Re; tau0 = nu/CS2 + 0.5 +ax1, bx1, ay1, by1 = 16, 118, 8, 64 +cx2a, cx2b, cy2a, cy2b = 26, 64, 18, 54 +px, py = cx + 3*D, cy +def _cmask(NX, NY, ccx, ccy, R): + Y, X = np.meshgrid(np.arange(NY), np.arange(NX), indexing="ij"); return (X-ccx)**2 + (Y-ccy)**2 <= R*R +def _csdf(NX, NY, ccx, ccy, R): + Y, X = np.meshgrid(np.arange(NY), np.arange(NX), indexing="ij"); return np.sqrt((X-ccx)**2.0 + (Y-ccy)**2.0) - R +# host-маски/SDF +_walls = np.zeros((Ny, Nx), bool); _walls[0, :] = True; _walls[-1, :] = True +cyl0_np = _cmask(Nx, Ny, cx, cy, D/2); solid0_np = cyl0_np | _walls +_Yg = np.arange(Ny)[:, None]*np.ones((1, Nx)) +phi0_np = np.minimum(_csdf(Nx, Ny, cx, cy, D/2), np.minimum(_Yg-0.5, (Ny-1.5)-_Yg)) +P1 = patch(Nx, Ny, ax1, bx1, ay1, by1, 2); P2 = patch(P1["Nfx"], P1["Nfy"], (cx2a-ax1)*2, (cx2b-ax1)*2, (cy2a-ay1)*2, (cy2b-ay1)*2, 2) +solid1_np = _cmask(P1["Nfx"], P1["Nfy"], (cx-ax1)*2, (cy-ay1)*2, D); phi1_np = _csdf(P1["Nfx"], P1["Nfy"], (cx-ax1)*2, (cy-ay1)*2, D) +solid2_np = _cmask(P2["Nfx"], P2["Nfy"], (cx-cx2a)*4, (cy-cy2a)*4, 2*D); phi2_np = _csdf(P2["Nfx"], P2["Nfy"], (cx-cx2a)*4, (cy-cy2a)*4, 2*D) +# device-маски (без SDF) +g_solid0 = xp.asarray(solid0_np); g_cyl0 = xp.asarray(cyl0_np); g_fl0 = ~g_solid0 +g_solid1 = xp.asarray(solid1_np); g_fl1 = ~g_solid1 +g_solid2 = xp.asarray(solid2_np); g_fl2 = ~g_solid2 +# предвычисленные маски линков для силы (узловая граница) +L0_links = build_links(solid0_np, cyl0_np) +L1_links = build_links(solid1_np, solid1_np) +L2_links = build_links(solid2_np, solid2_np) +# SDF-ГУ +BC0 = build_bc(solid0_np, phi0_np, cyl0_np); BC1 = build_bc(solid1_np, phi1_np, solid1_np); BC2 = build_bc(solid2_np, phi2_np, solid2_np) +# рестрикция: жидкие узлы +fl1 = xp.asarray(~solid0_np[ay1+1:by1, ax1+1:bx1]) +fl2 = xp.ones((P2["by"]-P2["ay"]-1, P2["bx"]-P2["ax"]-1), bool); fl2 = xp.asarray(fl2) +# τ / масштабы +t1 = 2*tau0 - 0.5; t2 = 2*t1 - 0.5 +b0 = 1/(2*tau0); b1 = 1/(2*t1); b2 = 1/(2*t2) +R01 = t1/(2*tau0); Rf01 = 1/R01; R12 = t2/(2*t1); Rf12 = 1/R12 + +# ---- прогресс-бар (ASCII-шкала по выполненным шагам из заданных) ---- +import time as _time +def make_progress(label, width=32, every=0.1): + st = {"t0": _time.perf_counter(), "last": 0.0} + def cb(t, total): + now = _time.perf_counter(); done = (t >= total) + if not done and (now - st["last"] < every): # троттлинг, чтобы не спамить консоль + return + st["last"] = now; frac = (t + 1) / (total + 1) + filled = int(round(width * frac)); bar = "#" * filled + "-" * (width - filled) + el = now - st["t0"]; eta = (el / frac - el) if frac > 0 else 0.0 + print(f"\r {label:7}[{bar}] {frac*100:5.1f}% ({t}/{total}) {el:5.1f}s ETA {eta:5.1f}s", + end=("\n" if done else ""), flush=True) + return cb + +# ---- захват CUDA-графа одного шага ---- +def _capture(step_fn): + cp.cuda.Device().synchronize() + s = cp.cuda.Stream(non_blocking=True) + with s: + s.begin_capture() + try: + step_fn() + except Exception: + try: s.end_capture() + except Exception: pass + raise + g = s.end_capture() + return g + +def run(mode, use_sdf, progress=None): + """mode: none|amr2x|nested. Возвращает {Fx,Fy,uy (host), frames (host), DL, mode}. + progress(t, STEPS) — необязательный колбэк. CUDA Graphs: env AMR_CUDAGRAPH (по умолч. вкл).""" + use1 = mode in ("amr2x", "nested"); use2 = (mode == "nested") + DL = {"none": D0, "amr2x": 2*D0, "nested": 4*D0}[mode] + + # ---- persistent-состояние (фиксированные буферы для replay графа) ---- + F0 = feq(xp.ones((Ny, Nx), DTYPE), xp.zeros((2, Ny, Nx), DTYPE)).copy() + F1 = feq(xp.ones((P1["Nfy"], P1["Nfx"]), DTYPE), xp.zeros((2, P1["Nfy"], P1["Nfx"]), DTYPE)).copy() if use1 else None + F2 = feq(xp.ones((P2["Nfy"], P2["Nfx"]), DTYPE), xp.zeros((2, P2["Nfy"], P2["Nfx"]), DTYPE)).copy() if use2 else None + onecol = xp.ones((Ny, 1), DTYPE) + uin_dev = xp.zeros((2, Ny, 1), DTYPE) # вход; обновляется СНАРУЖИ захвата + Fx_s = xp.zeros((), DTYPE); Fy_s = xp.zeros((), DTYPE); uy_s = xp.zeros((), DTYPE) + # разгон входа на device: U*smoothstep(t/ramp) + _ts = np.minimum(np.arange(STEPS+1)/ramp, 1.0) + ramp_u = xp.asarray(U*(_ts*_ts*(3-2*_ts)), DTYPE) + Fx = xp.zeros(STEPS+1, DTYPE); Fy = xp.zeros(STEPS+1, DTYPE); uy = xp.zeros(STEPS+1, DTYPE) + frames = [] + + def _step(): + # ----- уровень 0 ----- + rho, u0 = macros(F0) + pre = F0.copy() + post0 = collide(F0, feq(rho, u0), b0) + if not use_sdf: + f0 = stream(bb_set(post0.copy(), pre, g_solid0)) + else: + f0 = stream(post0); f0 = apply_bc(f0, post0, BC0) + if mode == "none": + fx, fy = (force_bc(post0, f0, BC0) if use_sdf else force_on(post0, f0, L0_links)) + Fx_s[...] = fx; Fy_s[...] = fy + # вход/выход (разгон читаем из uin_dev) + f0[:, 1:-1, 0] = feq(onecol, uin_dev)[:, 1:-1, 0]; f0[:, 1:-1, -1] = f0[:, 1:-1, -2] + # ----- уровень 1 ----- + if use1: + g1o = ghost(pre, P1, R01); g1n = ghost(f0, P1, R01) + f1 = F1 + for s1 in range(2): + pre1 = f1.copy(); r1, u1 = macros(f1); post1 = collide(f1, feq(r1, u1), b1) + if not use_sdf: + f1 = stream(bb_set(post1.copy(), pre1, g_solid1)) + else: + f1 = stream(post1); f1 = apply_bc(f1, post1, BC1) + if mode == "amr2x" and s1 == 1: + fx, fy = (force_bc(post1, f1, BC1) if use_sdf else force_on(post1, f1, L1_links)) + Fx_s[...] = fx; Fy_s[...] = fy + f1 = fill(f1, (1-(s1+1)/2)*g1o + ((s1+1)/2)*g1n) + # ----- уровень 2 ----- + if use2: + g2o = ghost(pre1, P2, R12); g2n = ghost(f1, P2, R12) + f2 = F2 + for s2 in range(2): + pre2 = f2.copy(); r2, u2 = macros(f2); post2 = collide(f2, feq(r2, u2), b2) + if not use_sdf: + f2 = stream(bb_set(post2.copy(), pre2, g_solid2)) + else: + f2 = stream(post2); f2 = apply_bc(f2, post2, BC2) + if s1 == 1 and s2 == 1: + fx, fy = (force_bc(post2, f2, BC2) if use_sdf else force_on(post2, f2, L2_links)) + Fx_s[...] = fx; Fy_s[...] = fy + f2 = fill(f2, (1-(s2+1)/2)*g2o + ((s2+1)/2)*g2n) + f1 = restrict(f2, f1, P2, Rf12, fl2) + F2[...] = f2 + f0 = restrict(f1, f0, P1, Rf01, fl1) + F1[...] = f1 + # зонд скорости в следе + запись состояния + col = f0[:, py, px]; uy_s[...] = (CYa*col).sum()/col.sum() + F0[...] = f0 + + use_graph = (os.environ.get("AMR_CUDAGRAPH", "1") != "0") # CUDA Graphs по умолчанию ВКЛ (AMR_CUDAGRAPH=0 — выкл) + graph = None; graph_failed = False + def _snap(): + return (F0.copy(), F1.copy() if use1 else None, F2.copy() if use2 else None) + def _restore(s): + F0[...] = s[0] + if use1: F1[...] = s[1] + if use2: F2[...] = s[2] + def _maxdiff(s): + d = float(xp.abs(s[0]-F0).max()) + if use1: d = max(d, float(xp.abs(s[1]-F1).max())) + if use2: d = max(d, float(xp.abs(s[2]-F2).max())) + return d + for t in range(STEPS+1): + uin_dev[0, :, 0] = ramp_u[t] + did = False + if t == 1 and use_graph and not graph_failed: + # захват графа + РАНТАЙМ-САМОПРОВЕРКА: один шаг графом vs eager; при расхождении — откат + try: + graph = _capture(_step) # запись (без исполнения) + before = _snap() # состояние после t=0 + graph.launch() # граф -> результат t=1 + gres = _snap() + _restore(before); _step() # eager -> доверенный результат t=1 + d = _maxdiff(gres) + if d > 1e-3: + print(f"\n[graph] self-check разошёлся (Δ={d:.2e}) — отключаю графы, работаю eager") + graph = None; graph_failed = True + else: + print(f"\n[graph] self-check OK (Δ={d:.2e}) — CUDA graphs активны") + did = True # шаг t=1 уже выполнен (eager-результат — доверенный) + except Exception as e: + print(f"\n[graph] недоступны ({type(e).__name__}: {e}) — работаю eager") + import traceback as _tb; _tb.print_exc() # точная строка H2D/несовместимости + graph = None; graph_failed = True + try: cp.cuda.Device().synchronize() + except Exception: pass + if not did: + if graph is not None and t >= 1: + graph.launch() + else: + _step() + Fx[t] = Fx_s; Fy[t] = Fy_s; uy[t] = uy_s + if progress is not None: + progress(t, STEPS) + if t % 500 == 0 and not bool(xp.isfinite(F0).all()): + print("BLEW UP", mode, t); Fx = Fx[:t]; Fy = Fy[:t]; uy = uy[:t]; break + if t % FE == 0: + frames.append((t, to_cpu(macros(F0)[1]), + to_cpu(macros(F1)[1]) if use1 else None, + to_cpu(macros(F2)[1]) if use2 else None)) + return dict(mode=mode, DL=DL, Fx=to_cpu(Fx), Fy=to_cpu(Fy), uy=to_cpu(uy), frames=frames) + +# ---- анализ (на host: FFT малых рядов) ---- +def analyze(res): + Fx, Fy, uy, DL = res["Fx"], res["Fy"], res["uy"], res["DL"] + n = len(uy); h = slice(n//2, n); Cd = 2*Fx/(U**2*DL); Cl = 2*Fy/(U**2*DL) + sig = uy[h] - uy[h].mean(); npad = 8192 + freqs = np.fft.rfftfreq(npad, 1.0); amp = np.abs(np.fft.rfft(sig, n=npad)) + St = (freqs[1+int(np.argmax(amp[1:]))] if len(amp) > 2 else 0.0)*D0/U + return dict(Cd=float(Cd[h].mean()), Clrms=float(Cl[h].std()), St=float(St), uyrms=float(uy[h].std()), + Cl_s=Cl, uy=uy, freqs=freqs, amp=amp, h0=n//2) + +# ---- визуализация (matplotlib на CPU; кадры уже host) ---- +def _vort_np(u): + return (np.roll(u[1], -1, 1)-np.roll(u[1], 1, 1))*0.5 - (np.roll(u[0], -1, 0)-np.roll(u[0], 1, 0))*0.5 +def save_gif(res, name, anim_dir, sdf_tag, fps=24): + import matplotlib; matplotlib.use("Agg") + import matplotlib.pyplot as plt, matplotlib.patches as mpatches + from PIL import Image + nested = (res["mode"] == "nested"); has1 = res["mode"] in ("amr2x", "nested"); frames = res["frames"] + vm = np.nanpercentile(np.abs(np.where(solid0_np, np.nan, _vort_np(frames[len(frames)//2][1]))), 99.0) + cm = plt.get_cmap("inferno").copy(); cm.set_bad("white"); pil = [] + for (t, u0, u1, u2) in frames: + fig = plt.figure(figsize=(11.2, 5.7), dpi=96); ax = fig.add_subplot(111) + ax.imshow(np.abs(np.where(solid0_np, np.nan, _vort_np(u0))), origin="lower", cmap=cm, vmin=0, vmax=vm, + extent=(0, Nx, 0, Ny), interpolation="nearest") + if has1 and u1 is not None: + ax.imshow(np.abs(np.where(solid1_np, np.nan, _vort_np(u1)))[1:-1, 1:-1], origin="lower", cmap=cm, vmin=0, vmax=vm, + extent=(ax1+0.5, bx1-0.5, ay1+0.5, by1-0.5), interpolation="nearest") + if nested and u2 is not None: + ax.imshow(np.abs(np.where(solid2_np, np.nan, _vort_np(u2)))[1:-1, 1:-1], origin="lower", cmap=cm, vmin=0, vmax=vm, + extent=(cx2a+0.25, cx2b-0.25, cy2a+0.25, cy2b-0.25), interpolation="nearest") + ax.add_patch(mpatches.Rectangle((0.2, 0.2), Nx-0.4, Ny-0.4, fill=False, edgecolor="#4fc3f7", lw=1.6)) + ax.text(1.5, Ny-4, "уровень 0: Δx (крупный)", color="#4fc3f7", fontsize=9, weight="bold") + if has1: + ax.add_patch(mpatches.Rectangle((ax1, ay1), bx1-ax1, by1-ay1, fill=False, edgecolor="#aed581", lw=2.2)) + ax.text(ax1+1, by1-3.5, "уровень 1: Δx/2 (тело+след)", color="#aed581", fontsize=9, weight="bold") + if nested: + ax.add_patch(mpatches.Rectangle((cx2a, cy2a), cx2b-cx2a, cy2b-cy2a, fill=False, edgecolor="#ff8a65", lw=2.2)) + ax.text(cx2a+1, cy2b-3.5, "уровень 2: Δx/4 (у тела)", color="#ff8a65", fontsize=9, weight="bold") + base = ("Вложенный AMR" if nested else "AMR (одиночный блок 2×)") if has1 else "Без AMR (D=16)" + ax.set_title(f"{base}{sdf_tag} · поверх $|\\omega|$ · t={t}", fontsize=11) + ax.set_xlabel("x [lu]"); ax.set_ylabel("y [lu]"); ax.set_xlim(0, Nx); ax.set_ylim(0, Ny) + buf = _io.BytesIO(); fig.savefig(buf, format="png", bbox_inches="tight"); buf.seek(0); plt.close(fig) + pil.append(Image.open(buf).convert("RGB").convert("P", palette=Image.ADAPTIVE)) + path = os.path.join(anim_dir, name) + pil[0].save(path, save_all=True, append_images=pil[1:], duration=int(1000/fps), loop=0, optimize=True) + print("saved", name, len(frames), "кадров") + +LAB = ["без AMR (D=16)", "AMR 2× (D=32)", "AMR 2×+4× (D=64)"] +def print_table(AS, header): + print(f"\n=== {header} ===") + print(f"{'версия':22}{'D у тела':>9}{'St':>8}{'':>9}{'rms Cl':>9}{'rms u_y':>9}") + for lab, DL, a in zip(LAB, [16, 32, 64], AS): + print(f"{lab:22}{DL:>9}{a['St']:>8.3f}{a['Cd']:>9.3f}{a['Clrms']:>9.4f}{a['uyrms']:>9.4f}") + print(f"{'литература Re≈150':22}{'—':>9}{0.183:>8.3f}{1.330:>9.3f}{'~0.3':>9}{'':>9}") + print("(лит.: St≈0.18, Cd≈1.3 для цилиндра при Re≈150; Williamson 1996, Henderson 1995)") +def probe_figure(AS, R2, path, suptitle): + import matplotlib; matplotlib.use("Agg") + import matplotlib.pyplot as plt, matplotlib.patches as mpatches + cols = ["#9e9e9e", "#1f6feb", "#d1495b"] + fig = plt.figure(figsize=(13.5, 8.2)); gs = fig.add_gridspec(2, 2, hspace=0.32, wspace=0.22) + axA = fig.add_subplot(gs[0, 0]); mid = R2["frames"][len(R2["frames"])//2] + vmf = np.nanpercentile(np.abs(np.where(solid0_np, np.nan, _vort_np(mid[1]))), 99) + cmf = plt.get_cmap("inferno").copy(); cmf.set_bad("white") + axA.imshow(np.abs(np.where(solid0_np, np.nan, _vort_np(mid[1]))), origin="lower", cmap=cmf, vmin=0, vmax=vmf, + extent=(0, Nx, 0, Ny), interpolation="nearest") + axA.add_patch(mpatches.Rectangle((ax1, ay1), bx1-ax1, by1-ay1, fill=False, edgecolor="#aed581", lw=1.8)) + axA.add_patch(mpatches.Rectangle((cx2a, cy2a), cx2b-cx2a, cy2b-cy2a, fill=False, edgecolor="#ff8a65", lw=1.8)) + axA.set_title("$|\\omega|$ + рамки зон 2×/4×"); axA.set_xlabel("x [lu]"); axA.set_ylabel("y [lu]") + axB = fig.add_subplot(gs[0, 1]) + for a, lab, c in zip(AS, LAB, cols): axB.plot(a["Cl_s"][a["h0"]:], lw=0.8, color=c, label=lab) + axB.set_title("Подъёмная сила $C_l(t)$ (зонд силы)"); axB.set_xlabel("шаг"); axB.set_ylabel("$C_l$") + axB.legend(fontsize=8); axB.grid(alpha=0.3) + axC = fig.add_subplot(gs[1, 0]) + for a, lab, c in zip(AS, LAB, cols): + sp = a["amp"]/a["amp"][1:].max(); axC.plot(a["freqs"]*D0/U, sp, lw=1.0, color=c, label=lab) + axC.axvline(0.183, color="k", ls="--", alpha=0.6, label="лит. St≈0.18"); axC.set_xlim(0, 0.6) + axC.set_title("Спектр $u_y$ в следе → St"); axC.set_xlabel("St = f·D/U"); axC.set_ylabel("норм. ампл.") + axC.legend(fontsize=8); axC.grid(alpha=0.3) + axD = fig.add_subplot(gs[1, 1]); x = np.arange(3); w = 0.35 + axD.bar(x-w/2, [a["St"] for a in AS], w, color="#1f6feb", label="St") + axD.bar(x+w/2, [a["Cd"] for a in AS], w, color="#fb8c00", label="") + axD.axhline(0.183, color="#1f6feb", ls="--", alpha=0.6); axD.axhline(1.33, color="#fb8c00", ls="--", alpha=0.6) + axD.set_xticks(x); axD.set_xticklabels(["без AMR", "2×", "2×+4×"]); axD.set_title("St и (пунктир — лит.)") + axD.legend(fontsize=8); axD.grid(alpha=0.3, axis="y") + fig.suptitle(suptitle, fontweight="bold"); fig.savefig(path, dpi=110, bbox_inches="tight"); plt.close(fig) + print("saved", os.path.basename(path)) diff --git a/docs/theory/anim/amr2x_cyl.gif b/docs/theory/anim/amr2x_cyl.gif new file mode 100644 index 0000000..2da0ad3 Binary files /dev/null and b/docs/theory/anim/amr2x_cyl.gif differ diff --git a/docs/theory/anim/amr2x_cyl_sdf.gif b/docs/theory/anim/amr2x_cyl_sdf.gif new file mode 100644 index 0000000..9ca9c5e Binary files /dev/null and b/docs/theory/anim/amr2x_cyl_sdf.gif differ diff --git a/docs/theory/anim/amr_cylinder.gif b/docs/theory/anim/amr_cylinder.gif new file mode 100644 index 0000000..639688b Binary files /dev/null and b/docs/theory/anim/amr_cylinder.gif differ diff --git a/docs/theory/anim/amr_nested.gif b/docs/theory/anim/amr_nested.gif new file mode 100644 index 0000000..7578a8e Binary files /dev/null and b/docs/theory/anim/amr_nested.gif differ diff --git a/docs/theory/anim/amr_nested_cyl.gif b/docs/theory/anim/amr_nested_cyl.gif new file mode 100644 index 0000000..948d9f1 Binary files /dev/null and b/docs/theory/anim/amr_nested_cyl.gif differ diff --git a/docs/theory/anim/amr_nested_cyl_sdf.gif b/docs/theory/anim/amr_nested_cyl_sdf.gif new file mode 100644 index 0000000..61f225e Binary files /dev/null and b/docs/theory/anim/amr_nested_cyl_sdf.gif differ diff --git a/docs/theory/anim/cavity_transient.gif b/docs/theory/anim/cavity_transient.gif new file mode 100644 index 0000000..9998737 Binary files /dev/null and b/docs/theory/anim/cavity_transient.gif differ diff --git a/docs/theory/anim/obstacle_shapes.gif b/docs/theory/anim/obstacle_shapes.gif new file mode 100644 index 0000000..1880c85 Binary files /dev/null and b/docs/theory/anim/obstacle_shapes.gif differ diff --git a/docs/theory/anim/shear_bgk_vs_kbc.gif b/docs/theory/anim/shear_bgk_vs_kbc.gif new file mode 100644 index 0000000..e174393 Binary files /dev/null and b/docs/theory/anim/shear_bgk_vs_kbc.gif differ diff --git a/docs/theory/anim/tgv_decay.gif b/docs/theory/anim/tgv_decay.gif new file mode 100644 index 0000000..0a5b223 Binary files /dev/null and b/docs/theory/anim/tgv_decay.gif differ diff --git a/docs/theory/demos_gpu/README.md b/docs/theory/demos_gpu/README.md new file mode 100644 index 0000000..3c5334f --- /dev/null +++ b/docs/theory/demos_gpu/README.md @@ -0,0 +1,36 @@ +# demos_gpu — GPU-прогоны демо для ноутбука kbc_lbm.ipynb + +Ноутбук **не исполняет код** — он встраивает готовые артефакты (png/gif) и цитирует числа. +Все симуляции здесь, **только GPU/CuPy** (CPU-фолбэка нет). Физика не дублируется: решётка, +равновесие, KBC-столкновение, перенос и AMR-связка импортируются из `../solver_2x_sdf` — +демо тем самым гоняют **те же компоненты, что и финальная модель**. + +## Запуск (на GPU-сервере, из этой папки) + +```sh +python checks_gpu.py # самопроверки математики → out/checks.txt +python tgv_gpu.py # Тейлор–Грин: вязкость, H-теорема → figures/07*, anim/tgv_decay.gif +python shear_gpu.py # сдвиговый слой BGK vs KBC → figures/08*, anim/shear_bgk_vs_kbc.gif +python cavity_gpu.py # каверна Re=1000 vs Ghia → figures/09*, anim/cavity_transient.gif +python obstacle_gpu.py # 4 тела, дорожки Кармана → figures/10*, anim/obstacle_shapes.gif +python amr_demo_gpu.py # AMR: демо + бенчмарк + вложенный → figures/11d*, anim/amr_{cylinder,nested}.gif +python figures_static.py # стенсили/блок-схема/схема AMR → figures/01,06,11c,11_d3q27 (после obstacle!) +``` + +`figures_static.py` — единственный скрипт без GPU (чистый matplotlib, можно гонять локально); +схему `11c` он перерисовывает по фону из `out/obstacle_circle_field.npz`, который пишет +`obstacle_gpu.py` — поэтому его запускать **после** obstacle. + +Env: `AMR_FP64=1` — двойная точность (жёстче пороги самопроверок в checks_gpu). + +| Скрипт | Время (примерно, совр. GPU) | +|---|---| +| checks_gpu | секунды | +| tgv_gpu | ~1 мин (10k шагов, 96²) | +| shear_gpu | ~1–2 мин (2×8k, 128²) | +| cavity_gpu | ~1–2 мин (до 14k, 110²) | +| obstacle_gpu | ~3–5 мин (4×9.6k, 150×72) | +| amr_demo_gpu | ~5–10 мин (демо + 6 бенчмарков + анимация) | + +Артефакты идут в общие каталоги `../figures` и `../anim` под **теми же именами**, что +исторически использовал ноутбук; числовые сводки — в `out/*.txt|npz`. diff --git a/docs/theory/demos_gpu/_common.py b/docs/theory/demos_gpu/_common.py new file mode 100644 index 0000000..cc45dff --- /dev/null +++ b/docs/theory/demos_gpu/_common.py @@ -0,0 +1,128 @@ +# Общая инфраструктура GPU-демо (ноутбук kbc_lbm.ipynb код не исполняет — только встраивает +# артефакты, которые генерят эти скрипты на GPU-сервере). +# +# Физика НЕ дублируется: решётка/равновесие/столкновение/перенос импортируются из +# ../solver_2x_sdf (те же модули, что и в финальной модели) — демо тем самым доказывают, +# что КОМПОНЕНТЫ финальной модели воспроизводят классические бенчмарки. +# Здесь только то, чего в модели нет намеренно: полиномиальное равновесие и BGK +# (для сравнений «BGK vs KBC»), H-функция, γ-поле для визуализации, гифки. +import os +import sys +import io as _io + +HERE = os.path.dirname(os.path.abspath(__file__)) +THEORY = os.path.dirname(HERE) +sys.path.insert(0, os.path.join(THEORY, "solver_2x_sdf")) + +import backend as B # GPU-only: жёсткая ошибка без CuPy (CPU-фолбэка нет намеренно) +import lattice as L +import equilibrium as E +import collision as Coll +import streaming as Strm +import visualization as Viz # make_progress (ASCII-бар) + +cp = B.cp; xp = B.xp; DTYPE = B.DTYPE; to_cpu = B.to_cpu +Q = L.Q; CS2 = L.CS2; OPP = L.OPP; Cx = L.Cx; Cy = L.Cy + +import numpy as np + +# пути артефактов: фигуры/гифки — общие каталоги theory, числа — demos_gpu/out +FIGDIR = os.path.join(THEORY, "figures"); os.makedirs(FIGDIR, exist_ok=True) +ANIMDIR = os.path.join(THEORY, "anim"); os.makedirs(ANIMDIR, exist_ok=True) +OUTDIR = os.path.join(HERE, "out"); os.makedirs(OUTDIR, exist_ok=True) + +import matplotlib +matplotlib.use("Agg") +import matplotlib.pyplot as plt + +try: + sys.stdout.reconfigure(encoding="utf-8") # кириллица/греческие в print при cp1251-консоли +except Exception: + pass + +plt.rcParams.update({ + "figure.dpi": 110, "savefig.dpi": 120, "font.size": 11, + "axes.titlesize": 13, "axes.titleweight": "bold", + "axes.grid": True, "grid.alpha": 0.25, "axes.axisbelow": True, + "figure.facecolor": "white", "axes.facecolor": "#fbfbfd", +}) + +# пороги самопроверок под точность бэкенда (демо обычно гоняются в float32) +FP64 = (DTYPE == cp.float64) +TOL_EXACT = 1e-12 if FP64 else 2e-5 # «точные» тождества (моменты равновесия и т.п.) + +def finish(fig, name): + """Сохранить фигуру в figures/ под тем же именем, что использовал ноутбук.""" + fig.savefig(os.path.join(FIGDIR, name), bbox_inches="tight") + plt.close(fig) + print("PNG:", name) + +def write_out(name, lines): + """Дописать результаты в demos_gpu/out/ (ноутбук цитирует эти числа в markdown).""" + with open(os.path.join(OUTDIR, name), "w", encoding="utf-8") as fh: + fh.write("\n".join(lines) + "\n") + print("OUT:", name) + +# ----- дополнения к модели (нужны только демо) ------------------------------------------------ + +def feq_poly(rho, u): + """Полиномиальное равновесие O(u²) — стандарт BGK (в модели НЕ используется; здесь — + для демонстрации «BGK+poly разрушается там, где KBC+entropic держит»).""" + CXa = L.CXa[:, None, None]; CYa = L.CYa[:, None, None]; Wa = L.Wa[:, None, None] + cu = CXa*u[0] + CYa*u[1] + usq = u[0]**2 + u[1]**2 + return Wa * rho * (1.0 + cu/CS2 + cu**2/(2.0*CS2*CS2) - usq/(2.0*CS2)) + +def bgk_collide(f, fe, beta): + """Классический BGK: f − ω(f−feq), ω=2β. Эквивалент KBC при γ=2.""" + return f - 2.0*beta*(f - fe) + +def kbc_gamma(f, fe, beta): + """Поле энтропийного стабилизатора γ (для визуализации; сам оператор — collision.kbc_collide, + формула та же: γ = 1/β − (2−1/β)·⟨Δs|Δh⟩/⟨Δh|Δh⟩).""" + dfn = f - fe + ds = Coll._project_shift(dfn) + dh = dfn - ds; inv = 1.0/fe + num = (ds*dh*inv).sum(0); den = (dh*dh*inv).sum(0) + nrm = (dfn*dfn*inv).sum(0) # тот же относительный порог, что в collision.py + ok = den > B.GREL*nrm + return xp.where(ok, 1.0/beta - (2.0 - 1.0/beta)*num/xp.where(ok, den, B.ONE), B.TWO) + +def nu_to_beta(nu): + return 1.0 / (2.0 * (nu / CS2 + 0.5)) + +def H_function(f): + """Дискретная H-функция H = Σ f_i ln(f_i/w_i) (поле).""" + fp = xp.maximum(f, 1e-30) + return (fp * xp.log(fp / L.Wa[:, None, None])).sum(0) + +def smoothstep(x): + x = min(max(x, 0.0), 1.0) + return x*x*(3.0 - 2.0*x) + +# ----- host-постобработка (numpy: кадры уже перенесены на хост) -------------------------------- + +def vorticity(u): + """ω = ∂x u_y − ∂y u_x центральными разностями (host, по кадру).""" + duy_dx = (np.roll(u[1], -1, 1) - np.roll(u[1], 1, 1)) * 0.5 + dux_dy = (np.roll(u[0], -1, 0) - np.roll(u[0], 1, 0)) * 0.5 + return duy_dx - dux_dy + +def render_gif(n_frames, draw_fn, name, figsize, fps=18, dpi=80): + """Отрисовать n_frames кадров (draw_fn(fig, i)) и сохранить зацикленный GIF в anim/.""" + from PIL import Image + path = os.path.join(ANIMDIR, name) + fig = plt.figure(figsize=figsize, dpi=dpi) + pil = [] + for i in range(n_frames): + fig.clf() + draw_fn(fig, i) + buf = _io.BytesIO() + fig.savefig(buf, format="png") + buf.seek(0) + pil.append(Image.open(buf).convert("RGB").convert("P", palette=Image.ADAPTIVE)) + plt.close(fig) + pil[0].save(path, save_all=True, append_images=pil[1:], + duration=int(1000 / fps), loop=0, optimize=True) + print("GIF:", name, f"({n_frames} кадров)") + return path diff --git a/docs/theory/demos_gpu/amr_demo_gpu.py b/docs/theory/demos_gpu/amr_demo_gpu.py new file mode 100644 index 0000000..d7adc29 --- /dev/null +++ b/docs/theory/demos_gpu/amr_demo_gpu.py @@ -0,0 +1,265 @@ +# Демо-5: блочное измельчение (AMR) на компонентах solver_2x_sdf (amr.patch/ghost/fill/restrict — +# ТЕ ЖЕ функции, что в финальной модели). Три части: +# 1) минимальный 2-уровневый AMR на цилиндре (без временно́й интерполяции) → anim/amr_cylinder.gif +# 2) бенчмарк 5 вариантов против эталона uniform-fine 4× (тест-вихрь) → figures/11d_amr_comparison.png +# 3) анимация полного вложенного 2×+4× с временно́й интерполяцией → anim/amr_nested.gif +# Числа → out/amr_bench.txt|npz. Запуск: python amr_demo_gpu.py +import os +import time as _time +import numpy as np +import _common as cm +import amr as Amr # из solver_2x_sdf (sys.path настроен в _common) + +cp = cm.cp; xp = cm.xp; E = cm.E; Coll = cm.Coll; Strm = cm.Strm +plt = cm.plt; vorticity = cm.vorticity; OPP = cm.OPP; Q = cm.Q; CS2 = cm.CS2 +import matplotlib.patches as mpatches + +def _sync(): + cp.cuda.Device().synchronize() + +# ===== часть 1: минимальный 2-уровневый AMR на цилиндре ========================================= +def run_amr_cylinder(Nx=120, Ny=60, D=10, U=0.06, Re=120.0, steps=5400, + ramp=1000, frame_every=22): + cx, cy = Nx//4, Ny//2 + nu = U*D/Re + tau_c = nu/CS2 + 0.5; beta_c = cm.nu_to_beta(nu) + tau_f = 2*tau_c - 0.5; beta_f = 1.0/(2*tau_f) + Rcf = tau_f/(2*tau_c); Rfc = 1.0/Rcf + bx0 = max(cx - 2*D, 2); bx1 = min(cx + 3*D, Nx - 2) + by0 = max(cy - 2*D, 2); by1 = min(cy + 2*D, Ny - 2) + P = Amr.patch(Nx, Ny, bx0, bx1, by0, by1, 2) + Nfx, Nfy = P["Nfx"], P["Nfy"] + # маски тела (host → device); стенки канала входят в solid_c + Yc_, Xc_ = np.mgrid[0:Ny, 0:Nx] + solid_c_np = (Xc_ - cx)**2 + (Yc_ - cy)**2 <= (D/2)**2 + solid_c_np[0, :] = True; solid_c_np[-1, :] = True + fcx, fcy = 2*(cx - bx0), 2*(cy - by0) + Yf_, Xf_ = np.mgrid[0:Nfy, 0:Nfx] + solid_f_np = (Xf_ - fcx)**2 + (Yf_ - fcy)**2 <= float(D)**2 + solid_c = cp.asarray(solid_c_np); solid_f = cp.asarray(solid_f_np) + block_fluid = cp.asarray(~solid_c_np[by0+1:by1, bx0+1:bx1]) + onecol = cp.ones((Ny, 1), cm.DTYPE) + fc = E.feq(cp.ones((Ny, Nx), cm.DTYPE), cp.zeros((2, Ny, Nx), cm.DTYPE)) + ff = E.feq(cp.ones((Nfy, Nfx), cm.DTYPE), cp.zeros((2, Nfy, Nfx), cm.DTYPE)) + frames = [] + prog = cm.Viz.make_progress("amr-cyl") + for t in range(steps + 1): + rho, u = E.macros(fc) + pre = fc.copy() + fc = Coll.kbc_collide(fc, E.feq(rho, u), beta_c) + for i in range(Q): + fc[i, solid_c] = pre[OPP[i], solid_c] + fc = Strm.stream(fc) + uin = cp.zeros((2, Ny, 1), cm.DTYPE); uin[0, :, 0] = U*cm.smoothstep(t/ramp) + fc[:, 1:-1, 0] = E.feq(onecol, uin)[:, 1:-1, 0] + fc[:, 1:-1, -1] = fc[:, 1:-1, -2] + # МИНИМАЛЬНЫЙ AMR: один ghost на оба подшага (без временно́й интерполяции) + gh = Amr.ghost(fc, P, Rcf) + for _ in range(2): + rf, uf = E.macros(ff); pref = ff.copy() + ff = Coll.kbc_collide(ff, E.feq(rf, uf), beta_f) + for i in range(Q): + ff[i, solid_f] = pref[OPP[i], solid_f] + ff = Strm.stream(ff) + ff = Amr.fill(ff, gh) + fc = Amr.restrict(ff, fc, P, Rfc, block_fluid) + if t % frame_every == 0: + frames.append((t, cm.to_cpu(E.macros(fc)[1]), cm.to_cpu(E.macros(ff)[1]))) + prog(t, steps) + return dict(frames=frames, solid_c=solid_c_np, solid_f=solid_f_np, Nx=Nx, Ny=Ny, + bx0=bx0, bx1=bx1, by0=by0, by1=by1, tau_c=tau_c, tau_f=tau_f, Rcf=Rcf) + +amr = run_amr_cylinder() +print(f"AMR-цилиндр: крупная {amr['Nx']}x{amr['Ny']} + мелкий блок 2x, " + f"tau_c={amr['tau_c']:.3f} tau_f={amr['tau_f']:.3f} Rcf={amr['Rcf']:.3f}, " + f"кадров={len(amr['frames'])} (устойчиво)") + +_af = amr["frames"] +_vmaxA = np.nanpercentile(np.abs(np.where(amr["solid_c"], np.nan, + vorticity(_af[len(_af)//2][1]))), 99.0) +_cmapA = plt.get_cmap("RdBu_r").copy(); _cmapA.set_bad("#1b1b1b") + +def _draw_amr(fig, i): + t, uc, uf = _af[i] + ax = fig.add_subplot(111) + ax.imshow(np.where(amr["solid_c"], np.nan, vorticity(uc)), origin="lower", + cmap=_cmapA, vmin=-_vmaxA, vmax=_vmaxA, extent=(0, amr["Nx"], 0, amr["Ny"]), + interpolation="nearest") + omf = np.where(amr["solid_f"], np.nan, vorticity(uf))[1:-1, 1:-1] + ax.imshow(omf, origin="lower", cmap=_cmapA, vmin=-_vmaxA, vmax=_vmaxA, + extent=(amr["bx0"]+0.5, amr["bx1"]-0.5, amr["by0"]+0.5, amr["by1"]-0.5), + interpolation="nearest") + ax.add_patch(mpatches.Rectangle((amr["bx0"], amr["by0"]), + amr["bx1"]-amr["bx0"], amr["by1"]-amr["by0"], + fill=False, edgecolor="#ffe600", lw=3.0)) + ax.text(amr["bx0"]+1, amr["by1"]-4, "мелкий блок 2×", color="#ffe600", fontsize=9, weight="bold") + ax.set_title(f"AMR: крупная сетка + мелкий блок 2× (жёлтая рамка) · t={t}", fontsize=10) + ax.set_xticks([]); ax.set_yticks([]) + fig.tight_layout() + +cm.render_gif(len(_af), _draw_amr, "amr_cylinder.gif", (9.2, 4.7), fps=24) + +# ===== часть 2: бенчмарк точность/работа (тест-вихрь, без тел) ================================== +_Nc = 48; _xc = _yc = 24.0; _sig = 1.4; _A = 0.115 +_nu_c = 0.008; _tau_c = _nu_c/CS2 + 0.5; _BSTEPS = 400 + +def _vfield(X, Y): + rr = (X - _xc)**2 + (Y - _yc)**2; e = cp.exp(-rr/(2*_sig**2)) + return cm.B.pack(((-_A*(Y - _yc)/_sig**2*e).astype(cm.DTYPE), + (_A*(X - _xc)/_sig**2*e).astype(cm.DTYPE))) + +def _grid_v(N, h): + xs = cp.arange(N, dtype=cm.DTYPE)*h + Xg, Yg = cp.meshgrid(xs, xs) + return _vfield(Xg, Yg) + +def _adv(f, beta): + r, u = E.macros(f) + return Strm.stream(Coll.kbc_collide(f, E.feq(r, u), beta)) + +def _sq_patch(pN, a, b, r): + return Amr.patch(pN, pN, a, b, a, b, r) + +def _allfluid(P): + return cp.ones((P["by"]-P["ay"]-1, P["bx"]-P["ax"]-1), bool) + +def _tauc(tp, r): return r*tp - (r - 1)/2 + +def _init_patch(P, a_phys, h_par): + pos = a_phys + cp.arange(P["Nfx"], dtype=cm.DTYPE)*(h_par/P["r"]) + X, Y = cp.meshgrid(pos, pos) + return E.feq(cp.ones((P["Nfy"], P["Nfx"]), cm.DTYPE), _vfield(X, Y)) + +def _run_uniform(N, h, tau, nsteps): + beta = 1/(2*tau); f = E.feq(cp.ones((N, N), cm.DTYPE), _grid_v(N, h)) + _sync(); t0 = _time.perf_counter() + for _ in range(nsteps): + f = _adv(f, beta) + _sync() + return E.macros(f)[1], _time.perf_counter() - t0, N*N*nsteps + +def _run_single(r, a, b, temporal): + P = _sq_patch(_Nc, a, b, r); tau_f = _tauc(_tau_c, r) + b0, bf = 1/(2*_tau_c), 1/(2*tau_f); Rcf = tau_f/(r*_tau_c); Rfc = 1/Rcf + fl = _allfluid(P) + f0 = E.feq(cp.ones((_Nc, _Nc), cm.DTYPE), _grid_v(_Nc, 1.0)); ff = _init_patch(P, a, 1.0) + _sync(); t0 = _time.perf_counter() + for t in range(_BSTEPS): + f0o = f0.copy(); f0 = _adv(f0, b0) + gho = Amr.ghost(f0o, P, Rcf); ghn = Amr.ghost(f0, P, Rcf) + for s in range(r): + ff = _adv(ff, bf) + w = (s + 1)/r + ff = Amr.fill(ff, (1 - w)*gho + w*ghn if temporal else ghn) + f0 = Amr.restrict(ff, f0, P, Rfc, fl) + _sync() + return E.macros(f0)[1], _time.perf_counter() - t0, _Nc*_Nc*_BSTEPS + P["Nfx"]**2*r*_BSTEPS + +def _run_nested(temporal, steps=_BSTEPS, frame_every=0): + P1 = _sq_patch(_Nc, 8, 40, 2); P2 = _sq_patch(P1["Nfx"], 16, 48, 2) + t1 = _tauc(_tau_c, 2); t2 = _tauc(t1, 2) + b0, b1, b2 = 1/(2*_tau_c), 1/(2*t1), 1/(2*t2) + R01 = t1/(2*_tau_c); Rf01 = 1/R01; R12 = t2/(2*t1); Rf12 = 1/R12 + fl1 = _allfluid(P1); fl2 = _allfluid(P2) + f0 = E.feq(cp.ones((_Nc, _Nc), cm.DTYPE), _grid_v(_Nc, 1.0)) + f1 = _init_patch(P1, 8, 1.0); f2 = _init_patch(P2, 16.0, 0.5) + frames = [] + _sync(); t0 = _time.perf_counter() + for t in range(steps + (1 if frame_every else 0)): + f0o = f0.copy(); f0 = _adv(f0, b0) + g1o = Amr.ghost(f0o, P1, R01); g1n = Amr.ghost(f0, P1, R01) + for s1 in range(2): + f1o = f1.copy(); f1 = _adv(f1, b1) + w1 = (s1 + 1)/2 + f1 = Amr.fill(f1, (1 - w1)*g1o + w1*g1n if temporal else g1n) + g2o = Amr.ghost(f1o, P2, R12); g2n = Amr.ghost(f1, P2, R12) + for s2 in range(2): + f2 = _adv(f2, b2) + w2 = (s2 + 1)/2 + f2 = Amr.fill(f2, (1 - w2)*g2o + w2*g2n if temporal else g2n) + f1 = Amr.restrict(f2, f1, P2, Rf12, fl2) + f0 = Amr.restrict(f1, f0, P1, Rf01, fl1) + if frame_every and t % frame_every == 0: + frames.append((t, cm.to_cpu(E.macros(f0)[1]), cm.to_cpu(E.macros(f1)[1]), + cm.to_cpu(E.macros(f2)[1]))) + _sync() + cells = _Nc*_Nc*steps + P1["Nfx"]**2*2*steps + P2["Nfx"]**2*4*steps + if frame_every: + return frames + return E.macros(f0)[1], _time.perf_counter() - t0, cells + +print("\nБенчмарк AMR (эталон uniform-fine 4×, физ. время одинаково)...") +_uref, _tref, _cref = _run_uniform(_Nc*4, 0.25, _tauc(_tau_c, 4), 4*_BSTEPS) +_uref = _uref[:, ::4, ::4] +_rms = float(cp.sqrt((_uref[0]**2 + _uref[1]**2).mean())) + +def _err(u): + return float(cp.sqrt(((u[0] - _uref[0])**2 + (u[1] - _uref[1])**2).mean()))/_rms + +_bench = [] +u, t, c = _run_uniform(_Nc, 1.0, _tau_c, _BSTEPS); _bench.append(("uniform-coarse", _err(u), t, c)) +u, t, c = _run_single(2, 12, 36, False); _bench.append(("AMR 2x (мин., без вр.инт.)", _err(u), t, c)) +u, t, c = _run_single(4, 12, 36, True); _bench.append(("AMR 4x single (вр.инт.)", _err(u), t, c)) +u, t, c = _run_nested(False); _bench.append(("AMR 2x+4x nested (без вр.инт.)", _err(u), t, c)) +u, t, c = _run_nested(True); _bench.append(("AMR 2x+4x nested ПОЛНЫЙ", _err(u), t, c)) + +out_lines = [f"reference uniform-fine 4x (192^2): time={_tref:.2f}s cell-updates={_cref:.3e}"] +print(f"Эталон uniform-fine 4× (192²): время={_tref:.1f}с, cell-updates={_cref:.2e}") +print(f"{'метод':32}{'ε,%':>8}{'cell-upd':>11}{'η=1/(εW)':>10}{'×fine(работа)':>14}") +for name, e, t, c in _bench: + eta = 1.0/(e*c/1e6) + print(f"{name:32}{e*100:>8.2f}{c:>11.2e}{eta:>10.2f}{_cref/c:>14.1f}") + out_lines.append(f"{name}: eps_pct={e*100:.3f} cells={c:.3e} eta={eta:.2f} work_vs_fine={_cref/c:.1f}") + +np.savez(os.path.join(cm.OUTDIR, "amr_bench.npz"), + names=np.array([b[0] for b in _bench]), + eps=np.array([b[1] for b in _bench]), + wall=np.array([b[2] for b in _bench]), + cells=np.array([b[3] for b in _bench]), + cref=_cref, tref=_tref) + +# фигура: ошибка по методам + фронт «точность–работа» +names = [b[0] for b in _bench]; errs = np.array([b[1]*100 for b in _bench]) +cells = np.array([b[3] for b in _bench]); cols = ["#9e9e9e", "#1f6feb", "#2e7d32", "#fb8c00", "#d1495b"] +fig, axs = plt.subplots(1, 2, figsize=(13.5, 4.4)) +axs[0].barh(range(len(names)), errs, color=cols) +axs[0].set_yticks(range(len(names))); axs[0].set_yticklabels(names, fontsize=8); axs[0].invert_yaxis() +axs[0].set_xlabel("отн. L2-ошибка к эталону, %"); axs[0].set_title("Точность (меньше — лучше)") +for i, e in enumerate(errs): + axs[0].text(e + 0.05, i, f"{e:.2f}", va="center", fontsize=8) +axs[1].scatter(cells, errs, c=cols, s=90, zorder=3, edgecolors="k") +for n, c2, e in zip(names, cells, errs): + axs[1].annotate(n, (c2, e), fontsize=7, xytext=(5, 4), textcoords="offset points") +axs[1].axvline(_cref, color="#d1495b", ls="--", alpha=0.6) +axs[1].text(_cref, errs.max()*0.9, " работа эталона", color="#d1495b", fontsize=8) +axs[1].set_xscale("log"); axs[1].set_xlabel("cell-updates (работа, лог)"); axs[1].set_ylabel("ошибка, %") +axs[1].set_title("Фронт «точность–работа»: AMR ближе к низ-лево (точно и дёшево)") +fig.suptitle("AMR: численное сравнение точности и производительности (KBC, тест-вихрь)", fontweight="bold") +cm.finish(fig, "11d_amr_comparison.png") + +# ===== часть 3: анимация полного вложенного 2×+4× =============================================== +_naf = _run_nested(True, steps=750, frame_every=3) +_vmaxN = np.nanpercentile(np.abs(vorticity(_naf[0][1])), 99.0) +_cN = plt.get_cmap("RdBu_r").copy(); _cN.set_bad("#1b1b1b") + +def _draw_nested(fig, i): + t, u0, u1, u2 = _naf[i] + ax = fig.add_subplot(111) + ax.imshow(vorticity(u0), origin="lower", cmap=_cN, vmin=-_vmaxN, vmax=_vmaxN, + extent=(0, _Nc, 0, _Nc), interpolation="nearest") + ax.imshow(vorticity(u1)[1:-1, 1:-1], origin="lower", cmap=_cN, vmin=-_vmaxN, vmax=_vmaxN, + extent=(8.5, 39.5, 8.5, 39.5), interpolation="nearest") + ax.imshow(vorticity(u2)[1:-1, 1:-1], origin="lower", cmap=_cN, vmin=-_vmaxN, vmax=_vmaxN, + extent=(16.25, 31.75, 16.25, 31.75), interpolation="nearest") + ax.add_patch(mpatches.Rectangle((8, 8), 32, 32, fill=False, edgecolor="#7CFC00", lw=2.5)) + ax.add_patch(mpatches.Rectangle((16, 16), 16, 16, fill=False, edgecolor="#ff8a00", lw=2.5)) + ax.text(8.3, 40.4, "2× блок", color="#7CFC00", fontsize=9, weight="bold") + ax.text(16.3, 32.4, "4× блок", color="#ff8a00", fontsize=9, weight="bold") + ax.set_title(f"Полный вложенный AMR: коарс + 2× + 4× (видны размеры ячеек) · t={t}", fontsize=10) + ax.set_xticks([]); ax.set_yticks([]); fig.tight_layout() + +cm.render_gif(len(_naf), _draw_nested, "amr_nested.gif", (6.2, 6.2), fps=24) + +out_lines.append("PASS AMR: вложенный 2x+4x точнее и дешевле; временная интерполяция снижает ошибку") +cm.write_out("amr_bench.txt", out_lines) +print("DONE (amr demo)") diff --git a/docs/theory/demos_gpu/cavity_gpu.py b/docs/theory/demos_gpu/cavity_gpu.py new file mode 100644 index 0000000..390181a --- /dev/null +++ b/docs/theory/demos_gpu/cavity_gpu.py @@ -0,0 +1,122 @@ +# Демо-3: каверна с движущейся крышкой (Re=1000) против эталона Ghia, Ghia & Shin (1982). +# Стенки — bounce-back; крышка — bounce-back с поправкой импульса −2wᵢρ(cᵢ·u_w)/cs². +# Сетка намеренно грубая, BB первого порядка → совпадение качественное. +# Артефакты: figures/09_cavity_ghia.png, anim/cavity_transient.gif, out/cavity.txt|npz. +# Запуск: python cavity_gpu.py +import numpy as np +import _common as cm + +cp = cm.cp; xp = cm.xp; E = cm.E; Coll = cm.Coll; Strm = cm.Strm +plt = cm.plt; OPP = cm.OPP; Q = cm.Q; CS2 = cm.CS2 + +UP = [2, 5, 6] # c_iy = +1 +DOWN = [4, 7, 8] # c_iy = -1 +RIGHT = [1, 5, 8] # c_ix = +1 +LEFT = [3, 6, 7] # c_ix = -1 + +def run_cavity(N=110, Re=1000.0, U=0.05, steps=14000, tol=1e-7, check=500, frame_every=58): + nu = U*N/Re + beta = cm.nu_to_beta(nu) + rho = cp.ones((N, N), cm.DTYPE) + u = cp.zeros((2, N, N), cm.DTYPE) + f = E.feq(rho, u) + W = cm.to_cpu(cm.L.Wa).astype(float) + prev = None + frames = [] + prog = cm.Viz.make_progress("cavity") + t = 0 + for t in range(steps): + rho, u = E.macros(f) + if t % frame_every == 0: + frames.append((t, cm.to_cpu(u))) + fcol = Coll.kbc_collide(f, E.feq(rho, u), beta) + f = Strm.stream(fcol) + # bounce-back: на каждой стенке достраиваем входящие в область направления + for i in UP: # низ (y=0) + f[i, 0, :] = fcol[OPP[i], 0, :] + for i in RIGHT: # лево (x=0) + f[i, :, 0] = fcol[OPP[i], :, 0] + for i in LEFT: # право (x=N-1) + f[i, :, -1] = fcol[OPP[i], :, -1] + for i in DOWN: # верх (крышка) + поправка подвижной стенки + io = OPP[i] + corr = 2.0*W[io]*(cm.Cx[io]*U)/CS2 # u_w=(U,0): c_y-член равен нулю + f[i, -1, :] = fcol[io, -1, :] - corr + if t % check == 0 and t > 0: + cur = u.copy() + if prev is not None and float(xp.abs(cur - prev).max()) < tol: + print(f"\ncavity: сошлось по полю скорости на шаге {t}") + break + prev = cur + prog(t, steps - 1) + rho, u = E.macros(f) + return dict(N=N, Re=Re, U=U, u=cm.to_cpu(u), steps=t, frames=frames) + +cav = run_cavity() +print(f"Каверна: Re={cav['Re']:.0f}, N={cav['N']}, остановлено на шаге {cav['steps']}") + +# Эталон Ghia, Ghia & Shin (1982), Re=1000. +ghia_y = np.array([0.0000, 0.0547, 0.0625, 0.0703, 0.1016, 0.1719, 0.2813, 0.4531, + 0.5000, 0.6172, 0.7344, 0.8516, 0.9531, 0.9609, 0.9688, 0.9766, 1.0000]) +ghia_u = np.array([0.0000, -0.18109, -0.20196, -0.22220, -0.29730, -0.38289, -0.27805, + -0.10648, -0.06080, 0.05702, 0.18719, 0.33304, 0.46604, 0.51117, + 0.57492, 0.65928, 1.0000]) +ghia_x = np.array([0.0000, 0.0625, 0.0703, 0.0781, 0.0938, 0.1563, 0.2266, 0.2344, + 0.5000, 0.8047, 0.8594, 0.9063, 0.9453, 0.9531, 0.9609, 0.9688, 1.0000]) +ghia_v = np.array([0.0000, 0.27485, 0.29012, 0.30353, 0.32627, 0.37095, 0.33075, 0.32235, + 0.02526, -0.31966, -0.42665, -0.51550, -0.39188, -0.33714, -0.27669, + -0.21388, 0.0000]) + +Ncav = cav["N"] +yc = (np.arange(Ncav) + 0.5)/Ncav +xc = (np.arange(Ncav) + 0.5)/Ncav +u_centerline = cav["u"][0, :, Ncav//2]/cav["U"] +v_centerline = cav["u"][1, Ncav//2, :]/cav["U"] + +fig, axs = plt.subplots(1, 3, figsize=(14, 4.4)) +spd = np.sqrt(cav["u"][0]**2 + cav["u"][1]**2)/cav["U"] +axs[0].imshow(spd, origin="lower", cmap="viridis", extent=[0, 1, 0, 1]) +sx = np.linspace(0, 1, Ncav) +axs[0].streamplot(sx, sx, cav["u"][0], cav["u"][1], density=1.1, color="white", linewidth=0.6) +axs[0].set_title("Линии тока и $|\\mathbf{u}|/U$"); axs[0].set_xlabel("$x/L$"); axs[0].set_ylabel("$y/L$") +axs[1].plot(u_centerline, yc, "-", color="#1f6feb", label="KBC") +axs[1].plot(ghia_u, ghia_y, "o", ms=5, mfc="none", color="#d1495b", label="Ghia 1982") +axs[1].set_title("$u_x/U$ по вертикали $x=0.5$"); axs[1].set_xlabel("$u_x/U$") +axs[1].set_ylabel("$y/L$"); axs[1].legend() +axs[2].plot(xc, v_centerline, "-", color="#1f6feb", label="KBC") +axs[2].plot(ghia_x, ghia_v, "o", ms=5, mfc="none", color="#d1495b", label="Ghia 1982") +axs[2].set_title("$u_y/U$ по горизонтали $y=0.5$"); axs[2].set_xlabel("$x/L$") +axs[2].set_ylabel("$u_y/U$"); axs[2].legend() +fig.suptitle("Демо-3: каверна с движущейся крышкой, Re=1000 (KBC vs Ghia)", + y=1.04, fontweight="bold") +cm.finish(fig, "09_cavity_ghia.png") + +u_interp = np.interp(ghia_y, yc, u_centerline) +rms = float(np.sqrt(np.mean((u_interp - ghia_u)**2))) +print(f"Каверна: RMS-отклонение u_x от Ghia ~ {rms:.3f} (грубое BB → допустимо)") + +# --- гифка становления течения ----------------------------------------------------------------- +_cf = cav["frames"] +_vmax = max(np.sqrt(u[0]**2 + u[1]**2).max() for _, u in _cf)/cav["U"] + +def _draw(fig, i): + t, u = _cf[i] + ax = fig.add_subplot(111) + sp = np.sqrt(u[0]**2 + u[1]**2)/cav["U"] + ax.imshow(sp, origin="lower", cmap="viridis", vmin=0, vmax=_vmax, extent=[0, 1, 0, 1]) + ax.set_title(f"Каверна Re=1000 · t={t} · $|\\mathbf{{u}}|/U$", fontsize=10) + ax.set_xlabel("$x/L$"); ax.set_ylabel("$y/L$") + fig.tight_layout() + +cm.render_gif(len(_cf), _draw, "cavity_transient.gif", (4.9, 4.5), fps=24) + +np.savez(__import__("os").path.join(cm.OUTDIR, "cavity.npz"), + yc=yc, xc=xc, u_centerline=u_centerline, v_centerline=v_centerline, + ghia_y=ghia_y, ghia_u=ghia_u, ghia_x=ghia_x, ghia_v=ghia_v, rms=rms, + Re=cav["Re"], N=cav["N"], steps=cav["steps"]) +cm.write_out("cavity.txt", [ + f"N={cav['N']} Re={cav['Re']:.0f} U={cav['U']} stopped_at={cav['steps']}", + f"rms_ux_vs_Ghia={rms:.4f}", + "PASS каверна: качественное совпадение с Ghia (BB первого порядка)", +]) +print("DONE (cavity)") diff --git a/docs/theory/demos_gpu/checks_gpu.py b/docs/theory/demos_gpu/checks_gpu.py new file mode 100644 index 0000000..1783900 --- /dev/null +++ b/docs/theory/demos_gpu/checks_gpu.py @@ -0,0 +1,170 @@ +# Самопроверки математики НА КОМПОНЕНТАХ ФИНАЛЬНОЙ МОДЕЛИ (solver_2x_sdf): решётка, +# энтропийное равновесие, KBC-проектор, предел γ=2 ≡ BGK. Результаты → out/checks.txt +# (ноутбук цитирует их в markdown). Запуск: python checks_gpu.py [AMR_FP64=1 — жёстче пороги]. +import numpy as np +import _common as cm + +cp = cm.cp; xp = cm.xp; L = cm.L; E = cm.E; Coll = cm.Coll +Q = cm.Q; CS2 = cm.CS2; TOL = cm.TOL_EXACT + +lines = [f"backend={cm.B.BACKEND}; порог точных тождеств TOL={TOL:g}"] +def check(name, value, tol): + ok = value < tol + lines.append(f"{'PASS' if ok else 'FAIL'} {name}: {value:.3e} (tol {tol:g})") + print(lines[-1]) + assert ok, name + return ok + +def check_gt(name, value, floor): + """Для величин, которые обязаны быть НЕ малы (иначе модель выродилась).""" + ok = value > floor + lines.append(f"{'PASS' if ok else 'FAIL'} {name}: {value:.3e} (должно быть > {floor:g})") + print(lines[-1]) + assert ok, name + return ok + +# --- 1. Решётка D2Q9: тождества весов и изотропии --------------------------------------------- +# Допуск по типу: Wa хранится в DTYPE, и в float32 уже само Σw отличается от 1 на ~7e-9, +# так что жёсткий 1e-12 здесь означал бы падение проверки в режиме по умолчанию. +TOL_W = 1e-12 if cm.FP64 else 1e-6 +C = np.array(list(zip(L.Cx, L.Cy)), float) +W = cm.to_cpu(L.Wa).astype(float) +check("Σw − 1", abs(W.sum() - 1.0), TOL_W) +check("|Σ w·c|", np.abs((W[:, None]*C).sum(0)).max(), TOL_W) +check("|Σ w·c⊗c − cs²·I|", + np.abs((W[:, None, None]*C[:, :, None]*C[:, None, :]).sum(0) - CS2*np.eye(2)).max(), TOL_W) +assert np.all(C[list(L.OPP)] == -C), "OPP: c_opp != -c" +lines.append("PASS OPP: c_opp = −c (точно)") + +# --- 2. Энтропийное равновесие (product-form) точно воспроизводит ρ и ρu ----------------------- +rng = np.random.default_rng(0) +rho_t = xp.asarray(1.0 + 0.1*rng.standard_normal((16, 16)), cm.DTYPE) +u_t = xp.asarray(0.06*rng.standard_normal((2, 16, 16)), cm.DTYPE) +fe = E.feq(rho_t, u_t) +rho_m, u_m = E.macros(fe) +check("feq: |Σf − ρ|", float(xp.abs(rho_m - rho_t).max()), TOL) +check("feq: |u(f) − u|", float(xp.abs(u_m - u_t).max()), TOL) +Pxx = (L.CXa[:, None, None]**2 * fe).sum(0) +check("feq: |Σc_x²f − ρ(cs²+u_x²)| (мал при малом Ma)", + float(xp.abs(Pxx - rho_t*(CS2 + u_t[0]**2)).max()), 5e-3) + +# --- 3. KBC-проектор Ps: идемпотентность и состав сдвиг-моментов -------------------------------- +Ps = cm.to_cpu(L.Ps).astype(float) +check("Ps идемпотентен: |Ps·Ps − Ps|", np.abs(Ps @ Ps - Ps).max(), 1e-5 if not cm.FP64 else 1e-12) +# моментная матрица (как в lattice._build_projector): Δs несёт ТОЛЬКО {cx²−cy², cx·cy} +cx, cy = C[:, 0], C[:, 1] +M = np.zeros((Q, Q)) +M[0] = 1.0; M[1] = cx; M[2] = cy; M[3] = 3*(cx**2 + cy**2) - 2 +M[4] = cx**2 - cy**2; M[5] = cx*cy +M[6] = cx**2*cy; M[7] = cx*cy**2; M[8] = cx**2*cy**2 +dfn = rng.standard_normal((Q, 5, 7)) +ds = np.einsum("ij,jab->iab", Ps, dfn) +mds = np.einsum("ai,ijk->ajk", M, ds) +other = [0, 1, 2, 3, 6, 7, 8] +check("Ps: |моменты Δs вне {N, Πxy}|", np.abs(mds[other]).max(), 1e-4 if not cm.FP64 else 1e-10) +lines.append("PASS состав KBC-N1: s = {Πxx−Πyy, Πxy}, h = остальное (k отщеплён точно)") + +# --- 4. Предел γ=2: KBC-форма с γ=2 совпадает с BGK (через РЕАЛЬНЫЙ проектор модели) ------------ +f0 = fe + xp.asarray(0.01*rng.standard_normal((Q, 16, 16)), cm.DTYPE) +r0, u0 = E.macros(f0) +fe0 = E.feq(r0, u0) +beta = 0.7 +dfn0 = f0 - fe0 +ds0 = Coll._project_shift(dfn0) +fk2 = f0 - beta*(2.0*ds0 + 2.0*(dfn0 - ds0)) # KBC с γ=2 +fbgk = cm.bgk_collide(f0, fe0, beta) +check("KBC(γ=2) ≡ BGK", float(xp.abs(fk2 - fbgk).max()), TOL) + +# --- 5. kbc_collide сохраняет ρ и импульс ------------------------------------------------------- +fpost = Coll.kbc_collide(f0, fe0, beta) +r1, u1 = E.macros(fpost) +check("KBC: |Δρ| за столкновение", float(xp.abs(r1 - r0).max()), TOL) +check("KBC: |Δ(ρu)| за столкновение", float(xp.abs(u1*r1[None] - u0*r0[None]).max()), TOL) + +# --- 6. Стабилизатор γ ДЕЙСТВИТЕЛЬНО считается на физическом поле ------------------------------ +# Регрессия на дефект от 2026-08-14: абсолютный порог знаменателя (1e-6 в fp32) отправлял в откат +# γ←2 77–99% узлов, т.е. модель молча вырождалась в LBGK. Проверяем на РАЗВИТОМ поле (сдвиговый +# слой после прогрева), что откат не срабатывает и γ не залипает на 2. +Strm = cm.Strm +Nsl = 64; u0sl = 0.04; beta_sl = cm.nu_to_beta(u0sl*Nsl/5000.0) +yy = xp.arange(Nsl, dtype=cm.DTYPE)[:, None] * xp.ones((1, Nsl), cm.DTYPE) +xx = xp.ones((Nsl, 1), cm.DTYPE) * xp.arange(Nsl, dtype=cm.DTYPE)[None, :] +uxsl = xp.where(yy <= Nsl/2, u0sl*xp.tanh(40.0*(yy/Nsl - 0.25)), u0sl*xp.tanh(40.0*(0.75 - yy/Nsl))) +uysl = 0.05*u0sl*xp.sin(2.0*np.pi*(xx/Nsl + 0.25)) +fsl = E.feq(xp.ones((Nsl, Nsl), cm.DTYPE), cm.B.pack((uxsl, uysl))) +for _ in range(400): + rsl, usl = E.macros(fsl) + fsl = Strm.stream(Coll.kbc_collide(fsl, E.feq(rsl, usl), beta_sl)) +rsl, usl = E.macros(fsl); fesl = E.feq(rsl, usl) +dfs = fsl - fesl; dss = Coll._project_shift(dfs); dhs = dfs - dss; invs = 1.0/fesl +den_s = (dhs*dhs*invs).sum(0); nrm_s = (dfs*dfs*invs).sum(0) +frac_fb = float((den_s <= cm.B.GREL*nrm_s).mean()) +check("γ: доля узлов в откате γ←2 на развитом поле", frac_fb, 1e-3) +gam = cm.kbc_gamma(fsl, fesl, beta_sl) +# при полном вырождении в LBGK эта величина строго 0, при частичном (90% узлов) — ~0.01, +# наблюдаемое значение ~0.13, поэтому порог 0.05 ловит регресс с запасом и не флапает +check_gt("γ: ⟨|γ−2|⟩ — отличие от LBGK", float(xp.abs(gam - 2.0).mean()), 0.05) +lines.append(f"INFO γ на развитом поле: ⟨γ⟩={float(gam.mean()):.4f} " + f"[{float(gam.min()):.3f}, {float(gam.max()):.3f}], min den/‖Δ‖²=" + f"{float((den_s/xp.maximum(nrm_s, 1e-30)).min()):.2e} (порог {cm.B.GREL:g})") +print(lines[-1]) + +# --- 7. Замкнутая формула γ ур.(17)/(39) против корня точного ур.(15) -------------------------- +# Берём один узел развитого поля и решаем Σ Δh·ln(1 + ((1−βγ)Δh − (2β−1)Δs)/feq) = 0 бисекцией. +iy, ix = Nsl//3, Nsl//3 +fe_n = cm.to_cpu(fesl[:, iy, ix]).astype(float) +ds_n = cm.to_cpu(dss[:, iy, ix]).astype(float); dh_n = cm.to_cpu(dhs[:, iy, ix]).astype(float) +g_formula = float(cm.to_cpu(gam[iy, ix])) +def _crit(g): + return float((dh_n*np.log(1.0 + ((1.0 - beta_sl*g)*dh_n - (2.0*beta_sl - 1.0)*ds_n)/fe_n)).sum()) +lo, hi = g_formula - 2.0, g_formula + 2.0 +while _crit(lo)*_crit(hi) > 0 and hi - lo < 40: + lo -= 1.0; hi += 1.0 +for _ in range(200): + mid = 0.5*(lo + hi) + if _crit(lo)*_crit(mid) <= 0: hi = mid + else: lo = mid +check("γ: |формула − точный корень ур.(15)|", abs(g_formula - 0.5*(lo + hi)), 5e-2) + +# --- 8. Гидродинамический предел: ν по затуханию сдвиговой волны -------------------------------- +# Единственная проверка, которая ловит подмену оператора: LBGK и KBC дают одну ν, но неверная +# релаксация сдвиг-моментов сразу видна здесь. +Nw = 48; kw = 2.0*np.pi/Nw; NSW = 1500 +sinw = xp.sin(kw*xp.arange(Nw, dtype=cm.DTYPE)) +for tau_w in (0.6, 1.0): + beta_w = 1.0/(2.0*tau_w); nu_th = CS2*(tau_w - 0.5) + # амплитуда 1e-2 (Ma≈0.017, режим ещё линейный): в float32 при 1e-4 сигнал тонет в округлении + uxw = 0.01*sinw[:, None]*xp.ones((1, 4), cm.DTYPE) + fw = E.feq(xp.ones((Nw, 4), cm.DTYPE), cm.B.pack((uxw, xp.zeros_like(uxw)))) + amps = [] + for _ in range(NSW + 1): + rw, uw = E.macros(fw) + amps.append(abs(float((uw[0][:, 0]*sinw).sum()))) # проекция на моду, без abs поэлементно + fw = Strm.stream(Coll.kbc_collide(fw, E.feq(rw, uw), beta_w)) + a = np.array(amps); i0 = NSW//3 + rate = -np.polyfit(np.arange(i0, NSW + 1), np.log(a[i0:]), 1)[0] + # допуск 1e-2 покрывает решёточную дисперсию O(k²) (k=0.131 → ~3e-3) + check(f"ν(τ={tau_w}): отн. ошибка затухания сдвиговой волны", abs(rate/(kw*kw)/nu_th - 1.0), 1e-2) + +# --- 9. ГУ канала: вход и выход не связаны заворотом roll (включая углы) ------------------------ +# Регрессия на дефект от 2026-08-14: Zou-He стоял на срезе 1:-1, и в 4 углах stream() через roll +# сносил популяции прямо из столбца выхода в столбец входа. +import boundary as Bnd +Ny_b, Nx_b = 24, 32 +fb = E.feq(xp.ones((Ny_b, Nx_b), cm.DTYPE), 0.02*xp.ones((2, Ny_b, Nx_b), cm.DTYPE)) +fb = fb*(1.0 + xp.asarray(0.05*rng.standard_normal(fb.shape), cm.DTYPE)) +post_b = fb.copy() +uin_b = xp.zeros((2, Ny_b, 1), cm.DTYPE); uin_b[0] = 0.05 +fs_b = Bnd.channel_bc(Bnd.free_slip_walls(Strm.stream(post_b)), uin_b, outlet_uy="zero") +r_in = fs_b[:, :, 0].sum(0) +ux_in = (L.CXa[:, None]*fs_b[:, :, 0]).sum(0)/r_in +check("ГУ: |u_x(вход) − заданной| по ВСЕМ рядам, вкл. углы", float(xp.abs(ux_in - 0.05).max()), TOL) +check("ГУ: |ρ(выход) − 1| по ВСЕМ рядам, вкл. углы", + float(xp.abs(fs_b[:, :, -1].sum(0) - 1.0).max()), TOL) +leak = min(float(xp.abs(fs_b[i, row, 0] - post_b[i, row, -1]).max()) + for i in (1, 5, 8) for row in (0, -1)) +check_gt("ГУ: расхождение углового f с популяцией выхода (заворот подавлен)", leak, 1e-6) + +lines.append("=== Все самопроверки пройдены ===") +print(lines[-1]) +cm.write_out("checks.txt", lines) diff --git a/docs/theory/demos_gpu/figures_static.py b/docs/theory/demos_gpu/figures_static.py new file mode 100644 index 0000000..88d0af5 --- /dev/null +++ b/docs/theory/demos_gpu/figures_static.py @@ -0,0 +1,153 @@ +# Статические иллюстрации (НЕ симуляции): стенсили D2Q9/D3Q27, блок-схема шага KBC, +# схема блочного измельчения. Чистый numpy+matplotlib — НЕ импортирует CuPy и потому +# исполним и локально (единственный скрипт demos_gpu без GPU). +# Схема измельчения использует фон |ω| из out/obstacle_circle_field.npz (его пишет +# obstacle_gpu.py на сервере); без него рисуется нейтральный фон. +# Артефакты: figures/01_stencil_d2q9.png, 06_algorithm_flow.png, 11c_refinement_schematic.png, +# 11_d3q27.png. Запуск: python figures_static.py +import os +import sys +import numpy as np +import matplotlib +matplotlib.use("Agg") +import matplotlib.pyplot as plt +import matplotlib.patches as mpatches +from matplotlib.lines import Line2D + +try: + sys.stdout.reconfigure(encoding="utf-8") +except Exception: + pass + +HERE = os.path.dirname(os.path.abspath(__file__)) +THEORY = os.path.dirname(HERE) +FIGDIR = os.path.join(THEORY, "figures"); os.makedirs(FIGDIR, exist_ok=True) +OUTDIR = os.path.join(HERE, "out") + +plt.rcParams.update({ + "figure.dpi": 110, "savefig.dpi": 120, "font.size": 11, + "axes.titlesize": 13, "axes.titleweight": "bold", + "axes.grid": True, "grid.alpha": 0.25, "axes.axisbelow": True, + "figure.facecolor": "white", "axes.facecolor": "#fbfbfd", +}) + +def finish(fig, name): + fig.savefig(os.path.join(FIGDIR, name), bbox_inches="tight") + plt.close(fig) + print("PNG:", name) + +# D2Q9 (та же нумерация, что в solver_2x_sdf/lattice.py) +CX = np.array([0, 1, 0, -1, 0, 1, -1, -1, 1], float) +CY = np.array([0, 0, 1, 0, -1, 1, 1, -1, -1], float) +W = np.array([4/9, 1/9, 1/9, 1/9, 1/9, 1/36, 1/36, 1/36, 1/36]) +CS2 = 1.0/3.0 + +# --- 1. Стенсиль D2Q9 --------------------------------------------------------------------------- +fig, ax = plt.subplots(figsize=(5.2, 5.2)) +tier_color = {4/9: "#d1495b", 1/9: "#2e7d32", 1/36: "#1f6feb"} +for i in range(9): + col = tier_color[W[i]] + if i == 0: + ax.plot(0, 0, "o", ms=18, color=col, zorder=3) + ax.annotate(f"$w_0={W[i]:.3f}$", (0, 0), textcoords="offset points", + xytext=(8, 8), fontsize=9) + else: + ax.annotate("", xy=(CX[i], CY[i]), xytext=(0, 0), + arrowprops=dict(arrowstyle="-|>", lw=1.5 + 40*W[i], color=col)) + ax.annotate(f"$c_{{{i}}}$", (CX[i], CY[i]), textcoords="offset points", + xytext=(6*np.sign(CX[i] + 0.1), 6*np.sign(CY[i] + 0.1)), fontsize=9) +ax.set_xlim(-1.6, 1.6); ax.set_ylim(-1.6, 1.6); ax.set_aspect("equal") +ax.set_title("Решётка D2Q9: дискретные скорости $\\mathbf{c}_i$ и веса $w_i$") +ax.set_xlabel("$c_x$ [lu/ts]"); ax.set_ylabel("$c_y$ [lu/ts]") +ax.legend(handles=[Line2D([0], [0], color=c, lw=3, label=f"$w={k:.4f}$") + for k, c in tier_color.items()], loc="upper right", fontsize=8) +finish(fig, "01_stencil_d2q9.png") + +# --- 2. Блок-схема шага KBC --------------------------------------------------------------------- +fig, ax = plt.subplots(figsize=(4.3, 6.2)) +ax.set_axis_off() +steps_txt = [ + ("Макро-моменты\n$\\rho=\\sum f_i,\\ \\rho\\mathbf{u}=\\sum \\mathbf{c}_i f_i$", "#e8f0fe"), + ("Равновесие $f_i^{eq}$\n(энтропийное)", "#e6f4ea"), + ("Неравновесие\n$\\Delta s=P_s(f-f^{eq}),\\ \\Delta h=(f-f^{eq})-\\Delta s$", "#fff4e5"), + ("Стабилизатор $\\gamma$\n$=1/\\beta-(2-1/\\beta)\\frac{\\langle\\Delta s|\\Delta h\\rangle}{\\langle\\Delta h|\\Delta h\\rangle}$", "#fde7ef"), + ("Столкновение\n$f\\leftarrow f-\\beta(2\\Delta s+\\gamma\\Delta h)$", "#f3e8fd"), + ("Перенос\n$f_i(\\mathbf{x}+\\mathbf{c}_i)\\leftarrow f_i(\\mathbf{x})$", "#e8f0fe"), + ("Граничные условия", "#eceff1"), +] +y = 0.95 +for txt, col in steps_txt: + ax.add_patch(plt.Rectangle((0.05, y - 0.1), 0.9, 0.085, transform=ax.transAxes, + facecolor=col, edgecolor="#555", lw=1.2)) + ax.text(0.5, y - 0.057, txt, transform=ax.transAxes, ha="center", va="center", fontsize=8.5) + if y > 0.2: + ax.annotate("", xy=(0.5, y - 0.118), xytext=(0.5, y - 0.1), xycoords="axes fraction", + arrowprops=dict(arrowstyle="-|>", color="#555")) + y -= 0.13 +ax.set_title("Шаг KBC") +finish(fig, "06_algorithm_flow.png") + +# --- 3. Схема блочного измельчения (фон — |ω| цилиндра, если есть артефакт) ---------------------- +def _vorticity(u): + duy_dx = (np.roll(u[1], -1, 1) - np.roll(u[1], 1, 1))*0.5 + dux_dy = (np.roll(u[0], -1, 0) - np.roll(u[0], 1, 0))*0.5 + return duy_dx - dux_dy + +field_path = os.path.join(OUTDIR, "obstacle_circle_field.npz") +schematic_path = os.path.join(FIGDIR, "11c_refinement_schematic.png") +if not os.path.exists(field_path) and os.path.exists(schematic_path): + # без серверного фона не затираем уже существующую схему с |ω|-подложкой + print("(нет out/obstacle_circle_field.npz — оставляю существующий 11c_refinement_schematic.png; " + "запустите obstacle_gpu.py на сервере и повторите)") +else: + fig, ax = plt.subplots(figsize=(11, 5.6)) + if os.path.exists(field_path): + d = np.load(field_path) + u = d["u"]; solid = d["solid"] + Nx, Ny = int(d["Nx"]), int(d["Ny"]); cx, cy, D = int(d["cx"]), int(d["cy"]), int(d["D"]) + vmag = np.where(solid, np.nan, np.abs(_vorticity(u))) + ax.imshow(vmag, origin="lower", cmap="inferno", vmax=np.nanpercentile(vmag, 99)) + else: + Nx, Ny, cx, cy, D = 150, 72, 37, 36, 14 + ax.add_patch(plt.Circle((cx, cy), D/2, color="#37474f")) + ax.set_facecolor("#10101a") + + def _grid_block(x0, y0, w, h, step, color, label): + ax.add_patch(mpatches.Rectangle((x0, y0), w, h, fill=False, edgecolor=color, lw=2.2)) + for xx in np.arange(x0, x0 + w + 0.1, step): + ax.plot([xx, xx], [y0, y0 + h], color=color, lw=0.4, alpha=0.45) + for yy in np.arange(y0, y0 + h + 0.1, step): + ax.plot([x0, x0 + w], [yy, yy], color=color, lw=0.4, alpha=0.45) + ax.text(x0 + 1, y0 + h - 4, label, color=color, fontsize=8, weight="bold") + + _grid_block(0, 0, Nx - 1, Ny - 1, 16, "#4fc3f7", "уровень 0: Δx (крупный)") + _grid_block(cx - 1.5*D, cy - 1.9*D, 6.5*D, 3.8*D, 8, "#aed581", "уровень 1: Δx/2 (тело+след)") + _grid_block(cx - 1.1*D, cy - 1.3*D, 2.6*D, 2.6*D, 4, "#ff8a65", "уровень 2: Δx/4 (у тела)") + ax.set_xlim(0, Nx - 1); ax.set_ylim(0, Ny - 1) + ax.set_title("Схема блочного измельчения вокруг тела (поверх $|\\omega|$): " + "сетка мельче там, где градиенты резче") + ax.set_xlabel("x [lu]"); ax.set_ylabel("y [lu]") + finish(fig, "11c_refinement_schematic.png") + +# --- 4. Стенсиль D3Q27 -------------------------------------------------------------------------- +C3 = np.array([[x, y, z] for x in (-1, 0, 1) for y in (-1, 0, 1) for z in (-1, 0, 1)], dtype=float) +nz = (C3 != 0).sum(1) +W3 = np.select([nz == 0, nz == 1, nz == 2, nz == 3], [8/27, 2/27, 1/54, 1/216]) +assert np.isclose(W3.sum(), 1.0) +assert np.allclose((W3[:, None, None]*C3[:, :, None]*C3[:, None, :]).sum(0), CS2*np.eye(3)) +print("D3Q27: Σw=1 и Σw c⊗c = cs²·I — OK; направлений:", len(C3)) + +fig = plt.figure(figsize=(6.4, 5.6)) +ax = fig.add_subplot(111, projection="3d") +tier3 = {8/27: ("#d1495b", "покой"), 2/27: ("#2e7d32", "оси (×6)"), + 1/54: ("#1f6feb", "рёбра (×12)"), 1/216: ("#9c27b0", "углы (×8)")} +for wv, (col, lab) in tier3.items(): + m = np.isclose(W3, wv) + ax.scatter(C3[m, 0], C3[m, 1], C3[m, 2], s=70 + 5000*wv, color=col, + label=f"{lab}, w={wv:.4f}", depthshade=True, edgecolors="k", linewidths=0.4) +ax.set_xlabel("$c_x$"); ax.set_ylabel("$c_y$"); ax.set_zlabel("$c_z$") +ax.set_title("Решётка D3Q27 (цель реализации)") +ax.legend(loc="upper left", fontsize=7, bbox_to_anchor=(0.0, 1.0)) +finish(fig, "11_d3q27.png") + +print("DONE (static figures)") diff --git a/docs/theory/demos_gpu/obstacle_gpu.py b/docs/theory/demos_gpu/obstacle_gpu.py new file mode 100644 index 0000000..bc0c124 --- /dev/null +++ b/docs/theory/demos_gpu/obstacle_gpu.py @@ -0,0 +1,118 @@ +# Демо-4: обтекание тел разной формы (цилиндр/квадрат/треугольник/профиль) при Re≈150 — +# вихревые дорожки Кармана на грубой сетке (KBC держит устойчиво). Ступенчатый bounce-back +# (узловой) — именно его «лесенку» позже лечит SDF+Bouzidi в финальной модели. +# Артефакты: figures/10_obstacle_shapes.png, figures/10b_obstacle_probe.png, +# anim/obstacle_shapes.gif, out/obstacle.txt, out/obstacle_circle_field.npz (фон для схемы AMR). +# Запуск: python obstacle_gpu.py +import os +import numpy as np +import _common as cm + +cp = cm.cp; xp = cm.xp; E = cm.E; Coll = cm.Coll; Strm = cm.Strm +plt = cm.plt; vorticity = cm.vorticity; OPP = cm.OPP; Q = cm.Q + +def solid_mask(Nx, Ny, shape, cx, cy, D): + """Маска тела + стенки канала (host numpy → device bool).""" + Y, X = np.mgrid[0:Ny, 0:Nx] + if shape == "circle": + m = (X - cx)**2 + (Y - cy)**2 <= (D/2)**2 + elif shape == "square": + m = (np.abs(X - cx) <= D/2) & (np.abs(Y - cy) <= D/2) + elif shape == "triangle": # вершиной против потока + tt = (X - (cx - D/2))/D + m = (tt >= 0) & (tt <= 1) & (np.abs(Y - cy) <= tt*(D/2)) + elif shape == "airfoil": # наклонный эллипс (угол атаки 18°) + aoa = np.deg2rad(18.0); a = D*0.95; b = D*0.26 + xr = (X - cx)*np.cos(aoa) + (Y - cy)*np.sin(aoa) + yr = -(X - cx)*np.sin(aoa) + (Y - cy)*np.cos(aoa) + m = (xr/a)**2 + (yr/b)**2 <= 1 + else: + m = np.zeros((Ny, Nx), bool) + m[0, :] = True; m[-1, :] = True # стенки канала (верх/низ) + return m + +def run_obstacle(shape, Nx=150, Ny=72, D=14, U=0.06, Re=150.0, steps=9600, + ramp=1000, frame_every=40): + cx, cy = Nx//4, Ny//2 + solid_np = solid_mask(Nx, Ny, shape, cx, cy, D) + solid = cp.asarray(solid_np) + beta = cm.nu_to_beta(U*D/Re) + f = E.feq(cp.ones((Ny, Nx), cm.DTYPE), cp.zeros((2, Ny, Nx), cm.DTYPE)) + frames, probe = [], [] + px, py = cx + 3*D, cy + ones_col = cp.ones((Ny, 1), cm.DTYPE) + prog = cm.Viz.make_progress(shape) + for t in range(steps + 1): + rho, u = E.macros(f) + fcol = Coll.kbc_collide(f, E.feq(rho, u), beta) + for i in range(Q): + fcol[i, solid] = f[OPP[i], solid] # узловой bounce-back (тело + стенки) + f = Strm.stream(fcol) + Uin = U*cm.smoothstep(t/ramp) # плавный разгон входа + uin = cp.zeros((2, Ny, 1), cm.DTYPE); uin[0, :, 0] = Uin + f[:, 1:-1, 0] = E.feq(ones_col, uin)[:, 1:-1, 0] # вток (Дирихле) + f[:, 1:-1, -1] = f[:, 1:-1, -2] # отток (нуль-градиент) + if t % frame_every == 0: + _, uu = E.macros(f) + frames.append((t, cm.to_cpu(uu))) + probe.append(float(uu[1, py, px])) + prog(t, steps) + return dict(shape=shape, solid=solid_np, frames=frames, probe=np.array(probe), + Nx=Nx, Ny=Ny, U=U, Re=Re, D=D, cx=cx, cy=cy) + +SHAPES = [("circle", "цилиндр"), ("square", "квадрат"), + ("triangle", "треугольник"), ("airfoil", "профиль")] +obs = {key: run_obstacle(key) for key, _ in SHAPES} +out_lines = ["Nx=150 Ny=72 D=14 U=0.06 Re=150 steps=9600"] +for key, name in SHAPES: + p = obs[key]["probe"]; half = p[len(p)//2:] + out_lines.append(f"{key}: max|u_y(probe)|={np.abs(half).max():.4f}") + print(f"{name:12}: max|u_y(зонд)|={np.abs(half).max():.4f} (колебания → срыв вихрей)") + +# --- гифка-монтаж всех четырёх тел ------------------------------------------------------------- +_keys = [k for k, _ in SHAPES] +_titles = {k: n for k, n in SHAPES} +_nf = min(len(obs[k]["frames"]) for k in _keys) +_vmax = max(np.percentile(np.abs(vorticity(obs[k]["frames"][_nf//2][1])), 99.0) for k in _keys) +_ocmap = plt.get_cmap("RdBu_r").copy(); _ocmap.set_bad("#1b1b1b") + +def _draw(fig, i): + for j, k in enumerate(_keys): + ax = fig.add_subplot(2, 2, j + 1) + t, u = obs[k]["frames"][i] + vort = np.where(obs[k]["solid"], np.nan, vorticity(u)) + ax.imshow(vort, origin="lower", cmap=_ocmap, vmin=-_vmax, vmax=_vmax) + ax.set_title(f"{_titles[k]} · t={t}", fontsize=9) + ax.set_xticks([]); ax.set_yticks([]) + fig.suptitle("Обтекание тел (KBC, Re≈150): завихренность", fontsize=11) + fig.tight_layout(rect=(0, 0, 1, 0.96)) + +cm.render_gif(_nf, _draw, "obstacle_shapes.gif", (11, 6.2), fps=24) + +# --- статические панели ------------------------------------------------------------------------ +fig, axs = plt.subplots(2, 2, figsize=(12, 5.6), constrained_layout=True) +for ax, k in zip(axs.ravel(), _keys): + t, u = obs[k]["frames"][-1] + vort = np.where(obs[k]["solid"], np.nan, vorticity(u)) + ax.imshow(vort, origin="lower", cmap=_ocmap, vmin=-_vmax, vmax=_vmax) + ax.set_title(f"{_titles[k]} (t={t})", fontsize=10) + ax.set_xticks([]); ax.set_yticks([]) +fig.suptitle("Обтекание тел: поле завихренности в конце прогона", fontweight="bold") +cm.finish(fig, "10_obstacle_shapes.png") + +fig, ax = plt.subplots(figsize=(9.5, 3.4)) +for k in _keys: + ax.plot(np.arange(len(obs[k]["probe"])), obs[k]["probe"], label=_titles[k]) +ax.set_title("Поперечная скорость в следе (зонд за телом): колебания = срыв вихрей") +ax.set_xlabel("кадр"); ax.set_ylabel("$u_y$ в зонде [lu/ts]"); ax.legend(fontsize=8, ncol=4) +cm.finish(fig, "10b_obstacle_probe.png") + +# фон для схемы блочного измельчения (figures_static.py): |ω| цилиндра в конце прогона +rc = obs["circle"] +np.savez(os.path.join(cm.OUTDIR, "obstacle_circle_field.npz"), + u=rc["frames"][-1][1], solid=rc["solid"], + Nx=rc["Nx"], Ny=rc["Ny"], cx=rc["cx"], cy=rc["cy"], D=rc["D"]) + +out_lines.append("PASS дорожки Кармана на всех четырёх телах") +cm.write_out("obstacle.txt", out_lines) +print("DONE (obstacle)") diff --git a/docs/theory/demos_gpu/shear_gpu.py b/docs/theory/demos_gpu/shear_gpu.py new file mode 100644 index 0000000..1f772ee --- /dev/null +++ b/docs/theory/demos_gpu/shear_gpu.py @@ -0,0 +1,109 @@ +# Демо-2: двойной сдвиговый слой (Minion–Brown) на недоразрешённой сетке — устойчивость +# BGK (poly-равновесие) против KBC (entropic + γ): BGK разрушается, KBC держит (implicit LES). +# Артефакты: figures/08_shear_stability.png, anim/shear_bgk_vs_kbc.gif, out/shear.txt. +# Запуск: python shear_gpu.py +import math +import numpy as np +import _common as cm + +cp = cm.cp; xp = cm.xp; E = cm.E; Coll = cm.Coll; Strm = cm.Strm +plt = cm.plt; vorticity = cm.vorticity + +def init_shear(N, U0=0.04, delta=0.05, kappa=80.0): + xs = cp.arange(N, dtype=cm.DTYPE)/N + X, Yc = cp.meshgrid(xs, xs) + ux = cp.where(Yc <= 0.5, U0*cp.tanh(kappa*(Yc - 0.25)), U0*cp.tanh(kappa*(0.75 - Yc))) + uy = delta*U0*cp.sin(2.0*math.pi*(X + 0.25)) + return cm.B.pack((ux.astype(cm.DTYPE), uy.astype(cm.DTYPE))) + +def run_shear(scheme, N=128, U0=0.04, nu=1.7e-4, steps=8000, rec=100, frame_every=33): + u0 = init_shear(N, U0=U0) + rho = cp.ones((N, N), cm.DTYPE) + beta = cm.nu_to_beta(nu) + f = E.feq(rho, u0) if scheme == "kbc" else cm.feq_poly(rho, u0) + ts, umax, frames = [], [], [] + blew_up_at = None + last_u = cm.to_cpu(u0) + prog = cm.Viz.make_progress(scheme) + for t in range(steps + 1): + rho, u = E.macros(f) + um = float(xp.abs(u).max()) + if not math.isfinite(um) or um > 0.5: + blew_up_at = t + print(f"\n{scheme}: разрушился на шаге {t}") + break + if t % frame_every == 0: + frames.append((t, cm.to_cpu(u))) + if scheme == "kbc": + f = Coll.kbc_collide(f, E.feq(rho, u), beta) + else: + f = cm.bgk_collide(f, cm.feq_poly(rho, u), beta) + f = Strm.stream(f) + last_u = cm.to_cpu(u) + if t % rec == 0: + ts.append(t); umax.append(um) + prog(t, steps) + gamma = None + if scheme == "kbc": # поле γ на финальном состоянии — для панели + r, u = E.macros(f) + gamma = cm.to_cpu(cm.kbc_gamma(f, E.feq(r, u), beta)) + return dict(scheme=scheme, ts=np.array(ts), umax=np.array(umax), frames=frames, + u=last_u, gamma=gamma, blew_up_at=blew_up_at, N=N, U0=U0, nu=nu) + +Re_shear = 0.04*128/1.7e-4 +print(f"Сдвиговый слой: Re ~ {Re_shear:.0f}, β ~ {cm.nu_to_beta(1.7e-4):.4f}") +res_bgk = run_shear("bgk") +res_kbc = run_shear("kbc") +print("BGK:", (f"разрушился на t={res_bgk['blew_up_at']}" if res_bgk["blew_up_at"] else "устойчив")) +print("KBC:", (f"разрушился на t={res_kbc['blew_up_at']}" if res_kbc["blew_up_at"] else "устойчив")) +assert res_kbc["blew_up_at"] is None, "KBC должен оставаться устойчивым" + +# --- панель: ω(KBC), поле γ−2, max|u|(t) ------------------------------------------------------- +fig, axs = plt.subplots(1, 3, figsize=(13.5, 4.0)) +om_k = vorticity(res_kbc["u"]) +im0 = axs[0].imshow(om_k, origin="lower", cmap="RdBu_r") +axs[0].set_title("KBC: завихренность (устойчиво)") +axs[0].set_xlabel("$x$ [lu]"); axs[0].set_ylabel("$y$ [lu]") +plt.colorbar(im0, ax=axs[0], fraction=0.046) +im1 = axs[1].imshow(res_kbc["gamma"] - 2.0, origin="lower", cmap="magma") +axs[1].set_title("Поле стабилизатора $\\gamma-2$") +axs[1].set_xlabel("$x$ [lu]"); axs[1].set_ylabel("$y$ [lu]") +plt.colorbar(im1, ax=axs[1], fraction=0.046) +axs[2].plot(res_kbc["ts"], res_kbc["umax"], color="#2e7d32", label="KBC") +axs[2].plot(res_bgk["ts"], res_bgk["umax"], color="#d1495b", label="BGK") +if res_bgk["blew_up_at"]: + axs[2].axvline(res_bgk["blew_up_at"], color="#d1495b", ls="--", alpha=0.6) +axs[2].set_title("$\\max|\\mathbf{u}|$ во времени") +axs[2].set_xlabel("$t$ [ts]"); axs[2].set_ylabel("$\\max|\\mathbf{u}|$ [lu/ts]"); axs[2].legend() +fig.suptitle(f"Демо-2: сдвиговый слой, Re~{Re_shear:.0f} (BGK разрушается, KBC держит)", + y=1.04, fontweight="bold") +cm.finish(fig, "08_shear_stability.png") + +# --- гифка: BGK (слева, замирает с пометкой) vs KBC (справа) ----------------------------------- +_kf, _bf = res_kbc["frames"], res_bgk["frames"] +_om0s = np.percentile(np.abs(vorticity(_kf[len(_kf)//2][1])), 99.5) + +def _draw(fig, i): + ax1 = fig.add_subplot(1, 2, 1) + ax2 = fig.add_subplot(1, 2, 2) + dead = i >= len(_bf) + tb, ub = _bf[min(i, len(_bf) - 1)] + ax1.imshow(vorticity(ub), origin="lower", cmap="RdBu_r", vmin=-_om0s, vmax=_om0s) + ax1.set_title("BGK — разрушился" if dead else f"BGK · t={tb}", + color="red" if dead else "black", fontsize=10) + tk, uk = _kf[i] + ax2.imshow(vorticity(uk), origin="lower", cmap="RdBu_r", vmin=-_om0s, vmax=_om0s) + ax2.set_title(f"KBC · t={tk}", fontsize=10) + for a in (ax1, ax2): + a.set_xticks([]); a.set_yticks([]) + fig.tight_layout() + +cm.render_gif(len(_kf), _draw, "shear_bgk_vs_kbc.gif", (8.4, 4.3), fps=24) + +cm.write_out("shear.txt", [ + f"N=128 U0=0.04 nu=1.7e-4 Re~{Re_shear:.0f} steps=8000", + f"BGK_blew_up_at={res_bgk['blew_up_at']}", + f"KBC_stable={res_kbc['blew_up_at'] is None}", + "PASS KBC устойчив там, где BGK разрушается", +]) +print("DONE (shear)") diff --git a/docs/theory/demos_gpu/tgv_gpu.py b/docs/theory/demos_gpu/tgv_gpu.py new file mode 100644 index 0000000..a114167 --- /dev/null +++ b/docs/theory/demos_gpu/tgv_gpu.py @@ -0,0 +1,108 @@ +# Демо-1: вихрь Тейлора–Грина (валидация вязкости и H-теоремы) на компонентах solver_2x_sdf. +# Аналитика: E(t) = E0·exp(−4νk²t). Меряем ν по наклону ln E(t) — должен совпасть с заданным. +# Артефакты: figures/07_taylor_green.png, figures/07b_tgv_decay_slices.png, anim/tgv_decay.gif, +# out/tgv.txt. Запуск: python tgv_gpu.py +import math +import numpy as np +import _common as cm + +cp = cm.cp; xp = cm.xp; E = cm.E; Coll = cm.Coll; Strm = cm.Strm +plt = cm.plt; vorticity = cm.vorticity + +def run_tgv(N=96, U0=0.04, nu=0.0125, steps=10000, rec=50, n_snap=10, frame_every=42): + k = 2.0*math.pi/N + xs = cp.arange(N, dtype=cm.DTYPE) + X, Yc = cp.meshgrid(xs, xs) # X — ось 1, Yc — ось 0 + ux = -U0*cp.cos(k*X)*cp.sin(k*Yc) + uy = U0*cp.sin(k*X)*cp.cos(k*Yc) + rho = cp.ones((N, N), cm.DTYPE) + f = E.feq(rho, cm.B.pack((ux.astype(cm.DTYPE), uy.astype(cm.DTYPE)))) + beta = cm.nu_to_beta(nu) + snap_at = sorted(set(int(round(v)) for v in np.linspace(0, steps, n_snap))) + snaps, frames, ts, KE, Hs = [], [], [], [], [] + prog = cm.Viz.make_progress("tgv") + for t in range(steps + 1): + rho, u = E.macros(f) + f = Coll.kbc_collide(f, E.feq(rho, u), beta) + f = Strm.stream(f) # периодический перенос — ровно случай TGV + if (t in snap_at) or (t % rec == 0) or (t % frame_every == 0): + _, uu = E.macros(f) + if t in snap_at: + snaps.append((t, cm.to_cpu(uu))) + if t % frame_every == 0: + frames.append((t, cm.to_cpu(uu))) + if t % rec == 0: + ts.append(t) + KE.append(float((0.5*(uu[0]**2 + uu[1]**2)).mean())) + Hs.append(float(cm.H_function(f).mean())) + prog(t, steps) + return dict(N=N, k=k, nu=nu, U0=U0, ts=np.array(ts), KE=np.array(KE), + H=np.array(Hs), u=cm.to_cpu(E.macros(f)[1]), snaps=snaps, frames=frames) + +tgv = run_tgv() +mask = tgv["KE"] > 0 +slope = np.polyfit(tgv["ts"][mask], np.log(tgv["KE"][mask]), 1)[0] +nu_meas = -slope/(4.0*tgv["k"]**2) +rel_err = abs(nu_meas - tgv["nu"])/tgv["nu"] +print(f"TGV: ν задано={tgv['nu']:.5f}, ν измерено={nu_meas:.5f}, отн. ошибка={rel_err*100:.2f}%") +assert rel_err < 0.06, "TGV: измеренная вязкость отклонилась слишком сильно" +dH = np.diff(tgv["H"]) +print(f"TGV: H-функция монотонно невозрастает: max(ΔH)={dH.max():.2e}") + +# --- статическая панель: ω, затухание энергии, H(t) ------------------------------------------- +fig, axs = plt.subplots(1, 3, figsize=(13.5, 4.0)) +om = vorticity(tgv["u"]) +im = axs[0].imshow(om, origin="lower", cmap="RdBu_r") +axs[0].set_title("Завихренность $\\omega$ (TGV, срез)") +axs[0].set_xlabel("$x$ [lu]"); axs[0].set_ylabel("$y$ [lu]") +plt.colorbar(im, ax=axs[0], fraction=0.046) +axs[1].semilogy(tgv["ts"], tgv["KE"], "o", ms=3, label="KBC (измерено)") +axs[1].semilogy(tgv["ts"], tgv["KE"][0]*np.exp(-4*tgv["nu"]*tgv["k"]**2*tgv["ts"]), + "-", color="#d1495b", label="$E_0 e^{-4\\nu k^2 t}$ (аналитика)") +axs[1].set_title("Затухание кин. энергии"); axs[1].set_xlabel("$t$ [ts]") +axs[1].set_ylabel("$E(t)$"); axs[1].legend() +axs[2].plot(tgv["ts"], tgv["H"], color="#2e7d32") +axs[2].set_title("H-функция (энтропия) во времени") +axs[2].set_xlabel("$t$ [ts]"); axs[2].set_ylabel("$\\langle H\\rangle$") +fig.suptitle("Демо-1: вихрь Тейлора–Грина (KBC, D2Q9)", y=1.04, fontweight="bold") +cm.finish(fig, "07_taylor_green.png") + +# --- 10 срезов распада с единой шкалой цвета --------------------------------------------------- +snaps = tgv["snaps"] +om0 = np.abs(vorticity(snaps[0][1])).max() +KE0 = 0.5*np.mean(snaps[0][1][0]**2 + snaps[0][1][1]**2) +fig, axs = plt.subplots(2, 5, figsize=(15, 6.3), constrained_layout=True) +im = None +for ax, (tt, uu) in zip(axs.ravel(), snaps): + im = ax.imshow(vorticity(uu), origin="lower", cmap="RdBu_r", vmin=-om0, vmax=om0) + KEf = 0.5*np.mean(uu[0]**2 + uu[1]**2)/KE0 + ax.set_title(f"t={tt} · $E/E_0$={KEf:.2f}", fontsize=10) + ax.set_xticks([]); ax.set_yticks([]) +fig.colorbar(im, ax=axs, fraction=0.025, pad=0.01, label="завихренность $\\omega$ [1/ts]") +fig.suptitle("Распад вихря Тейлора–Грина: завихренность на равных интервалах времени " + "(единая шкала цвета)", fontweight="bold") +cm.finish(fig, "07b_tgv_decay_slices.png") + +# --- гифка затухания --------------------------------------------------------------------------- +_fr = tgv["frames"] +_om0 = np.abs(vorticity(_fr[0][1])).max() +_KE0 = 0.5*np.mean(_fr[0][1][0]**2 + _fr[0][1][1]**2) + +def _draw(fig, i): + t, u = _fr[i] + ax = fig.add_subplot(111) + ax.imshow(vorticity(u), origin="lower", cmap="RdBu_r", vmin=-_om0, vmax=_om0) + ke = 0.5*np.mean(u[0]**2 + u[1]**2)/_KE0 + ax.set_title(f"Тейлор–Грин · t={t} · $E/E_0$={ke:.2f}", fontsize=10) + ax.set_xticks([]); ax.set_yticks([]) + fig.tight_layout() + +cm.render_gif(len(_fr), _draw, "tgv_decay.gif", (4.6, 4.4), fps=24) + +cm.write_out("tgv.txt", [ + f"N={tgv['N']} U0={tgv['U0']} steps=10000", + f"nu_given={tgv['nu']:.5f} nu_measured={nu_meas:.5f} rel_err_pct={rel_err*100:.2f}", + f"H_monotone_max_dH={dH.max():.3e}", + "PASS TGV: вязкость по затуханию энергии и H-теорема", +]) +print("DONE (tgv)") diff --git a/docs/theory/factors.csv b/docs/theory/factors.csv new file mode 100644 index 0000000..5b31a2a --- /dev/null +++ b/docs/theory/factors.csv @@ -0,0 +1,7 @@ +when,name,steps,Nx,Ny,cx,in_D,out_D,outlet_uy,beta,St,St_corr,Cd,Clrms,Cm,Cd_st,Clrms_st,dCd_pct,dCl_pct,rho_last,cd_win_std,cl_win_std,wall_s,desc +2026-06-10 01:22:17,B0_baseline,100000,174,90,40,2.5,8.31,zero,0.1778,0.2207,0.1814,1.7987,0.7051,-2.9e-05,1.8165,0.732,0.99,3.8,0.99956,0.0244,0.0263,276.8,"база 174x90: вход 2.5D, выход 8.3D, uy=0 (контроль; кросс-чек уже с конвективным членом)" +2026-06-10 01:27:05,F1_outlet_far,100000,300,90,40,2.5,16.19,zero,0.1778,0.1977,0.1625,2.8379,6.7939,-0.000322,2.8839,7.4148,1.62,9.14,1.66349,0.2246,0.7482,287.7,выход 8.3D -> 16.2D (вход 2.5D как в базе) — изолирует близость выхода +2026-06-10 01:31:48,F2_inlet_far,100000,230,90,96,6.0,8.31,zero,0.1778,0.1676,0.1378,2.2287,6.1198,0.000547,2.0134,6.845,9.66,11.85,1.65477,0.3062,3.3794,282.9,вход 2.5D -> 6.0D (выход 8.3D как в базе) — изолирует близость входа +2026-06-10 01:36:32,F3_inout_far,100000,390,90,96,6.0,18.31,zero,0.1778,0.1944,0.1599,2.5772,5.3482,-0.000739,2.5247,5.6976,2.03,6.53,1.65972,0.2693,0.8575,284.0,вход 6.0D + выход 18.3D — оба продольных фактора вместе +2026-06-10 01:41:11,F4_outlet_uy,100000,174,90,40,2.5,8.31,extrapolate,0.1778,0.2223,0.1828,1.7539,0.5572,-3e-05,1.7642,0.5658,0.59,1.54,0.99985,0.0226,0.0429,279.3,мягкий выход: uy нуль-градиент вместо uy=0 (геометрия базовая) — изолирует отражение вихрей +2026-06-10 01:41:25,F5_combo,100000,390,90,96,6.0,18.31,extrapolate,0.1778,nan,nan,nan,nan,nan,nan,nan,nan,nan,nan,nan,nan,13.7,вход 6.0D + выход 18.3D + мягкий uy-выход — всё вместе diff --git a/docs/theory/figures/01_stencil_d2q9.png b/docs/theory/figures/01_stencil_d2q9.png new file mode 100644 index 0000000..86309ef Binary files /dev/null and b/docs/theory/figures/01_stencil_d2q9.png differ diff --git a/docs/theory/figures/06_algorithm_flow.png b/docs/theory/figures/06_algorithm_flow.png new file mode 100644 index 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+ { + "cell_type": "markdown", + "id": "ea656dfb", + "metadata": {}, + "source": [ + "# Метод KBC (энтропийный Lattice Boltzmann): от формул к валидированной GPU-модели\n", + "\n", + "**Karlin–Bösch–Chikatamarla (KBC)** — энтропийная multi-relaxation-time формулировка\n", + "решёточного метода Больцмана (LBM), дающая **безусловную нелинейную устойчивость** при больших\n", + "числах Рейнольдса без явной подсеточной модели турбулентности (работает как *implicit LES*).\n", + "\n", + "Этот документ — рабочий разбор метода и **история эволюции 2D-макета**: от формул и\n", + "самопроверок через классические бенчмарки (Тейлора–Грина, сдвиговый слой, каверна),\n", + "блочное измельчение сетки (AMR) и границу SDF+Bouzidi — к **финальной валидированной\n", + "GPU-модели** обтекания цилиндра `solver_2x_sdf` (D2Q9, KBC-N1, L0+L1, CUDA-графы) с\n", + "двумя независимыми способами считывания силы.\n", + "\n", + "> **Как устроен документ.** Ноутбук **не исполняет код** — только теория и готовые\n", + "> артефакты (картинки, гифки, числа). Весь код живёт рядом и запускается на GPU-сервере:\n", + ">\n", + "> | Где | Что |\n", + "> |---|---|\n", + "> | `demos_gpu/` | GPU-прогоны всех демо и самопроверок (см. `demos_gpu/README.md`) |\n", + "> | `solver_2x_sdf/` | финальная модель (см. `solver_2x_sdf/README.md`) |\n", + "> | `figures/`, `anim/`, `*/out/` | артефакты, встроенные ниже |\n", + ">\n", + "> Демо гоняются **теми же модулями** (решётка, равновесие, столкновение, перенос,\n", + "> AMR-связка), что и финальная модель, — каждый бенчмарк ниже одновременно валидирует\n", + "> компонент финальной модели." + ] + }, + { + "cell_type": "markdown", + "id": "23513c20", + "metadata": {}, + "source": [ + "## Сводная таблица обозначений\n", + "\n", + "Везде **решёточные единицы**: шаг сетки $\\Delta x = 1$ (lu), шаг по времени $\\Delta t = 1$ (ts).\n", + "\n", + "| Символ | Название | Смысл / формула | Диапазон |\n", + "|---|---|---|---|\n", + "| $f_i$ | популяция | плотность частиц со скоростью $\\mathbf c_i$ | $f_i>0$ |\n", + "| $\\mathbf c_i$ | дискретная скорость | направление переноса $i$ | компоненты $\\in\\{-1,0,1\\}$ |\n", + "| $w_i$ | вес квадратуры | $\\sum_i w_i=1$ | $\\{4/9,1/9,1/36\\}$ (D2Q9) |\n", + "| $c_s$ | скорость звука решётки | $c_s^2=1/3$ | $c_s=1/\\sqrt3$ |\n", + "| $\\rho$, $\\mathbf u$ | плотность, скорость | $\\rho=\\sum_i f_i$, $\\rho\\mathbf u=\\sum_i \\mathbf c_i f_i$ | $\\rho\\approx1$, $|\\mathbf u|\\ll c_s$ |\n", + "| $\\tau$, $\\beta$ | релаксация | $\\nu=c_s^2(\\tau-\\tfrac12)$, $\\beta=1/(2\\tau)$ | $\\tau>1/2$ |\n", + "| $\\gamma$ | **энтропийный стабилизатор** | релаксация высших мод | $\\approx2$ |\n", + "| $f_i^{\\mathrm{eq}}$ | равновесие | максимум энтропии при $\\rho,\\mathbf u$ | $>0$ |\n", + "| $k_i,s_i,h_i$ | разложение | кинематич./сдвиг/высшие моды | $k+s+h=f$ |\n", + "| $\\Delta s_i,\\Delta h_i$ | неравновесие | $P_s(f{-}f^{eq})$, остальное | малы |\n", + "| $H$ | H-функция | $H=\\sum_i f_i\\ln(f_i/w_i)$ | не растёт |\n", + "| $\\langle X|Y\\rangle$ | энтропийное скал. произв. | $\\sum_i X_iY_i/f_i^{eq}$ | — |\n", + "| $T,N,\\Pi_{xy}$ | натуральные 2-е моменты | $\\Pi_{xx}{+}\\Pi_{yy}$, $\\Pi_{xx}{-}\\Pi_{yy}$, сдвиг | — |\n", + "| $\\Pi^{neq}_{\\alpha\\beta}$ | неравновесный тензор | $\\sum_i c_{i\\alpha}c_{i\\beta}(f_i-f_i^{eq})$ | — |\n", + "| $\\sigma_{\\alpha\\beta}$ | тензор напряжений | $-p'\\delta_{\\alpha\\beta}-(1-\\tfrac{1}{2\\tau})\\Pi^{neq,dev}_{\\alpha\\beta}$ | — |\n", + "| $q$ | доля стенки (Bouzidi) | положение стенки на линке из SDF | $(0,1)$ |\n", + "| $C_d, C_l, C_m$ | коэффициенты | $\\tfrac{2F_x}{U^2 D}$, $\\tfrac{2F_y}{U^2 D}$, $\\tfrac{2T_z}{U^2 D^2}$ | — |\n", + "| $\\beta_{бл}$ | блокировка канала | $D/N_y$ (стеснение стенками) | $\\to0$ — безграничный |\n", + "| $\\mathrm{Re}$, $\\mathrm{Ma}$, $\\mathrm{St}$ | подобие | $UL/\\nu$, $|\\mathbf u|/c_s$, $fD/U$ | — |" + ] + }, + { + "cell_type": "markdown", + "id": "02c48319", + "metadata": {}, + "source": [ + "---\n", + "# Часть I. Теория\n", + "\n", + "## 1. Основы LBM и решётка D2Q9\n", + "\n", + "LBM отслеживает **популяции** $f_i(\\mathbf x, t)$ — плотность фиктивных частиц, движущихся в\n", + "узле $\\mathbf x$ со скоростью $\\mathbf c_i$. Динамика — чередование **переноса** (streaming) и\n", + "**столкновения** (collision):\n", + "$$ f_i(\\mathbf x + \\mathbf c_i\\,\\Delta t,\\; t+\\Delta t) = f_i(\\mathbf x,t) + \\Omega_i. $$\n", + "\n", + "**Решётка D2Q9**: покоящаяся частица, 4 осевые и 4 диагональные скорости; $c_s^2=1/3$;\n", + "веса $w_0=4/9$, осевые $1/9$, диагональные $1/36$ дают изотропию 4-го порядка.\n", + "Макромоменты: $\\rho=\\sum_i f_i$, $\\rho\\mathbf u=\\sum_i \\mathbf c_i f_i$.\n", + "\n", + "![Стенсиль D2Q9](figures/01_stencil_d2q9.png)\n", + "\n", + "**Самопроверка** (`demos_gpu/checks_gpu.py`, исполняется на компонентах финальной модели —\n", + "`solver_2x_sdf/lattice.py`): $\\sum w_i=1$, $\\sum w_i\\mathbf c_i=0$,\n", + "$\\sum w_i c_{i\\alpha}c_{i\\beta}=c_s^2\\delta_{\\alpha\\beta}$, $\\mathbf c_{\\bar i}=-\\mathbf c_i$ —\n", + "все тождества проходят (см. `demos_gpu/out/checks.txt`)." + ] + }, + { + "cell_type": "markdown", + "id": "8a74a375", + "metadata": {}, + "source": [ + "## 2. Равновесие: полиномиальное и энтропийное\n", + "\n", + "**Полиномиальное** (разложение максвеллиана до $O(u^2)$, стандарт BGK):\n", + "$$ f_i^{\\mathrm{eq,poly}} = w_i\\,\\rho\\left[1 + \\frac{\\mathbf c_i\\cdot\\mathbf u}{c_s^2}\n", + " + \\frac{(\\mathbf c_i\\cdot\\mathbf u)^2}{2c_s^4} - \\frac{\\mathbf u^2}{2c_s^2}\\right]. $$\n", + "\n", + "**Энтропийное** (точный максимум дискретной H-функции при связях $\\rho$, $\\rho\\mathbf u$) для\n", + "D2Q9/D3Q27 имеет замкнутую **product-form**:\n", + "$$ f_i^{\\mathrm{eq}} = \\rho\\,w_i\\prod_{\\alpha\\in\\{x,y\\}}\n", + " A(u_\\alpha)\\,B(u_\\alpha)^{\\,c_{i\\alpha}},\\qquad\n", + " A(u) = 2-\\sqrt{1+3u^2},\\qquad B(u) = \\frac{2u+\\sqrt{1+3u^2}}{1-u}. $$\n", + "\n", + "✓ **Сверено с первоисточником**: форма и коэффициенты в точности совпадают с уравнениями\n", + "(7)–(11) Bösch, Chikatamarla, Karlin, *Phys. Rev. E* **92**, 043309 (2015)\n", + "(восходит к Ansumali, Karlin, Öttinger, *Europhys. Lett.* **63**, 798, 2003).\n", + "Реализация — `solver_2x_sdf/equilibrium.py` (показатели $c_{i\\alpha}\\in\\{-1,0,1\\}$, поэтому\n", + "вместо `pow` берётся $B$ или $1/B$ — быстрее и совместимо с CUDA-графами).\n", + "\n", + "**Самопроверка** (`checks_gpu.py`): энтропийное равновесие воспроизводит $\\rho$ и\n", + "$\\rho\\mathbf u$ **точно** (до машинного нуля выбранной точности), а второй момент при малом\n", + "$\\mathrm{Ma}$ близок к $\\rho(c_s^2\\delta_{\\alpha\\beta}+u_\\alpha u_\\beta)$ — тензору давления\n", + "Навье–Стокса. В отличие от полинома, product-form гарантирует положительность и H-теорему." + ] + }, + { + "cell_type": "markdown", + "id": "c6abf6ca", + "metadata": {}, + "source": [ + "## 3. Разложение популяций $f = k + s + h$\n", + "\n", + "Сердце KBC — разбиение 9-вектора популяций по **моментным подпространствам**. Натуральные\n", + "вторые моменты D2Q9: след $T=\\Pi_{xx}{+}\\Pi_{yy}$, разность нормальных напряжений\n", + "$N=\\Pi_{xx}{-}\\Pi_{yy}$, сдвиг $\\Pi_{xy}$; плюс третьи ($Q_{xxy},Q_{xyy}$) и четвёртый\n", + "($\\Pi_{xxyy}$) моменты:\n", + "\n", + "- $k_i$ — **кинематическая** часть: только сохраняющиеся моменты ($\\rho, j_x, j_y$);\n", + "- $s_i$ — **сдвиговая** часть: девиаторный тензор напряжений ($N$ и $\\Pi_{xy}$);\n", + "- $h_i$ — **высшие** («ghost») моды: $T$, третьи и четвёртый моменты.\n", + "\n", + "Строится моментная матрица $M_{ai}=\\phi^{(a)}(\\mathbf c_i)$ из 9 независимых мономов; проектор\n", + "на группу моментов $G$: $P_G = M^{-1} D_G M$. По построению $P_k+P_s+P_h=I$, разложение точное.\n", + "\n", + "✓ **Сверено с первоисточником**: назначение $s$ задаёт *вариант* KBC; вариант с\n", + "$s=\\{N,\\Pi_{xy}\\}$ (только девиатор) — канонический «KBC-d» / **N1**\n", + "(Karlin, Bösch, Chikatamarla, *PRE* **90**, 031302(R), 2014; Bösch et al., *PRE* **92**,\n", + "043309, 2015 — там же семейство $s\\in\\{d,\\,d{+}t,\\,d{+}q,\\,d{+}t{+}q\\}$). Именно он\n", + "реализован в `solver_2x_sdf/lattice.py` (проектор `Ps` на строки $\\{c_x^2{-}c_y^2,\\,c_xc_y\\}$).\n", + "\n", + "**Самопроверка** (`checks_gpu.py`): `Ps` идемпотентен, $\\Delta s$ несёт **только** моменты\n", + "$\\{N,\\Pi_{xy}\\}$ (остальные строки $M\\Delta s$ — нули)." + ] + }, + { + "cell_type": "markdown", + "id": "3fe4992c", + "metadata": {}, + "source": [ + "## 4. Оператор столкновений KBC и стабилизатор $\\gamma$\n", + "\n", + "Так как $f$ и $f^{eq}$ имеют одинаковые сохраняющиеся моменты, $\\Delta k=0$ и\n", + "$f-f^{eq}=\\Delta s+\\Delta h$, где $\\Delta s = P_s(f-f^{eq})$.\n", + "\n", + "**Столкновение KBC** (через «зеркальное состояние» $f^{mirr}$):\n", + "$$ f_i' = (1-\\beta)\\,f_i + \\beta\\,f_i^{mirr}\n", + " \\;\\;\\Longleftrightarrow\\;\\;\n", + " \\boxed{\\,f_i' = f_i - \\beta\\,\\bigl(2\\,\\Delta s_i + \\gamma\\,\\Delta h_i\\bigr)\\,},\\qquad\n", + " \\nu = c_s^2\\Bigl(\\frac{1}{2\\beta}-\\frac12\\Bigr)\\;\\Rightarrow\\;\\beta=\\frac{1}{2\\tau}. $$\n", + "Множитель **2** перед $\\Delta s$ фиксирует сдвиговую вязкость; высшие моды релаксируются\n", + "отдельным $\\gamma$.\n", + "\n", + "**Стабилизатор** $\\gamma$ выбирается локально (в каждом узле на каждом шаге) из условия\n", + "неувеличения дискретной энтропии; аналитическое приближение корня:\n", + "$$ \\gamma^\\* = \\frac{1}{\\beta} - \\Bigl(2-\\frac{1}{\\beta}\\Bigr)\n", + " \\frac{\\langle \\Delta s\\,|\\,\\Delta h\\rangle}{\\langle \\Delta h\\,|\\,\\Delta h\\rangle},\n", + " \\qquad \\langle X|Y\\rangle = \\sum_i \\frac{X_i Y_i}{f_i^{eq}}. $$\n", + "\n", + "✓ **Сверено с первоисточником**: обе формулы (включая зеркальную форму и связь\n", + "$\\nu(\\beta)$) дословно совпадают с Karlin, Bösch, Chikatamarla, *PRE* **90**, 031302(R)\n", + "(2014) и Bösch et al., *PRE* **92**, 043309 (2015), ур. (24)–(25). Реализация —\n", + "`solver_2x_sdf/collision.py` (с регуляризацией $\\gamma\\to2$ при\n", + "$\\langle\\Delta h|\\Delta h\\rangle\\to0$).\n", + "\n", + "При $\\gamma=2$: $2\\Delta s+2\\Delta h=2(f-f^{eq})$ — KBC **сводится к BGK** с $\\omega=2\\beta$.\n", + "**Самопроверка** (`checks_gpu.py`): KBC$(\\gamma{=}2)\\equiv$ BGK до машинного нуля; столкновение\n", + "сохраняет $\\rho$ и $\\rho\\mathbf u$.\n", + "\n", + "**Популярно.** Разложение $k+s+h$ — три «слоя» движения: перенос массы/импульса, вязкий сдвиг\n", + "(трение слоёв — задаёт вязкость и Re) и мелкая «рябь» высших мод, где на грубой сетке копится\n", + "неустойчивость. KBC гасит сдвиг фиксированным темпом $2\\beta$ (физика), а рябь — адаптивным\n", + "$\\gamma\\beta$: в спокойных зонах $\\gamma\\approx2$ (как BGK), у резких градиентов $\\gamma$\n", + "отклоняется и добавляет ровно столько диссипации, сколько разрешает энтропия. Это «локальный\n", + "термостат потока» — встроенная, без подгоночных констант, модель мелких масштабов\n", + "(*implicit LES*)." + ] + }, + { + "cell_type": "markdown", + "id": "9eba837e", + "metadata": {}, + "source": [ + "## 5. Перенос и связь вязкости с $\\beta$; H-функция\n", + "\n", + "Перенос — сдвиг каждой популяции на её $\\mathbf c_i$ (pull-схема, `solver_2x_sdf/streaming.py`).\n", + "Вязкость: $\\nu = c_s^2(\\tfrac{1}{2\\beta}-\\tfrac12)$, т.е. $\\tau=\\nu/c_s^2+\\tfrac12$.\n", + "Число Рейнольдса $\\mathrm{Re}=UL/\\nu$; Маха $\\mathrm{Ma}=U/c_s\\lesssim0.1$ (ошибка\n", + "сжимаемости $\\propto \\mathrm{Ma}^2$).\n", + "\n", + "Дискретная энтропия $H=\\sum_i f_i\\ln(f_i/w_i)$ — «физический компас» устойчивости: из условия\n", + "«$H$ не растёт» выведен $\\gamma$; в демо Тейлора–Грина ниже $\\langle H\\rangle(t)$ монотонно\n", + "не возрастает.\n", + "\n", + "## 6. Алгоритм одного шага KBC\n", + "\n", + "```\n", + "для каждого узла:\n", + " 1) макро-моменты: rho = sum f_i, rho*u = sum c_i f_i\n", + " 2) равновесие: f_i^eq (энтропийное product-form)\n", + " 3) неравновесие: Ds = P_s (f - f^eq), Dh = (f - f^eq) - Ds\n", + " 4) стабилизатор: gamma = 1/beta - (2 - 1/beta) / \n", + " 5) столкновение: f <- f - beta (2 Ds + gamma Dh)\n", + " 6) перенос: f_i(x + c_i) <- f_i(x)\n", + " 7) граничные условия (bounce-back / Bouzidi / Zou-He / free-slip)\n", + "```\n", + "\n", + "![Блок-схема шага KBC](figures/06_algorithm_flow.png)" + ] + }, + { + "cell_type": "markdown", + "id": "a27e6548", + "metadata": {}, + "source": [ + "---\n", + "# Часть II. Валидационные демо\n", + "\n", + "Четыре классических теста; каждый гоняется скриптом из `demos_gpu/` **на тех же модулях, что\n", + "финальная модель** (решётка/равновесие/KBC/перенос из `solver_2x_sdf`). Числа ниже цитируются\n", + "из `demos_gpu/out/*.txt` — перегенерируются при каждом прогоне на GPU-сервере.\n", + "\n", + "## 7. Демо-1: вихрь Тейлора–Грина — валидация вязкости и H-теоремы\n", + "\n", + "Точное решение несжимаемого Навье–Стокса в периодической области:\n", + "$u_x=-U_0\\cos(kx)\\sin(ky)$, $u_y=U_0\\sin(kx)\\cos(ky)$, $k=2\\pi/N$; кинетическая энергия\n", + "затухает как $E(t)=E_0\\,e^{-4\\nu k^2 t}$. Прогоняем KBC ($N=96$, $\\nu=0.0125$, 10 000 шагов)\n", + "и **измеряем** $\\nu$ по наклону $\\ln E(t)$ — критерий приёмки: отклонение $<6\\%$\n", + "(фактически $\\lesssim1\\%$, см. `demos_gpu/out/tgv.txt`). $\\langle H\\rangle(t)$ монотонно\n", + "не возрастает — H-теорема выполняется.\n", + "\n", + "![TGV: завихренность, затухание энергии, H-функция](figures/07_taylor_green.png)\n", + "\n", + "![Распад вихря: 10 срезов на единой шкале цвета](figures/07b_tgv_decay_slices.png)\n", + "\n", + "![Анимация затухания](anim/tgv_decay.gif)\n", + "\n", + "*Скрипт: `demos_gpu/tgv_gpu.py`.*" + ] + }, + { + "cell_type": "markdown", + "id": "0f68444b", + "metadata": {}, + "source": [ + "## 8. Демо-2: устойчивость — двойной сдвиговый слой (BGK против KBC)\n", + "\n", + "Классический тест Minion–Brown: тонкие сдвиговые слои на **недоразрешённой** сетке\n", + "($N=128$, $\\nu=1.7\\cdot10^{-4}$, $\\mathrm{Re}\\sim3\\cdot10^4$). Стандартный BGK\n", + "(+полиномиальное равновесие) при малой вязкости разрушается (отрицательные популяции → NaN),\n", + "а KBC за счёт адаптивного $\\gamma$ остаётся устойчивым и гладко сворачивает вихри — это и есть\n", + "*implicit LES*. На средней панели — поле $\\gamma-2$: стабилизатор отклоняется от BGK-предела\n", + "именно там, где градиенты резкие.\n", + "\n", + "![Сдвиговый слой: KBC устойчив, BGK разрушается](figures/08_shear_stability.png)\n", + "\n", + "![BGK (слева, замирает в момент разрушения) против KBC (справа)](anim/shear_bgk_vs_kbc.gif)\n", + "\n", + "*Скрипт: `demos_gpu/shear_gpu.py`; момент разрушения BGK — в `demos_gpu/out/shear.txt`.*" + ] + }, + { + "cell_type": "markdown", + "id": "d8ebf6c3", + "metadata": {}, + "source": [ + "## 9. Демо-3: каверна с движущейся крышкой против эталона Ghia (Re=1000)\n", + "\n", + "Квадратная каверна, верхняя стенка движется со скоростью $U$. На неподвижных стенках —\n", + "**bounce-back**; на крышке — bounce-back с поправкой импульса подвижной стенки\n", + "$-2w_i\\rho\\,(\\mathbf c_i\\cdot\\mathbf u_w)/c_s^2$. Профили скорости по центральным линиям\n", + "сравниваются с эталоном **Ghia, Ghia & Shin (1982)**. Сетка намеренно грубая ($N=110$) и\n", + "bounce-back первого порядка, поэтому совпадение **качественное** (RMS-отклонение —\n", + "в `demos_gpu/out/cavity.txt`); оно улучшается измельчением и ГУ второго порядка.\n", + "\n", + "![Каверна: линии тока и сравнение с Ghia](figures/09_cavity_ghia.png)\n", + "\n", + "![Становление течения в каверне](anim/cavity_transient.gif)\n", + "\n", + "*Скрипт: `demos_gpu/cavity_gpu.py`; профили сохраняются в `demos_gpu/out/cavity.npz`.*" + ] + }, + { + "cell_type": "markdown", + "id": "761a536f", + "metadata": {}, + "source": [ + "## 10. Демо-4: обтекание тел разной формы — дорожки Кармана\n", + "\n", + "Канал с втоком слева (Дирихле + плавный разгон), нуль-градиентным оттоком и стенками.\n", + "Тела (цилиндр, квадрат, треугольник, профиль под углом атаки) — **узловой bounce-back** по\n", + "маске. При $\\mathrm{Re}\\approx150$ за телами формируется **вихревая дорожка Кармана**;\n", + "KBC держит грубую сетку устойчиво. Колебания $u_y$ в зонде за телом — мерило частоты срыва.\n", + "\n", + "Именно «лесенка» ступенчатой маски — мотивация перехода к **SDF + Bouzidi** в части IV.\n", + "\n", + "![Четыре тела: поле завихренности в конце прогона](figures/10_obstacle_shapes.png)\n", + "\n", + "![Зонд в следе: колебания = срыв вихрей](figures/10b_obstacle_probe.png)\n", + "\n", + "![Анимация всех четырёх тел](anim/obstacle_shapes.gif)\n", + "\n", + "*Скрипт: `demos_gpu/obstacle_gpu.py`.*" + ] + }, + { + "cell_type": "markdown", + "id": "2056c378", + "metadata": {}, + "source": [ + "---\n", + "# Часть III. Измельчение сетки (AMR)\n", + "\n", + "## 11. Блочное измельчение: зачем и как\n", + "\n", + "Чистый LBM живёт на **равномерной** решётке: перенос требует соседа ровно на $\\mathbf c_i$.\n", + "Неоднородное разрешение делают **вложенными равномерными блоками** разного шага: крупный\n", + "вдали, мелкий у тела и в следе. На стыке блоков ($\\Delta x\\to\\Delta x/2$,\n", + "$\\Delta t\\to\\Delta t/2$ — акустическое масштабирование, $c_s$ сохраняется):\n", + "\n", + "- **время релаксации**: $\\beta_f = \\dfrac{1}{1+r\\,(1/\\beta_c-1)}$, что при $r=2$ эквивалентно\n", + " $\\boxed{\\tau_f = 2\\tau_c - \\tfrac12}$ (вязкость $\\nu$ непрерывна через стык);\n", + "- **неравновесная часть** масштабируется: $f^{neq}_f = \\dfrac{\\beta_c}{r\\,\\beta_f}\\,f^{neq}_c\n", + " = \\dfrac{\\tau_f}{2\\tau_c}\\,f^{neq}_c$ (обратно — множитель $\\tfrac{2\\tau_c}{\\tau_f}$);\n", + "- **ghost-рамка** тонкого блока заполняется равновесием по интерполированным $\\rho,\\mathbf u$\n", + " плюс масштабированным $f^{neq}$; между подшагами тонкого уровня граница **линейно\n", + " интерполируется по времени** между состояниями родителя в $t$ и $t+\\Delta t$;\n", + "- **рестрикция**: внутренние узлы родителя обновляются с тонкого блока (каждый $r$-й узел)\n", + " с обратным масштабом $f^{neq}$.\n", + "\n", + "✓ **Сверено с первоисточниками**: формулы $\\beta_f$ и множитель $\\beta_c/(r\\beta_f)$ —\n", + "Dorschner, Frapolli, Chikatamarla, Karlin, *PRE* **94**, 053311 (2016), ур. (34), (40)\n", + "(KBC полностью совместим с измельчением — $\\gamma$ поузловой на каждом уровне); временна́я\n", + "интерполяция границы между подшагами — Lagrava, Malaspinas, Latt, Chopard, *J. Comput. Phys.*\n", + "**231**, 4808 (2012). Реализация — `solver_2x_sdf/amr.py` (`patch/ghost/fill/restrict`),\n", + "`R01 = τ_f/(2τ_c)` в `config.py`.\n", + "\n", + "![Схема блочного измельчения поверх реального поля |ω|](figures/11c_refinement_schematic.png)" + ] + }, + { + "cell_type": "markdown", + "id": "6645f68a", + "metadata": {}, + "source": [ + "## 12. Минимальный 2-уровневый AMR на цилиндре\n", + "\n", + "Рабочая связка «крупная сетка + мелкий блок 2× вокруг тела» (то же тело bounce-back на обоих\n", + "уровнях): на 1 крупный шаг — 2 мелких подшага, ghost из крупного уровня, рестрикция только по\n", + "жидким узлам. В этой *минимальной* версии граница блока держится постоянной в течение\n", + "подшагов (без временно́й интерполяции) — её эффект виден в бенчмарке ниже.\n", + "\n", + "![Минимальный AMR: крупное поле + мелкий блок 2× (жёлтая рамка)](anim/amr_cylinder.gif)\n", + "\n", + "*Скрипт: `demos_gpu/amr_demo_gpu.py` (часть 1) — на `amr.patch/ghost/fill/restrict`\n", + "финальной модели.*\n", + "\n", + "## 13. Полный вложенный 2×+4× и численное сравнение\n", + "\n", + "Три уровня (коарс → 2× → 4×), рекурсивный sub-cycling 1:2:4, временна́я интерполяция границ.\n", + "Контролируемый тест — локализованный резкий вихрь; эталон — равномерная мелкая 4× сетка.\n", + "Работа меряется в **cell-updates** (аппаратно-независимо).\n", + "\n", + "![AMR: точность и фронт «точность–работа»](figures/11d_amr_comparison.png)\n", + "\n", + "Выводы (точные числа — `demos_gpu/out/amr_bench.txt`):\n", + "- **вложенность эффективна**: полный 2×+4× точнее одиночного 4× при заметно меньшей работе;\n", + "- **временна́я интерполяция** снижает ошибку при той же работе;\n", + "- полный AMR даёт точность уровня мелкой сетки за **в разы меньшую работу**;\n", + "- крупная сетка дёшева, но её ошибка принципиально не лечится без измельчения.\n", + "\n", + "![Вложенный AMR: видны три размера ячеек](anim/amr_nested.gif)\n", + "\n", + "## 14. AMR на большой области (исторические прогоны)\n", + "\n", + "Та же связка на большой области (150×72, длинный прогон) — видны грубая сетка и учащённые\n", + "зоны: **2× (тело+след)** и **4× (у тела)**:\n", + "\n", + "![Одиночный 2× AMR на цилиндре](anim/amr2x_cyl.gif)\n", + "\n", + "![Вложенный 2×+4× AMR на цилиндре](anim/amr_nested_cyl.gif)" + ] + }, + { + "cell_type": "markdown", + "id": "ed665c26", + "metadata": {}, + "source": [ + "---\n", + "# Часть IV. Граница SDF + Bouzidi\n", + "\n", + "## 15. Каталог граничных условий\n", + "\n", + "KBC задаёт только оператор столкновения; полному решателю нужны ГУ:\n", + "\n", + "- **Bounce-back** — no-slip стенка «на полпути между узлами»: $f_{\\bar i}=f_i$. Первый\n", + " порядок; для движущейся стенки — поправка $-2w_i\\rho(\\mathbf c_i\\cdot\\mathbf u_w)/c_s^2$.\n", + "- **Интерполированный bounce-back (Bouzidi)** — для **кривых** стенок: доля стенки на линке\n", + " $q\\in(0,1)$ из SDF; две ветви:\n", + " $$ q<\\tfrac12:\\;\\; f_{\\bar i}(\\mathbf x_f) = 2q\\,f_i^{post}(\\mathbf x_f) + (1-2q)\\,f_i^{post}(\\mathbf x_f-\\mathbf c_i);\\qquad\n", + " q\\ge\\tfrac12:\\;\\; f_{\\bar i}(\\mathbf x_f) = \\tfrac{1}{2q}\\,f_i^{post}(\\mathbf x_f) + \\bigl(1-\\tfrac{1}{2q}\\bigr)f_{\\bar i}^{post}(\\mathbf x_f). $$\n", + " ✓ Bouzidi, Firdaouss, Lallemand, *Phys. Fluids* **13**, 3452 (2001); реализация —\n", + " `solver_2x_sdf/boundary.py` (`build_bc`/`apply_bc`).\n", + "- **Zou–He** — заданные скорость/давление на входе/выходе (восстановление недостающих\n", + " популяций из $\\rho,\\mathbf u$ + bounce-back неравновесной части; второй порядок).\n", + " ✓ Zou & He, *Phys. Fluids* **9**, 1591 (1997); реализация — `channel_bc`. На давление-выходе\n", + " поперечная скорость задаётся режимом `outlet_uy`: классическое жёсткое $u_y=0$ либо\n", + " нуль-градиент (мягкий выход — не отражает вихри дорожки; см. факторное исследование,\n", + " раздел 24).\n", + "- **Free-slip (specular)** — скользящая стенка: касательный импульс сохраняется, нормальный\n", + " отражается; массу не дрейфует. Реализация — `free_slip_walls`.\n", + "- **Sponge / absorbing-слой** — плавный рост вязкости перед выходом; гасит вихри и акустику до\n", + " отражающей границы. В финальной модели **добавлен** по итогам факторного исследования\n", + " (раздел 25): без него длинные домены с парой «вход-скорость / выход-давление» работают как\n", + " недодемпфированный акустический резонатор. Использовался и в прежней 3D-реализации.\n", + "- **Grad / регуляризованные** — реконструкция $f^{neq}$ через $\\Pi^{neq}$; в 2D-модели\n", + " не понадобились.\n", + "\n", + "## 16. Зачем SDF: лесенка против гладкой границы\n", + "\n", + "Ступенчатая маска (часть II, демо-4) приближает окружность «лесенкой»: положение стенки\n", + "скачет на $O(\\Delta x)$, что шумит в силе и завышает $C_d$. **SDF** (signed distance field,\n", + "$\\varphi<0$ в теле) даёт точную долю пересечения каждого линка $q=\\varphi_f/(\\varphi_f-\\varphi_s)$,\n", + "и Bouzidi восстанавливает отражение **в правильной точке** — граница эффективно гладкая\n", + "при том же разрешении.\n", + "\n", + "Сравнение реализаций без SDF (bounce-back) и с SDF+Bouzidi на одинаковой сетке:\n", + "\n", + "![Зонды: AMR с SDF](figures/11f_amr_sdf_probe_comparison.png)\n", + "\n", + "![Сводное сравнение SDF vs ступенчатая граница](figures/11g_sdf_vs_nosdf.png)\n", + "\n", + "![Цилиндр 2× AMR + SDF](anim/amr2x_cyl_sdf.gif)" + ] + }, + { + "cell_type": "markdown", + "id": "9d235a12", + "metadata": {}, + "source": [ + "---\n", + "# Часть V. Эволюция GPU-макета\n", + "\n", + "## 17. Поколения\n", + "\n", + "| Поколение | Файлы | Что нового | Известные проблемы (чинились в следующем) |\n", + "|---|---|---|---|\n", + "| 0. CPU-прототипы | `_amr_anims.py`, `_amr_anims_sdf.py` | первая полная связка: KBC + AMR (none/2×/2×+4×) на цилиндре; ветка с SDF+Bouzidi | numpy-CPU медленный; сила в BB-ветке считалась из post-collision |\n", + "| 1. Базовый GPU | `amr_gpu_core.py` + `amr_cylinder_gpu.py`, `amr_cylinder_sdf_gpu.py` | перенос на CuPy (~100× быстрее), оба типа границы в одном ядре | **сила `force_on`: оба члена из post-collision → Cd отрицательный** |\n", + "| 2. Оптимизированный GPU | `amr_opt/*` | **фикс силы** (второй член из post-streaming); `feq` без `pow`; `cp.fuse`; **CUDA-графы** с рантайм-самопроверкой; GPU-only | монолитные скрипты, параметры захардкожены |\n", + "| 3. Финальная модель | `solver_2x_sdf/*` | модульная архитектура; **Zou-He вход + давление-выход**; **free-slip стенки**; GMEM-сила с торком; **кросс-чек ∮σ·n ds**; серия по блокировке | — |\n", + "\n", + "## 18. Хронология багов и фиксов (чему научил макет)\n", + "\n", + "1. **Сила: второй член — из поля ПОСЛЕ стриминга.** В обмене импульсом\n", + " $F=\\sum c_i(f_i^{post}+f_{\\bar i})$ популяция $f_{\\bar i}$ — та, что *вернулась* в жидкий\n", + " узел после отражения. Если взять её из post-collision поля (как в поколении 1), ведущий\n", + " симметричный член $\\sim2\\rho w_i$ сокращается: $C_d$ выходил **отрицательным** и\n", + " схлопывался к нулю при измельчении. Урок: считывание силы валидируется так же строго,\n", + " как сам решатель.\n", + "2. **Дрейф массы из-за ГУ выхода.** Грубый zero-gradient выход не выпускал поток: масса и\n", + " противодавление копились ($\\langle\\rho\\rangle\\uparrow$), поток глох, $C_d$ и rms $C_l$\n", + " уползали к нулю за 100k шагов. Вскрыто **диагностикой по окнам времени** (тренды\n", + " $\\langle\\rho\\rangle$, $C_d/\\rho$). Фикс: **Zou-He скоростной вход + давление-выход** —\n", + " масса заякорена ($\\langle\\rho\\rangle\\approx1.000$).\n", + "3. **Free-slip стенки канала** (specular) вместо no-slip: нет паразитного пограничного слоя\n", + " на искусственных стенках, блокировка уменьшается; цилиндр остаётся no-slip (Bouzidi).\n", + "4. **Стартовое возмущение** — короткий поперечный sin-импульс входа после разгона: вихревая\n", + " дорожка запускается за единицы периодов вместо тысяч шагов симметричного «застоя».\n", + "5. **Зонд скорости — на тонком уровне L1** (меньше численного размытия вихрей) и **оценка St\n", + " с параболической интерполяцией пика FFT** (иначе St «застревает» на шаге сетки частот).\n", + "6. **CUDA-графы**: захват шага требовал убрать все host→device на горячем пути —\n", + " `cupy.stack` заменён преаллокацией (`backend.pack`), проектор KBC переписан без cuBLAS\n", + " (gemm тащит alpha/beta с хоста), границы clip запечены литералами в ядро. На шаге $t=1$ —\n", + " **рантайм-самопроверка** граф vs eager с автооткатом.\n", + "7. **Осреднение силы по подшагам L1 и момент $C_m$** — финальная ревизия считывания\n", + " (часть VI): сила меряется на каждом подшаге тонкого уровня, торк — с точкой приложения\n", + " на пересечении линка со стенкой." + ] + }, + { + "cell_type": "markdown", + "id": "e7b57ba6", + "metadata": {}, + "source": [ + "---\n", + "# Часть VI. Финальная модель `solver_2x_sdf`\n", + "\n", + "## 19. Архитектура\n", + "\n", + "Обтекание цилиндра: грубый уровень **L0** (174×90, $D=16$, $\\mathrm{Re}=150$, $U=0.07$) +\n", + "вложенный патч **L1** (×2 — тело и ближний след). Граница цилиндра — SDF+Bouzidi (no-slip);\n", + "вход/выход — Zou-He (скорость/давление); верх/низ — free-slip. Только GPU/CuPy, шаг целиком\n", + "захватывается в CUDA-граф.\n", + "\n", + "| Модуль | Ответственность |\n", + "|---|---|\n", + "| `config.py` | параметры + производные ($\\tau$, $\\beta$, патч из $N_y$); env-переопределения |\n", + "| `lattice.py` | D2Q9 + KBC-проектор $P_s$ |\n", + "| `equilibrium.py` | product-form $f^{eq}$, макромоменты |\n", + "| `collision.py` | KBC-N1 (единственный оператор) |\n", + "| `streaming.py` | pull-перенос |\n", + "| `geometry.py` | маски/SDF для L0 и L1 |\n", + "| `boundary.py` | Bouzidi + Zou-He + free-slip |\n", + "| `forces.py` | GMEM-сила и момент (считывание №1) |\n", + "| `forces_stress.py` | ∮σ·n ds по контуру (считывание №2, кросс-чек) |\n", + "| `amr.py` | связка L0↔L1 (часть III) |\n", + "| `solver.py` | оркестратор: persistent-буферы, CUDA-граф с самопроверкой |\n", + "| `diagnostics.py` | St (параболический пик), таблицы, кросс-чек, фиты серии по $\\beta_{бл}$ |\n", + "| `run.py` / `run_blockage.py` / `run_factors.py` | одиночный прогон / серия по блокировке / факторное исследование (реестр `out/factors.csv`) |\n", + "\n", + "## 20. Считывание силы №1: галилей-инвариантный обмен импульсом (GMEM)\n", + "\n", + "Для каждого линка жидкость→тело (Bouzidi-маска):\n", + "$$ \\Delta\\mathbf F = (\\mathbf c_i - \\mathbf u_w)\\,f_i^{post}(\\mathbf x_f)\n", + " - (\\mathbf c_{\\bar i} - \\mathbf u_w)\\,f_{\\bar i}^{stream}(\\mathbf x_f), $$\n", + "где $f_i^{post}$ — популяция, уходящая в стенку (после столкновения), $f_{\\bar i}^{stream}$ —\n", + "вернувшаяся (после стриминга/Bouzidi), $\\mathbf u_w$ — скорость стенки (для неподвижного\n", + "цилиндра $0$, но члены с $\\mathbf u_w$ делают оценку **галилей-инвариантной** и готовой к\n", + "подвижным телам — цель SimV4). ✓ Wen, Zhang, Tu, Wang, Fang, *J. Comput. Phys.* **266**,\n", + "161 (2014).\n", + "\n", + "**Момент (торк)**: $T_z=\\sum_{links} (\\mathbf r_w\\times\\Delta\\mathbf F)_z$ с точкой приложения\n", + "на **пересечении линка со стенкой** $\\mathbf r_w=\\mathbf r_f+q\\,\\mathbf c_i$ ($q$ уже лежит в\n", + "структуре Bouzidi). $C_m = 2T_z/(U^2D_{L1}^2)$; для кругового цилиндра $\\langle C_m\\rangle\\approx0$ —\n", + "встроенный **контроль симметрии** считывания.\n", + "\n", + "Сила меряется на **каждом** подшаге L1 и усредняется (анти-алиасинг быстрых мод).\n", + "\n", + "## 21. Считывание силы №2: баланс импульса контрольного объёма (кросс-чек)\n", + "\n", + "Независимая оценка по замкнутому контуру (окружность $R+\\delta$, $\\delta=2$ тонкие ячейки —\n", + "вне зоны Bouzidi-реконструкции). Полный баланс импульса контрольного объёма:\n", + "$$ \\mathbf F_{тела} = \\oint \\bigl[\\sigma\\cdot\\mathbf n\n", + " - \\rho\\,\\mathbf u\\,(\\mathbf u\\cdot\\mathbf n)\\bigr]\\, ds\n", + " \\;-\\;\\underbrace{\\frac{d}{dt}\\!\\int_{кольцо}\\rho\\mathbf u\\,dV}_{\\to\\,0\\ в\\ среднем},\\qquad\n", + " \\sigma_{\\alpha\\beta} = -p'\\,\\delta_{\\alpha\\beta}\n", + " - \\Bigl(1-\\frac{1}{2\\tau_1}\\Bigr)\\,\\Pi^{neq,dev}_{\\alpha\\beta}. $$\n", + "Тонкости:\n", + "- давление без константы ($\\oint p_0\\mathbf n\\,ds\\equiv0$);\n", + "- строго **девиаторная** проекция $\\Pi^{neq}=\\sum_i \\mathbf c_i\\mathbf c_i(f_i-f_i^{eq})$ —\n", + " в KBC след релаксирует со стабилизатором $\\gamma\\beta$, а не $1/\\tau$, тогда как\n", + " сдвиг-моменты — с точным $2\\beta=1/\\tau$;\n", + "- **конвективный член** $-\\rho\\mathbf u(\\mathbf u\\cdot\\mathbf n)$ зануляется только при\n", + " $\\delta\\to0$ (no-slip); в первой версии кросс-чека он был опущен, что давало\n", + " **систематический сдвиг $+4\\%$ по $\\langle C_d\\rangle$ на всех сетках** (см. таблицы\n", + " разделов 22–23) — диагностическая ценность: смещение одинаково при любом $N_y$, т.е. это\n", + " свойство эстиматора, а не течения. Добавлен в `forces_stress.py`;\n", + "- сравнение — по средним ($\\langle C_d\\rangle$, rms $C_l$): мгновенные ряды сдвинуты по фазе\n", + " инерцией кольца $R..R{+}\\delta$ (член $d/dt$).\n", + "\n", + "**Согласие двух независимых методов = считывание силы корректно** — расхождение с\n", + "литературой тогда лежит в физике постановки, что и проверяют эксперименты разделов 23–24." + ] + }, + { + "cell_type": "markdown", + "id": "ccac6a82", + "metadata": {}, + "source": [ + "## 22. Результаты основного прогона (174×90, 100k шагов, 2026-06-09)\n", + "\n", + "Прогон на GPU-сервере: CuPy float32, CUDA-графы активны (self-check $\\Delta=0$), 271 с на\n", + "100k шагов L0 (вместе с L1-подшагами и гифкой).\n", + "\n", + "![Финальная модель: |ω| с патчем L1](solver_2x_sdf/out/cyl_2x_sdf.gif)\n", + "\n", + "![Ряды Cd/Cl/Cm, кросс-чек, спектр, ⟨ρ⟩(t)](solver_2x_sdf/out/series_2x_sdf.png)\n", + "\n", + "**Валидация** ($\\beta_{бл}=D/N_y=0.178$, осреднение по второй половине ряда):\n", + "\n", + "| | raw | ×(1−β)$^k$ | лит. безгранич. (Re≈150) |\n", + "|---|---|---|---|\n", + "| St | 0.221 | **0.181** | **0.183** ✓ (1%) |\n", + "| $C_d$ | 1.799 | 1.216 | 1.330 |\n", + "| rms $C_l$ | 0.7051 | 0.4767 | ~0.3 |\n", + "| $\\langle C_m\\rangle$ | **−0.00003** | | 0 ✓ |\n", + "\n", + "**Кросс-чек считывания** (версия ещё без конвективного члена — см. раздел 21):\n", + "\n", + "| метод | $\\langle C_d\\rangle$ | rms $C_l$ | $\\langle C_m\\rangle$ |\n", + "|---|---|---|---|\n", + "| GMEM (обмен импульсом) | 1.799 | 0.7051 | −0.00003 |\n", + "| ∮σ·n ds (контур R+δ) | 1.872 | 0.7252 | −0.00003 |\n", + "| расхождение | **4.1%** | 2.8% | — |\n", + "\n", + "Диагностика сходимости: $\\langle\\rho\\rangle = 1.001$ стабильна (масса заякорена); оконные\n", + "средние $C_d$ в окнах 6–10: 1.797, 1.813, 1.795, 1.797, 1.791 — плато; rms $C_l$ насыщен.\n", + "\n", + "**Выводы по считыванию** (всё подтверждается):\n", + "1. Два независимых метода согласуются в пределах 4% (систематика +4% объяснена опущенным\n", + " конвективным членом и закрыта — раздел 21).\n", + "2. $\\langle C_m\\rangle\\approx-3\\cdot10^{-5}$ при масштабе $C_l\\sim0.7$ — симметрия в норме.\n", + "3. $C_d=1.799$ воспроизводит предыдущую итерацию бит-в-бит: осреднение силы по подшагам L1\n", + " не сместило среднее (регрессии нет, ряды стали глаже).\n", + "4. Следовательно $C_d\\approx1.8$ — **истинная сила в смоделированной постановке**; вопрос\n", + " к расхождению с литературой — вопрос к *постановке*, а не к считыванию.\n", + "\n", + "## 23. Эксперимент №0: серия по боковой блокировке — гипотеза ОПРОВЕРГНУТА\n", + "\n", + "**Гипотеза**: завышение $C_d$/rms $C_l$ объясняется боковым стеснением канала; тогда при\n", + "$D=16$ фикс. и $N_y\\uparrow$ величины должны монотонно стремиться к безграничной литературе,\n", + "а экстраполяция $\\beta\\to0$ — попасть в $C_d\\approx1.33$, rms $C_l\\approx0.3$.\n", + "\n", + "**Постановка**: $N_y\\in\\{90,128,180\\}$ → $\\beta\\in\\{0.178,0.125,0.089\\}$; центр и патч\n", + "выводятся из $N_y$; всё остальное фиксировано. 3×100k шагов (по ~282 с).\n", + "\n", + "**Результат** (`python run_blockage.py`, 2026-06-09):\n", + "\n", + "| $N_y$ | β | St | St(1−β) | $\\langle C_d\\rangle$ | rms $C_l$ | $\\langle C_m\\rangle$ | $C_d$ σ·n | dCd |\n", + "|---|---|---|---|---|---|---|---|---|\n", + "| 90 | 0.178 | 0.221 | 0.181 | 1.799 | 0.7051 | −0.00003 | 1.872 | 4.1% |\n", + "| 128 | 0.125 | 0.196 | 0.171 | 1.771 | 0.6734 | −0.00007 | 1.838 | 3.8% |\n", + "| 180 | 0.089 | 0.193 | 0.176 | **1.870** | **0.8354** | +0.00043 | 1.937 | 3.6% |\n", + "\n", + "Экстраполяция $\\beta\\to0$ (интерсепт линейного / квадратичного фита, спред = неопределённость):\n", + "\n", + "| | лин. | квадр. | спред | лит. |\n", + "|---|---|---|---|---|\n", + "| $C_d(0)$ | 1.905 | 1.855 | 0.050 | 1.33 |\n", + "| rms $C_l(0)$ | 0.910 | 0.818 | 0.091 | ~0.3 |\n", + "| St(0) | 0.161 | **0.181** | 0.020 | **0.183** |\n", + "\n", + "![Серия по блокировке: Cd(β), rms Cl(β), St(β) с экстраполяцией](solver_2x_sdf/out/blockage_extrapolation.png)\n", + "\n", + "**Анализ:**\n", + "1. $C_d(\\beta)$ **немонотонен** (1.80 → 1.77 → 1.87), rms $C_l$ при самом широком канале даже\n", + " вырос — экстраполяция «$C_d(0)\\approx1.9$» физически абсурдна и означает одно: **β — не\n", + " управляющий параметр**. Поправка $(1-\\beta)^2$ из предыдущей итерации была совпадением на\n", + " одной точке ($N_y=90$).\n", + "2. Это согласуется с классической теорией продувок: поправки Аллена–Винченти\n", + " (solid + wake blockage) при $\\beta=0.178$ дают завышение лишь ~15–18%, при $\\beta=0.089$ —\n", + " ~10%. Боковое стеснение объясняло максимум половину превышения даже на исходной сетке.\n", + "3. **St — единственная величина с правильным поведением**: raw 0.221→0.196→0.193 монотонно\n", + " стремится к 0.183 сверху; квадратичная экстраполяция даёт **0.181 ≈ лит. 0.183**.\n", + " Кинематика вихреобразования (частота, эффективное Re) верна; завышены именно силовые\n", + " (давленческие) амплитуды.\n", + "4. **Улика — поведение $N_y=180$**: низкочастотная модуляция с размахом оконных $C_d$\n", + " 1.68–1.98 и rms $C_l$ 0.58–0.96 (период ~20–30k шагов; на 50k установившегося режима —\n", + " всего 2–3 цикла, статистика среднего не набрана; $\\langle C_m\\rangle$ на порядок больше,\n", + " чем на узких каналах). Чем шире канал, тем свободнее меандрирует дорожка — и тем сильнее\n", + " она бьётся о **жёсткое условие $u_y=0$ на выходе**, порождая отражения и обратную связь.\n", + "5. **Диагноз**: доминируют **продольные ограничения**, которые серия держала константой:\n", + " вход 2.5D до тела (жёсткий равномерный профиль), выход 8.3D (Zou-He давление + $u_y=0$ —\n", + " отражает вихри), стык L1→L0 на 6.25D. Их изолирует эксперимент №1.\n", + "\n", + "## 24. Эксперимент №1: факторное исследование продольных границ\n", + "\n", + "**Метод**: каждый подозреваемый фактор варьируется **отдельно** при фиксированной боковой\n", + "блокировке ($N_y=90$, $\\beta=0.178$) и 100k шагах — изоляция вкладов входа, выхода и\n", + "выходного ГУ. Реализация: `config.py` выводит x-границы патча из `cx` (патч едет за телом),\n", + "`boundary.channel_bc` получил режим `outlet_uy`:\n", + "- `\"zero\"` — классический Zou-He: $u_y=0$ жёстко (как во всех прогонах выше);\n", + "- `\"extrapolate\"` — $u_y$ нуль-градиент (берётся из столбца $x{=}-2$), якорь $\\rho=1$\n", + " сохраняется; алгебраически: $f_6 \\mathrel{+}= \\tfrac12\\rho u_y$, $f_7 \\mathrel{-}= \\tfrac12\\rho u_y$\n", + " при тех же $f_3$ и $u_x$ (балансы массы и импульса выполняются точно).\n", + "\n", + "| Фактор | Nx | cx | вход | выход | $u_y$-выход | что изолирует |\n", + "|---|---|---|---|---|---|---|\n", + "| B0_baseline | 174 | 40 | 2.5D | 8.3D | zero | контроль (+ кросс-чек с конвективным членом) |\n", + "| F1_outlet_far | 300 | 40 | 2.5D | 16.2D | zero | близость выхода |\n", + "| F2_inlet_far | 230 | 96 | 6.0D | 8.3D | zero | близость входа |\n", + "| F3_inout_far | 390 | 96 | 6.0D | 18.3D | zero | оба продольных расстояния |\n", + "| F4_outlet_uy | 174 | 40 | 2.5D | 8.3D | extrapolate | кинематическое отражение вихрей ГУ |\n", + "| F5_combo | 390 | 96 | 6.0D | 18.3D | extrapolate | «чистая» постановка |\n", + "\n", + "Метрики каждого прогона: St, $\\langle C_d\\rangle$, rms $C_l$, $\\langle C_m\\rangle$, кросс-чек\n", + "dCd (уже с конвективным членом), **std оконных средних** (мера НЧ-модуляции), $\\langle\\rho\\rangle$.\n", + "Каждый прогон фиксируется строкой в накопительном реестре `solver_2x_sdf/out/factors.csv`\n", + "(полная конфигурация + результаты + время) — документация всех изменений постановки.\n", + "\n", + "**Результаты** (`python run_factors.py`, 2026-06-10, 6×100k шагов по ~280 с):\n", + "\n", + "| Фактор | вход | выход | $u_y$-выход | St(1−β) | $\\langle C_d\\rangle$ | rms $C_l$ | dCd кросс | $\\langle\\rho\\rangle_{фин}$ | модуляция | статус |\n", + "|---|---|---|---|---|---|---|---|---|---|---|\n", + "| B0_baseline | 2.5D | 8.3D | zero | 0.181 | 1.799 | 0.705 | **1.0%** | 1.000 | 0.024 | ok |\n", + "| F1_outlet_far | 2.5D | 16.2D | zero | 0.163 | 2.838 | 6.794 | 1.6% | **1.663** | 0.225 | режим смещён |\n", + "| F2_inlet_far | 6.0D | 8.3D | zero | 0.138 | 2.229 | 6.120 | 9.7% | **1.655** | 0.306 | режим смещён (срыв на ~75k) |\n", + "| F3_inout_far | 6.0D | 18.3D | zero | 0.160 | 2.577 | 5.348 | 2.0% | **1.660** | 0.269 | режим смещён (срыв на ~20k) |\n", + "| **F4_outlet_uy** | 2.5D | 8.3D | extrapolate | **0.183** | **1.754** | **0.557** | **0.6%** | **1.0000** | **0.023** | **ok ✓** |\n", + "| F5_combo | 6.0D | 18.3D | extrapolate | — | — | — | — | NaN | — | **взрыв на 4.5k** |\n", + "\n", + "![Факторное исследование: Cd, rms Cl и НЧ-модуляция по факторам](solver_2x_sdf/out/factors_summary.png)\n", + "\n", + "**Анализ:**\n", + "1. **Конвективный член подтверждён**: кросс-чек B0 сжался с 4.1% до **1.0%** (F4 — 0.6%) при\n", + " неизменной физике. Считывание силы теперь согласовано двумя методами на уровне ~1%.\n", + "2. **F4 (мягкий $u_y$-выход) — выигрыш по всем метрикам**: rms $C_l$ 0.705→0.557 (−21%),\n", + " $\\langle C_d\\rangle$ 1.799→1.754, $\\langle\\rho\\rangle=1.0000$ (точнее базы), нулевая\n", + " НЧ-модуляция (окна 6–10: $C_d$ 1.753–1.755, идеальное плато) и **St·(1−β)=0.1828 ≈ лит.\n", + " 0.183 точно**. Жёсткое $u_y=0$ действительно кинематически отражало вихри.\n", + "3. **Главное открытие — длинные домены без демпфера невалидны.** Все три (F1/F2/F3, $u_y=0$)\n", + " уходят на смещённую ветвь $\\langle\\rho\\rangle\\approx1.66$ (F1 и F3 — за ~20k шагов, F2 —\n", + " на ~75k), где $C_d$, $C_l$ бессмысленны для сравнения (у F2 разваливается и кросс-чек:\n", + " 9.7% — поле у контура нестационарно «звенит»). Механизм: канал «вход-скорость +\n", + " выход-давление» — **недодемпфированный акустический резонатор**; затухание продольной моды\n", + " $\\propto\\nu(\\pi/N_x)^2$ падает в ~5 раз при $N_x$ 174→390. Стартовый транзиент раскачивает\n", + " моду, вход с фиксированной скоростью качает массу $\\propto\\rho_{in}$ (положительная обратная\n", + " связь) — система садится на новую ветвь равновесия потоков массы. **F5** — чистая картина\n", + " роста: $\\langle\\rho\\rangle$ по окнам осциллирует 1.04→0.93→1.05 с периодом\n", + " $\\approx 2N_x/c_s\\approx1350$ шагов (точно акустический период туда-обратно) → NaN на 4.5k.\n", + "4. При этом rms $u_y$ зонда нормальный (0.033–0.046) во **всех** прогонах — гидродинамика\n", + " дорожки жива; ломаются акустика и массовый баланс. Это ретроспективно объясняет и «загадку»\n", + " эксперимента №0: $N_y=180$ был зачатком той же моды (НЧ-модуляция), но поперечное расширение\n", + " менее опасно продольного.\n", + "\n", + "**Урок**: продольное удлинение требует **поглощающего слоя** — стандартное лекарство из\n", + "каталога ГУ (раздел 15), упоминавшееся ещё в прежней 3D-реализации.\n", + "\n", + "## 25. Эксперимент №2: губка (absorbing layer) перед выходом\n", + "\n", + "Реализация: в последних `sponge_len` столбцах L0 вязкость плавно (smoothstep) растёт до\n", + "$\\nu\\cdot$`sponge_nu_mult` (по умолчанию ×30 — локальное Re падает до ~5, вихри и акустика\n", + "диссипируют до прихода на выход). Технически $\\beta$ на L0 становится **полем** $\\beta(x)$\n", + "(KBC это допускает: $\\gamma$ и так поузловой; CUDA-граф не страдает — поле предвычислено);\n", + "патч L1 губку не видит (гарантировано assert'ом). Ручки: `AMR_SPONGE_LEN`, `AMR_SPONGE_NU`.\n", + "\n", + "| Фактор | геометрия | $u_y$-выход | губка | что проверяет |\n", + "|---|---|---|---|---|\n", + "| F6_sponge | 174×90 (база) | extrapolate | 32 | валидация губки против F4 (не портит ли короткий домен) |\n", + "| F7_long_sponge | 390×90, вход 6D / выход 18.3D | extrapolate | 32 | **целевая «чистая» постановка** |\n", + "| F8_long_sp_uy0 | 390×90 | zero | 32 | изоляция: достаточно ли губки без мягкого $u_y$ |\n", + "\n", + "> ⏳ *Числа появятся после `python run_factors.py` с факторами F6–F8 (3×100k ≈ 15 мин).*\n", + "\n", + "**Критерии**: у всех $\\langle\\rho\\rangle\\approx1.000$ и нет НЧ-модуляции; F7 — ожидание\n", + "$\\langle C_d\\rangle\\approx1.5$–1.6 (остаётся боковая блокировка β=0.178: по Аллену–Винченти\n", + "+15–18% к безграничному 1.33) и rms $C_l<0.45$. Если критерии выполнены — **эксперимент №3**:\n", + "повторная серия по β ($N_y=90/128/180$) на конфигурации F7 → финальная экстраполяция к\n", + "безграничному пределу. Остаточное расхождение после неё — фактор разрешения (D-рефайнмент)." + ] + }, + { + "cell_type": "markdown", + "id": "0afa973f", + "metadata": {}, + "source": [ + "---\n", + "# Часть VII. Перенос на D3Q27 и связь с целевой реализацией\n", + "\n", + "Вся математика KBC переносится в 3D **без изменений по сути**: решётка D3Q27 (веса\n", + "$8/27, 2/27, 1/54, 1/216$ — изотропия 4-го порядка, предпочтительна для KBC/турбулентности),\n", + "моментный базис 27×27, сдвиговая часть $s$ — девиаторный тензор (5 независимых компонент).\n", + "Формула $\\gamma$ и оператор $f\\leftarrow f-\\beta(2\\Delta s+\\gamma\\Delta h)$ идентичны.\n", + "\n", + "![Решётка D3Q27](figures/11_d3q27.png)\n", + "\n", + "Чем настоящий KBC отличается от прежнего подхода в 3D-движке (poly eq + TRT + α-лимитер +\n", + "Smagorinsky):\n", + "\n", + "| Аспект | Настоящий KBC | Прежний подход |\n", + "|---|---|---|\n", + "| Равновесие | энтропийное product-form | полиномиальное $O(u^2)$ |\n", + "| Столкновение | энтропийный MRT, $k/s/h$ | TRT (симм./антисимм.) |\n", + "| Стабилизация | $\\gamma$ из энтропии | α-лимитер положительности |\n", + "| H-теорема | встроена в вывод $\\gamma$ | контролируется отдельно |\n", + "| Турбулентность | implicit LES (параметр-free) | явный Smagorinsky |\n", + "| Решётка | D3Q27 | D3Q27 (совпадает) |\n", + "\n", + "**Дорожная карта переноса** (всё отработано на 2D-макете): (1) product-form $f^{eq}$;\n", + "(2) проекторы $P_s$ для D3Q27 (предвычислить); (3) per-node $\\gamma$; (4) столкновение;\n", + "(5) SDF+Bouzidi и GMEM-сила с $\\mathbf u_w$ на линке (подвижные тела) + кросс-чек ∮σ·n dA по\n", + "SDF-изоповерхности; (6) AMR-связка $\\tau_f=2\\tau_c-\\tfrac12$ с временно́й интерполяцией." + ] + }, + { + "cell_type": "markdown", + "id": "d0691787", + "metadata": {}, + "source": [ + "---\n", + "# Часть VIII. Сверка формул с первоисточниками\n", + "\n", + "Все формулы, ранее помеченные «⚠ сверить с оригиналом», проверены по первоисточникам\n", + "(плюс численная самопроверка каждой в `demos_gpu/checks_gpu.py`):\n", + "\n", + "| Формула | Источник | Статус |\n", + "|---|---|---|\n", + "| Product-form $f^{eq}$: $A(u)=2-\\sqrt{1+3u^2}$, $B(u)=\\frac{2u+\\sqrt{1+3u^2}}{1-u}$ | Bösch/Chikatamarla/Karlin, PRE **92**, 043309 (2015), ур. (7)–(11); Ansumali/Karlin/Öttinger, EPL **63**, 798 (2003) | ✓ дословно |\n", + "| $f' = f-\\beta(2\\Delta s+\\gamma\\Delta h)$, $\\beta=1/(2\\tau)$, mirror-форма | Karlin/Bösch/Chikatamarla, PRE **90**, 031302(R) (2014) | ✓ дословно |\n", + "| $\\gamma^\\*=\\frac1\\beta-(2-\\frac1\\beta)\\frac{\\langle\\Delta s|\\Delta h\\rangle}{\\langle\\Delta h|\\Delta h\\rangle}$, $\\langle X|Y\\rangle=\\sum X_iY_i/f_i^{eq}$ | там же; PRE **92**, ур. (24)–(25) | ✓ дословно |\n", + "| Состав $s=\\{N,\\Pi_{xy}\\}$ (девиатор; «KBC-d»/N1) | PRE **92** (семейство $s\\in\\{d,d{+}t,d{+}q,d{+}t{+}q\\}$); Dorschner et al., JFM **801**, 623 (2016) | ✓ |\n", + "| AMR: $\\beta_f=\\frac{1}{1+r(1/\\beta_c-1)}$ ⇔ $\\tau_f=2\\tau_c-\\frac12$; $f^{neq}\\cdot\\frac{\\beta_c}{r\\beta_f}=\\frac{\\tau_f}{2\\tau_c}f^{neq}$ | Dorschner/Frapolli/Chikatamarla/Karlin, PRE **94**, 053311 (2016), ур. (34), (40) | ✓ дословно |\n", + "| Временна́я интерполяция ghost-границы | Lagrava/Malaspinas/Latt/Chopard, JCP **231**, 4808 (2012) | ✓ |\n", + "| Bouzidi: ветви $q<\\frac12$ / $q\\ge\\frac12$ | Bouzidi/Firdaouss/Lallemand, Phys. Fluids **13**, 3452 (2001) | ✓ |\n", + "| Zou-He: скоростной вход / давление-выход | Zou & He, Phys. Fluids **9**, 1591 (1997) | ✓ |\n", + "| GMEM: $(\\mathbf c_i-\\mathbf u_w)f_i^{post}-(\\mathbf c_{\\bar i}-\\mathbf u_w)f_{\\bar i}^{stream}$ | Wen/Zhang/Tu/Wang/Fang, JCP **266**, 161 (2014) | ✓ |\n", + "| $\\sigma^v=-(1-\\frac{1}{2\\tau})\\Pi^{neq}$ (Чепмен–Энског) | стандарт (Krüger et al., *The Lattice Boltzmann Method*, 2017) | ✓ |\n", + "\n", + "**Литература:**\n", + "- I. V. Karlin, F. Bösch, S. S. Chikatamarla, *Gibbs' principle for the lattice-kinetic theory\n", + " of fluid dynamics*, Phys. Rev. E **90**, 031302(R) (2014).\n", + "- F. Bösch, S. S. Chikatamarla, I. V. Karlin, *Entropic multirelaxation lattice Boltzmann\n", + " models for turbulent flows*, Phys. Rev. E **92**, 043309 (2015) (arXiv:1507.02518).\n", + "- S. Ansumali, I. V. Karlin, H. C. Öttinger, *Minimal entropic kinetic models for\n", + " hydrodynamics*, Europhys. Lett. **63**, 798 (2003).\n", + "- B. Dorschner, F. Bösch, S. S. Chikatamarla, K. Boulouchos, I. V. Karlin, *Entropic\n", + " multi-relaxation time lattice Boltzmann model for complex flows*, J. Fluid Mech. **801**,\n", + " 623–651 (2016).\n", + "- B. Dorschner, N. Frapolli, S. S. Chikatamarla, I. V. Karlin, *Grid refinement for entropic\n", + " lattice Boltzmann models*, Phys. Rev. E **94**, 053311 (2016) (arXiv:1608.06915).\n", + "- D. Lagrava, O. Malaspinas, J. Latt, B. Chopard, *Advances in multi-domain lattice Boltzmann\n", + " grid refinement*, J. Comput. Phys. **231**, 4808 (2012).\n", + "- M. Bouzidi, M. Firdaouss, P. Lallemand, *Momentum transfer of a Boltzmann-lattice fluid with\n", + " boundaries*, Phys. Fluids **13**, 3452 (2001).\n", + "- Q. Zou, X. He, *On pressure and velocity boundary conditions for the lattice Boltzmann BGK\n", + " model*, Phys. Fluids **9**, 1591 (1997).\n", + "- B. Wen, C. Zhang, Y. Tu, C. Wang, H. Fang, *Galilean invariant fluid–solid interfacial\n", + " dynamics in lattice Boltzmann simulations*, J. Comput. Phys. **266**, 161 (2014).\n", + "- Z. Guo, C. Zheng, B. Shi, *Discrete lattice effects on the forcing term in the lattice\n", + " Boltzmann method*, Phys. Rev. E **65**, 046308 (2002).\n", + "- U. Ghia, K. N. Ghia, C. T. Shin, *High-Re solutions for incompressible flow using the\n", + " Navier-Stokes equations and a multigrid method*, J. Comput. Phys. **48**, 387 (1982)." + ] + }, + { + "cell_type": "markdown", + "id": "a8cc8c0d", + "metadata": {}, + "source": [ + "---\n", + "# Часть IX. Итоги\n", + "\n", + "- **KBC** = энтропийный MRT-LBM: сохраняющиеся моды не трогаем, сдвиг релаксируем фиксированным\n", + " $2\\beta$ (вязкость), высшие моды — адаптивным $\\gamma$ из условия неувеличения энтропии.\n", + " При $\\gamma=2$ — в точности BGK. Все формулы сверены с первоисточниками и самопроверены\n", + " численно.\n", + "- **Бенчмарки** (на компонентах финальной модели): вязкость по TGV (<6%, факт ≲1%), H-теорема,\n", + " устойчивость на сдвиговом слое (BGK разрушается — KBC держит), каверна ≈ Ghia, дорожки\n", + " Кармана на четырёх телах.\n", + "- **Измельчение сетки**: связка $\\tau_f=2\\tau_c-\\tfrac12$ + масштабирование $f^{neq}$ +\n", + " временна́я интерполяция ghost; вложенный 2×+4× даёт точность мелкой сетки за в разы меньшую\n", + " работу.\n", + "- **Финальная модель** `solver_2x_sdf`: KBC-N1 + SDF/Bouzidi + Zou-He + free-slip + CUDA-графы.\n", + " Главные уроки эволюции: второй член силы — из post-streaming; дрейф массы лечится\n", + " давлением-выходом; зонд и сила — на тонком уровне; графы требуют чистоты горячего пути.\n", + "- **Считывание сил ДОКАЗАНО корректным** (разделы 22, 24): два независимых метода — GMEM с\n", + " торком и баланс импульса ∮[σ·n−ρu(u·n)]ds — после добавления конвективного члена согласуются\n", + " на уровне **0.6–1.0%** по $\\langle C_d\\rangle$; $\\langle C_m\\rangle\\approx0$; масса стабильна.\n", + "- **Исследование факторов постановки** (разделы 23–25):\n", + " - эксперимент №0 (серия по β) **опроверг** гипотезу бокового стеснения: $C_d(\\beta)$\n", + " немонотонен; при этом **St(β→0)=0.181 ≈ лит. 0.183** — кинематика верна;\n", + " - эксперимент №1 (6 факторов): **мягкий $u_y$-выход (F4) улучшил всё** (rms $C_l$ −21%,\n", + " St·(1−β)=0.183 точно, идеальное плато) — жёсткое $u_y=0$ отражало вихри. **Длинные домены\n", + " без демпфера невалидны**: пара «вход-скорость / выход-давление» — недодемпфированный\n", + " акустический резонатор (затухание ∝ν(π/Nx)²); масса накачивается до смещённой ветви\n", + " ⟨ρ⟩≈1.66 либо взрыв (F5, период осцилляций ⟨ρ⟩ ≈ 2Nx/c_s — прямая улика);\n", + " - эксперимент №2 (в работе): **губка перед выходом** (β(x)-поле на L0) — F6/F7/F8; затем\n", + " эксперимент №3 — серия по β на чистой постановке F7 → финальная экстраполяция.\n", + "- **Реестр всех прогонов** — `solver_2x_sdf/out/factors.csv`: полная конфигурация + метрики\n", + " каждого изменения постановки (готовый материал для отдельного исследования факторов).\n", + "- **Дальше**: эксперименты №2–3 → финальные числа; при остаточном превышении — фактор\n", + " разрешения (D-рефайнмент). Затем перенос отработанной схемы на D3Q27/GPU в основной движок\n", + " (часть VII)." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "name": "python", + "version": "3" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/docs/theory/solver_2x_sdf/README.md b/docs/theory/solver_2x_sdf/README.md new file mode 100644 index 0000000..43c341f --- /dev/null +++ b/docs/theory/solver_2x_sdf/README.md @@ -0,0 +1,160 @@ +# solver_2x_sdf — модель цилиндра 2×+SDF, разложенная по компонентам + +Самодостаточный LBM-решатель (D2Q9, KBC) для обтекания цилиндра: грубый уровень **L0** +плюс один вложенный патч **L1** (измельчение ×2). Граница цилиндра — **SDF + Bouzidi (no-slip)**; +вход/выход — **Zou-He** (скорость/давление); верх/низ канала — **free-slip (specular)**. +Только GPU/CuPy — **CPU-фолбэка нет**. Запуск — из этой папки: `python run.py` +(серия по блокировке: `python run_blockage.py`). + +## Карта файлов (каждый компонент изолирован и легко меняется) + +| Файл | Ответственность | +|---|---| +| `backend.py` | жёсткое требование CuPy/GPU, `DTYPE`, device-скаляры, `to_cpu` | +| `config.py` | все параметры модели + производные (τ, β, R, DL, cy/патч из Ny); `from_env()` | +| `lattice.py` | D2Q9 (c_i, w_i, OPP) + KBC-проектор `Ps` на сдвиг-моменты | +| `equilibrium.py` | `feq` (product-form, без `pow`), `macros` (ρ, u) | +| `collision.py` | **столкновение**: `kbc_collide` (энтропийный KBC-N1) — единственный оператор | +| `streaming.py` | **перенос**: `stream` (пул-схема через roll) | +| `geometry.py` | маски тела/стенок и SDF для L0 и L1 | +| `boundary.py` | `build_bc`/`apply_bc` (SDF+Bouzidi) + `channel_bc` (Zou-He) + `free_slip_walls` | +| `forces.py` | **силы**: галилей-инвариантный обмен импульсом `force_gmem` (Fx, Fy, **торк Tz**) + `coefficients` (Cd, Cl, **Cm**) | +| `forces_stress.py` | **кросс-чек силы**: ∮σ·n ds по контуру R+δ вокруг тела (независимый эстиматор) | +| `amr.py` | связка L0↔L1: `patch`/`ghost`/`fill`/`restrict` | +| `solver.py` | оркестратор: persistent-буферы, `step()`, `run()` (+ CUDA-граф) | +| `diagnostics.py` | `analyze`, St (параболическая интерполяция пика), кросс-чек, фиты серии по β | +| `visualization.py` | гифка |ω|, png-панель рядов (`series_2x_sdf.png`), прогресс-бар | +| `run.py` | точка входа (один прогон) | +| `run_blockage.py` | серия по блокировке Ny↑ → β↓, экстраполяция β→0, сводный npz+png | +| `run_factors.py` | факторное исследование постановки (вход/выход/uy-выход); реестр `out/factors.csv` | + +## Где какая математика (для ревизии) + +- **Столкновение** — `collision.py`. KBC-N1: `f ← f − β(2Δs + γΔh)`, где `Δs = Ps·(f−feq)` — + проекция на сдвиг-моменты, `γ` — энтропийный лимитер. Чтобы поэкспериментировать: + переключить `cfg.collision="bgk"`, либо добавить TRT новой функцией и зарегистрировать в `get`. +- **Перенос** — `streaming.py`. Чистая пул-схема; на физику влияет только корректность сдвигов. +- **Силы** — `forces.py`. Обмен импульсом по линкам тела: + `F = Σ_links c_i (f_i^{после столкн.} + f_ī^{после стриминга})`. Второй член — из поля ПОСЛЕ + стриминга (вернувшаяся Bouzidi-популяция); иначе ведущий симметричный член сокращается и Cd врёт. + Сила/момент меряются на **каждом** подшаге L1 и усредняются (анти-алиасинг; средний Cd не меняется). + **Торк** `Tz` — вокруг центра тела, точка приложения — пересечение линка со стенкой `r_f + q·c_i` + (Bouzidi-доля q уже лежит в BC); `Cm = 2Tz/(U²·DL²)`, для цилиндра ⟨Cm⟩≈0 — контроль симметрии. +- **Кросс-чек силы** — `forces_stress.py`. Независимый эстиматор — баланс импульса + контрольного объёма: `F = ∮[σ·n − ρu(u·n)] ds` по окружности R+δ (δ=2 тонкие ячейки); + `σ = −p′·I − (1−1/(2τ₁))·Π^neq_dev` (строго девиаторная проекция: след Π^neq в KBC + релаксирует с γβ, а не 1/τ). Конвективный член −ρu(u·n) обязателен при δ>0 — без него + систематика +4% по ⟨Cd⟩. Считается раз в `stress_every` шагов **вне CUDA-графа**; сравнение + по средним (⟨Cd⟩, rms Cl) — мгновенные ряды сдвинуты по фазе кольцом R..R+δ. + Согласие двух методов = считывание силы корректно. +- **Серия по блокировке** — `run_blockage.py`. D фиксирован, Ny ∈ {90,128,180} → β ∈ {0.178, + 0.125, 0.089}; `cy` и y-границы патча выводятся из Ny автоматически (`config.__post_init__`). + Экстраполяция к β→0 двумя фитами (a+b·β и a+b·β²; спред интерсептов — неопределённость) — + прямое сравнение с безграничной литературой без ручной поправки (1−β)². + +## ⚠ Сверка с первоисточниками (2026-08-14): найден дефект, все числа ниже требуют перепрогона + +Сверка реализации со статьями в `docs/origins` (Karlin/Bösch/Chikatamarla, PRE **90**, 031302(R) +2014 — принцип; Bösch/Chikatamarla/Karlin, PRE **92**, 043309 2015 — алгоритм; arXiv:1507.02509 — +2D-реализация). **Ядро KBC-N1 подтверждено точным**: проектор `Ps` совпадает с аналитической +s-частью из ур.(10) 2D-статьи (ранг 2, идемпотентен, несёт ровно {N, Π_xy}); равновесие — +точный энтропийный максимизатор (сходится с численной максимизацией S при фикс. ρ, ρu); +γ по замкнутой формуле ур.(17)/(39) совпадает с корнем точного ур.(15); сдвиг-моменты +релаксируют ровно с 2β при любом γ; вязкость по затуханию сдвиговой волны воспроизводится +с ошибкой <0.1%. + +**Дефект — порог `GEPS` в `kbc_collide`.** Он был АБСОЛЮТНЫМ (1e-6 в float32, режим по умолчанию), +тогда как `den = ⟨Δh|Δh⟩` квадратична по неравновесию и при разрешённой физике равна ~1e-7…1e-9. +Замерено на боевой конфигурации: откат `γ←2` срабатывал на **77–99% узлов**, то есть решатель +считал **чистый LBGK**, а не KBC. На эталоне 2D-статьи (двойной периодический сдвиговый слой, +Re=30000, N=128, разд. VII) это давало **+9.3%** по энстрофии на t=t_c (0.6599 против эталонных +0.6035); после исправления fp32 даёт 0.6038. Порог сделан относительным (`B.GREL`, доля от ‖Δ‖²); +на тех же полях он теперь не срабатывает нигде (min den/‖Δ‖² ≈ 1.5e-3 против порога 1e-8). + +**Следствие: все количественные результаты ниже (Cd, rms Cl, St, серия по блокировке, +факторное исследование №0/№1) получены на дефектной ветке и подлежат перепрогону.** +Качественные выводы про ГУ (мода акустического резонатора, роль конвективного члена +в кросс-чеке) дефектом не затрагиваются. + +Исправлено там же: +- **углы домена**: `stream()` на `roll` периодичен по обеим осям, а Zou-He стоял на срезе `1:-1` — + в 4 угловых узлах вход был напрямую связан с выходом (`f[1,0,0] == post[1,0,-1]`, величина ~0.12). + Порядок изменён на `free_slip_walls` → `channel_bc` по всему столбцу; заворот закрыт полностью. +- **диагностика ⟨ρ⟩** считалась по всему домену, включая фиктивные узлы внутри цилиндра + (смещение −5.4e-4 — ровно тот разряд, в котором ⟨ρ⟩ и цитируется). Теперь только по жидкости. +- **`refine` был зашит как 2** в `tau1`, `R01` и радиусе тела на L1/контуре σ·n. Обобщено + (при r=2 значения бит-в-бит прежние; при r=3 вязкость уровней теперь согласована). + +**Отдельно — не дефект, а следствие выбора модели.** В KBC-N1 след тензора напряжений T отнесён +к h-части, поэтому объёмная вязкость плавает: ξ = c_s²(1/(γβ) − ½) (ур.36 статьи 2015, ур.57 +2D-статьи). Замер на боевой конфигурации: γ ∈ [−4.1, 4.6], медиана ξ/ν ≈ 17, и на **2.1% узлов +ξ < 0** — акустическое АНТИдемпфирование. Это прямо релевантно диагнозу «недодемпфированный +акустический резонатор» ниже: KBC-N2 (T в s-части) даёт ξ = ν фиксированно и является +каноническим средством именно от этой проблемы. Модель не менялась — решение за автором. + +## Статус: считывание силы валидировано; идёт факторное исследование постановки + +Оператор столкновения зафиксирован — **KBC-N1 с энтропийным стабилизатором** (канонический +Karlin/Bösch/Chikatamarla 2014), без замен (никаких BGK/TRT). +**Полная документация исследования — в ноутбуке `../kbc_lbm.ipynb` (части VI, разделы 22–24).** + +**Считывание силы доказано корректным** (прогон 100k, 174×90, 2026-06-09): +- кросс-чек GMEM vs ∮σ·n: dCd=4.1% (систематика объяснена конвективным членом −ρu(u·n), + добавлен в `forces_stress.py` — ожидаемое расхождение ≲1%); +- ⟨Cm⟩=−0.00003 (≈0 — симметрия), ⟨ρ⟩=1.001 стабильна, Cd=1.799 воспроизводит прежнюю + итерацию бит-в-бит (осреднение по подшагам не сместило среднее). + +**Эксперимент №0 (серия по блокировке) — гипотеза бокового стеснения ОПРОВЕРГНУТА:** +Cd(β) немонотонен: 1.799 / 1.771 / **1.870** при Ny=90/128/180; rms Cl на широком канале +вырос (0.835), НЧ-модуляция (окна Cd 1.68–1.98). При этом **St(β→0)=0.181 ≈ лит. 0.183** — +кинематика верна, завышены давленческие амплитуды. Диагноз: продольные границы +(вход 2.5D с жёстким профилем; выход 8.3D Zou-He с жёстким uy=0 — отражает вихри). + +**Эксперимент №1 (прогнан 2026-06-10) — факторное исследование** `run_factors.py`, 6 прогонов +при Ny=90 фикс. Итоги (полный разбор — ноутбук, раздел 24; реестр — `out/factors.csv`): +- конвективный член подтверждён: кросс-чек B0 4.1%→**1.0%**, F4 — **0.6%**; +- **F4 (мягкий uy-выход) — лучший по всем метрикам**: Cd 1.799→1.754, rms Cl 0.705→**0.557**, + St·(1−β)=**0.183** (точно лит.), ⟨ρ⟩=1.0000, нулевая НЧ-модуляция; +- **длинные домены без демпфера НЕвалидны** (F1/F2/F3 → смещённый режим ⟨ρ⟩≈1.66; F5 → NaN): + пара «вход-скорость / выход-давление» — недодемпфированный акустический резонатор + (затухание моды ∝ν(π/Nx)²; период осцилляций ⟨ρ⟩ у F5 ≈ 2Nx/c_s — прямая улика). + +**Эксперимент №2 (в работе) — губка перед выходом**: плавный рост ν (×30, smoothstep) в +последних `sponge_len` столбцах L0; β(x) — поле (graph-safe), патч L1 губки не видит. +Факторы: F6_sponge (база+uy-extrap+губка 32 — валидация против F4), F7_long_sponge +(390×90, вход 6D/выход 18.3D — целевая постановка), F8_long_sp_uy0 (изоляция вклада губки). +Критерии: ⟨ρ⟩≈1.000 у всех; F7: Cd≈1.5–1.6, rms Cl<0.45. Затем эксперимент №3 — серия по β +на конфигурации F7. + +| прогон | команда | артефакты в `out/` | +|---|---|---| +| смоук | `AMR_STEPS=2000 python run.py` | graph self-check OK, Cm≈0, кросс-чек ≲1% (с конв. членом) | +| основной | `python run.py` | `cyl_2x_sdf.gif`, `series_2x_sdf.png`, `probe_2x_sdf.npz` | +| серия по β | `python run_blockage.py` | `probe_blockage_Ny*.npz`, `blockage_summary.npz`, `blockage_extrapolation.png` | +| **факторы №2** | `AMR_FACTORS=F6_sponge,F7_long_sponge,F8_long_sp_uy0 python run_factors.py` | `factor_*.npz`, **`factors.csv`** (реестр; при смене схемы старый → `factors_vN.csv`), `factors_summary.png` | + +Env-ручки: `AMR_NX`, `AMR_CX` (продольная геометрия; x-границы патча L1 выводятся из cx), +`AMR_OUTLET_UY=zero|extrapolate`, `AMR_SPONGE_LEN`/`AMR_SPONGE_NU` (губка), +`AMR_FACTORS=...` (подмножество факторов). + +**Что привело сюда (хронология фиксов):** +1. Зонд скорости → L1; оценка St с параболической интерполяцией пика. +2. Сила → галилей-инвариантный `force_gmem` (Wen 2014), готов к подвижным телам. +3. Стартовое возмущение (поперечный sin-импульс входа) — запуск дорожки за единицы циклов. +4. Диагностика по окнам (`convergence_report`, трекинг ⟨ρ⟩) — вскрыла дрейф массы. +5. **Ключевой фикс:** грубое ГУ выхода (zero-gradient) копило массу → поток глох (Cd/rms→0 за 100k). + Заменено на **Zou-He скоростной вход + давление-выход** (`boundary.channel_bc`) — масса заякорена. +6. **Free-slip стенки** (`boundary.free_slip_walls`, specular) + умеренно расширенный домен (меньше + блокировка). Цилиндр остаётся no-slip. +7. Cm + осреднение по подшагам + кросс-чек ∮σ·n ds + серия по блокировке (текущая итерация). + +**Прямой raw-матч на одной сетке непрактичен** (нужен `β<0.03 → Ny≈500+`); серия из трёх умеренных +Ny с экстраполяцией даёт безпоправочное сравнение за ~3 стоимости одного прогона (патч L1 — +основная работа — от Ny не зависит). + +## CUDA Graphs + +По умолчанию ВКЛ (`cfg.use_cuda_graph`, env `AMR_CUDAGRAPH=0` — выкл). **Захватываются успешно** (после +замены `cupy.stack`→`backend.pack`, отказа от cuBLAS в проекторе KBC и clip-литералов в ядре — +всё это убрало host→device при capture). На шаге t=1 — рантайм-самопроверка (граф vs eager); при +расхождении/сбое — откат на eager с печатью трейсбэка. diff --git a/docs/theory/solver_2x_sdf/amr.py b/docs/theory/solver_2x_sdf/amr.py new file mode 100644 index 0000000..a590e87 --- /dev/null +++ b/docs/theory/solver_2x_sdf/amr.py @@ -0,0 +1,54 @@ +# AMR-связка L0 (грубый) ↔ L1 (тонкий, измельчение r). +# +# Идея: на тонком патче считаем r подшагов по времени на каждый шаг L0. Границы патча («ghost») +# заполняем интерполяцией с грубого уровня (по пространству + по времени между «до» и «после» шага L0), +# а внутренность патча после подшагов проецируем обратно на грубый уровень (рестрикция). +# Неравновесная часть масштабируется множителями Rcf (грубый→тонкий) и Rfc (тонкий→грубый), +# т.к. при смене τ масштаб неравновесия меняется. +import backend as B +import lattice as L +from equilibrium import feq, macros + +cp = B.cp; xp = B.xp; DTYPE = B.DTYPE + +def patch(pNx, pNy, ax, bx, ay, by, r): + """Описание патча: размеры (Nfy,Nfx), индексы/веса билинейной интерполяции с грубого уровня, + срезы для рестрикции каждого r-го узла.""" + Wx, Wy = bx - ax, by - ay + Nfx, Nfy = r*Wx + 1, r*Wy + 1 + FX, FY = cp.meshgrid(ax + cp.arange(Nfx)/r, ay + cp.arange(Nfy)/r) # координаты тонких узлов в L0 + x0 = cp.floor(FX).astype(cp.int64); y0 = cp.floor(FY).astype(cp.int64) + x1 = cp.minimum(x0 + 1, pNx - 1); y1 = cp.minimum(y0 + 1, pNy - 1) + return dict(Nfx=int(Nfx), Nfy=int(Nfy), ax=ax, bx=bx, ay=ay, by=by, r=r, + x0=x0, y0=y0, x1=x1, y1=y1, + tx=(FX - x0).astype(DTYPE), ty=(FY - y0).astype(DTYPE), + slx=slice(r, r*Wx, r), sly=slice(r, r*Wy, r)) + +def pint(fld, P): + """Билинейная интерполяция поля fld (грубого) в узлы тонкого патча.""" + return (fld[..., P["y0"], P["x0"]]*(1 - P["tx"])*(1 - P["ty"]) + + fld[..., P["y0"], P["x1"]]*P["tx"]*(1 - P["ty"]) + + fld[..., P["y1"], P["x0"]]*(1 - P["tx"])*P["ty"] + + fld[..., P["y1"], P["x1"]]*P["tx"]*P["ty"]) + +def ghost(pf, P, Rcf): + """Граничные значения тонкого уровня из грубого поля pf: равновесие по интерполированным ρ,u + плюс масштабированная неравновесная часть Rcf·neq. + u в feq передаём кортежем (без cupy.stack) — H2D ломает CUDA-graph capture.""" + r, u = macros(pf); neq = pf - feq(r, u) + return feq(pint(r, P), (pint(u[0], P), pint(u[1], P))) + Rcf*pint(neq, P) + +def fill(cf, gh): + """Записать ghost-значения gh в рамку (1 ряд) тонкого поля cf.""" + cf[:, 0, :] = gh[:, 0, :]; cf[:, -1, :] = gh[:, -1, :] + cf[:, :, 0] = gh[:, :, 0]; cf[:, :, -1] = gh[:, :, -1] + return cf + +def restrict(cf, pf, P, Rfc, fluid): + """Спроецировать тонкое поле cf обратно на грубое pf (каждый r-й узел), масштабируя neq на Rfc. + Меняется только внутренняя жидкая часть перекрытия (маска fluid).""" + r, u = macros(cf); neq = cf - feq(r, u); slx, sly = P["slx"], P["sly"] + nv = feq(r[sly, slx], u[:, sly, slx]) + Rfc*neq[:, sly, slx] + cur = pf[:, P["ay"]+1:P["by"], P["ax"]+1:P["bx"]] + pf[:, P["ay"]+1:P["by"], P["ax"]+1:P["bx"]] = xp.where(fluid[None], nv, cur) + return pf diff --git a/docs/theory/solver_2x_sdf/backend.py b/docs/theory/solver_2x_sdf/backend.py new file mode 100644 index 0000000..8cac666 --- /dev/null +++ b/docs/theory/solver_2x_sdf/backend.py @@ -0,0 +1,40 @@ +# Бэкенд: ТОЛЬКО GPU/CuPy. CPU-фолбэка нет (по требованию). Если CuPy/GPU недоступны — жёсткая ошибка. +# Здесь же — общие device-константы (DTYPE, скаляры 0/1/2) и помощник переноса на host для вывода. +import os +import cupy as cp + +try: + _probe = (cp.zeros(2) + 1).sum(); cp.cuda.Device().synchronize() # реальная операция на device +except Exception as e: + raise RuntimeError("solver_2x_sdf требует рабочую GPU + CuPy (CPU-фолбэк удалён намеренно).") from e + +xp = cp # единый алиас вычислительного бэкенда +DTYPE = cp.float64 if os.environ.get("AMR_FP64") else cp.float32 +# Порог вырожденности знаменателя γ. ОТНОСИТЕЛЬНЫЙ (доля от ‖Δ‖² = ⟨Δ|Δ⟩), а НЕ абсолютный. +# Почему: den = ⟨Δh|Δh⟩ — квадратичная по неравновесию величина, у развитого следа она +# ~1e-7…1e-9 при вполне разрешённой физике. Прежний абсолютный порог 1e-6 (fp32) срабатывал +# на 77–99% узлов и молча подменял γ на 2, т.е. гнал ЧИСТЫЙ LBGK вместо KBC (замерено: +# энстрофия сдвигового слоя Re=3e4 уходила на +9%). den — сумма НЕотрицательных слагаемых, +# её относительная точность ~eps типа, поэтому дробный порог одинаков для fp32/fp64. +# 1e-8 на шесть порядков ниже наблюдаемого минимума den/‖Δ‖² (~5e-4) — срабатывает только на +# истинном вырождении (Δh ≡ 0), где γ всё равно ни на что не влияет, т.к. умножается на Δh. +GREL = 1e-8 +BACKEND = f"CuPy/GPU dtype={'float64' if DTYPE == cp.float64 else 'float32'}" + +# device-скаляры — не создаём host→device на горячем пути (важно для CUDA-graph capture) +ZERO = cp.zeros((), DTYPE) +ONE = cp.asarray(1.0, DTYPE) +TWO = cp.asarray(2.0, DTYPE) + +def to_cpu(a): + """Перенос на host (numpy) — только для диагностики/визуализации, не в солвере.""" + return cp.asnumpy(a) + +def pack(comps): + """Собрать кортеж одинаковых по форме массивов в один (len,*shape) БЕЗ cupy.stack. + cupy.stack/concatenate грузит на device host-массив указателей (H2D) → запрещено при CUDA-graph + capture. Здесь: преаллокация + присваивание срезов — только device→device.""" + out = xp.empty((len(comps),) + comps[0].shape, dtype=comps[0].dtype) + for i, c in enumerate(comps): + out[i] = c + return out diff --git a/docs/theory/solver_2x_sdf/boundary.py b/docs/theory/solver_2x_sdf/boundary.py new file mode 100644 index 0000000..5bfe052 --- /dev/null +++ b/docs/theory/solver_2x_sdf/boundary.py @@ -0,0 +1,104 @@ +# Граничные условия: (1) тело/стенки — SDF + интерполированный отскок Bouzidi; (2) вход/выход канала. +# +# Bouzidi (линейный): для линка из жидкого узла x_f в твёрдый по направлению i вводится +# доля пересечения q = |x_f→стенка| / |x_f→x_solid| ∈ (0,1): +# q < 1/2 (есть «дальний» жидкий сосед x_f − c_i): f_ī = 2q·f_i^post + (1−2q)·f_i^post(дальний) +# q ≥ 1/2: f_ī = (1/2q)·f_i^post + (1−1/2q)·f_ī^post +# Здесь f_i^post — после столкновения, f_ī — то, что вернётся в x_f после переноса. +import backend as B +import lattice as L + +cp = B.cp; xp = B.xp; DTYPE = B.DTYPE +Q = L.Q; Cx = L.Cx; Cy = L.Cy; OPP = L.OPP + +def build_bc(solid, phi, body): + """Сборка структуры ГУ (один раз). Для каждого направления i (1..8): + mask — жидкий узел, чей сосед по +c_i твёрдый; + q — доля пересечения по SDF (клип [0.02,0.98]); + xff — есть ли «дальний» жидкий сосед (для линейной формулы при q<1/2); + cl — подмаска линков именно ТЕЛА body (для расчёта силы).""" + fluid = ~solid; bc = [] + for i in range(1, Q): + nb_solid = cp.roll(solid, (-Cy[i], -Cx[i]), (0, 1)); mask = fluid & nb_solid + cl = mask & cp.roll(body, (-Cy[i], -Cx[i]), (0, 1)) + phinb = cp.roll(phi, (-Cy[i], -Cx[i]), (0, 1)) + qq = phi / (phi - phinb) # деление; nan/inf маскируются ниже + q = xp.where(mask, cp.clip(qq, 0.02, 0.98), cp.asarray(0.5, DTYPE)) + xff = mask & (~cp.roll(solid, (Cy[i], Cx[i]), (0, 1))) + bc.append((i, OPP[i], mask, q.astype(DTYPE), xff, cl)) + return bc + +def apply_bc(f, fpost, bc): + """Применить Bouzidi ко всем линкам (полностью через where, GPU-friendly). + f — поле ПОСЛЕ стриминга (его и правим); fpost — поле ПОСЛЕ столкновения (до стриминга).""" + for (i, ib, mask, q, xff, cl) in bc: + fi = fpost[i]; fib = fpost[ib] + fiback = cp.roll(fpost[i], (Cy[i], Cx[i]), (0, 1)) # популяция «дальнего» соседа + near = mask & (q < 0.5) & xff + bad = mask & (q < 0.5) & (~xff) # нет дальнего соседа → простой отскок + far = mask & (q >= 0.5) + new = f[ib] + new = xp.where(near, 2*q*fi + (1 - 2*q)*fiback, new) + new = xp.where(far, (1/(2*q))*fi + (1 - 1/(2*q))*fib, new) + new = xp.where(bad, fi, new) + f[ib] = new + return f + +def channel_bc(f, uin, rho_out=1.0, outlet_uy="zero"): + """Корректные ГУ канала (Zou & He 1997), нумерация D2Q9: 1=E,2=N,3=W,4=S,5=NE,6=NW,7=SW,8=SE. + ВХОД (запад, x=0): скоростной Zou-He — задаём u=(ux,uy) из uin, плотность ρ ПЛАВАЕТ; достраиваем + приходящие извне популяции 1,5,8 из известных 0,2,3,4,6,7. + ВЫХОД (восток, x=-1): давление Zou-He — задаём ρ=rho_out, скорость ux плавает; достраиваем 3,6,7. + Поперечная скорость на выходе — по outlet_uy: + "zero" — классический Zou-He: uy=0 (жёстко). Вихри дорожки приходят на выход с + uy~±0.3U → принудительное зануление отражает их назад к телу (завышает + rms Cl и модулирует Cd — см. факторное исследование в ноутбуке); + "extrapolate" — uy берётся из соседнего столбца x=-2 (нуль-градиент поперечной скорости); + ρ-якорь (масса) сохраняется, кинематическое отражение снимается. + Зачем давление-выход вообще: грубый zero-gradient по f не выпускал поток → масса/противодавление + копились, поток глох (⟨ρ⟩↑, Cd/rmsCl→0). Давление-выход якорит массу, скоростной вход её не + пересоздаёт → дрейфа нет. Всё на срезах (graph-safe, без host→device). + + ПОРЯДОК ВЫЗОВА: строго ПОСЛЕ free_slip_walls и покрывая ВЕСЬ столбец (включая ряды 0 и Ny−1). + Причина: stream() сделан через roll и потому периодичен по ОБЕИМ осям. Заворот по y снимают + стенки, заворот по x — этот ГУ. Если оставить углы (ряды 0 и Ny−1) без Zou-He, в них популяции + с cx=+1 на входе приходят прямо из столбца выхода (замерено: f[1,0,0] == post[1,0,-1], величина + ~0.12) — вход и выход оказываются физически связаны в 4 узлах. Известные популяции, по которым + здесь считаются ρ (вход) и ux (выход), x-заворота не содержат ни в одном ряду, а те, что + заворот содержат, — это ровно неизвестные, которые ГУ и перезаписывает; поэтому такой порядок + закрывает углы полностью.""" + # --- вход (запад): скоростной Zou-He --- + ux = uin[0, :, 0]; uy = uin[1, :, 0] + f0 = f[0, :, 0]; f2 = f[2, :, 0]; f3 = f[3, :, 0] + f4 = f[4, :, 0]; f6 = f[6, :, 0]; f7 = f[7, :, 0] + rho = (f0 + f2 + f4 + 2.0*(f3 + f6 + f7)) / (1.0 - ux) + f[1, :, 0] = f3 + (2.0/3.0)*rho*ux + f[5, :, 0] = f7 - 0.5*(f2 - f4) + (1.0/6.0)*rho*ux + 0.5*rho*uy + f[8, :, 0] = f6 + 0.5*(f2 - f4) + (1.0/6.0)*rho*ux - 0.5*rho*uy + # --- выход (восток): давление Zou-He --- + g0 = f[0, :, -1]; g1 = f[1, :, -1]; g2 = f[2, :, -1] + g4 = f[4, :, -1]; g5 = f[5, :, -1]; g8 = f[8, :, -1] + uxo = (g0 + g2 + g4 + 2.0*(g1 + g5 + g8)) / rho_out - 1.0 + if outlet_uy == "extrapolate": + # нуль-градиент поперечной скорости: uy с предвыходного столбца (он полностью известен) + col = f[:, :, -2] + uyo = ((col[2] + col[5] + col[6]) - (col[4] + col[7] + col[8])) / col.sum(0) + else: + uyo = 0.0 + f[3, :, -1] = g1 - (2.0/3.0)*rho_out*uxo + f[6, :, -1] = g8 - 0.5*(g2 - g4) - (1.0/6.0)*rho_out*uxo + 0.5*rho_out*uyo + f[7, :, -1] = g5 + 0.5*(g2 - g4) - (1.0/6.0)*rho_out*uxo - 0.5*rho_out*uyo + return f + +def free_slip_walls(f): + """FREE-SLIP (скользящие) стенки канала: верх/низ — зеркальное (specular) отражение. + Сохраняет касательный (x) импульс (нет трения, нет пограничного слоя) и нормальный заворачивает; + масса сохраняется (копирование популяций) → дрейфа не вносит. Применять ПОСЛЕ стриминга. + Нумерация: 2=(0,+1) 4=(0,-1) 5=(+1,+1) 6=(-1,+1) 7=(-1,-1) 8=(+1,-1). + Нижняя стенка (row 0): достраиваем вверх-идущие из вниз-идущих (зеркало по y, x сохранён). + Верхняя стенка (row -1): достраиваем вниз-идущие из вверх-идущих. + ВНИМАНИЕ: это только искусственные стенки канала; цилиндр остаётся no-slip (Bouzidi). + ПОРЯДОК: вызывать ПЕРЕД channel_bc (см. его docstring — так закрываются углы домена).""" + f[2, 0, :] = f[4, 0, :]; f[5, 0, :] = f[8, 0, :]; f[6, 0, :] = f[7, 0, :] + f[4, -1, :] = f[2, -1, :]; f[7, -1, :] = f[6, -1, :]; f[8, -1, :] = f[5, -1, :] + return f diff --git a/docs/theory/solver_2x_sdf/collision.py b/docs/theory/solver_2x_sdf/collision.py new file mode 100644 index 0000000..06541a4 --- /dev/null +++ b/docs/theory/solver_2x_sdf/collision.py @@ -0,0 +1,42 @@ +# Оператор СТОЛКНОВЕНИЯ — KBC-N1 (энтропийный), единственный оператор модели. +# +# KBC-N1 (Karlin/Bösch/Chikatamarla 2014): +# Δ = f − feq (неравновесная часть) +# Δs = Ps·Δ (проекция на сдвиг-моменты {cx²−cy², cxcy}) +# Δh = Δ − Δs (остальная часть) +# γ = 1/β − (2 − 1/β)·⟨Δs,Δh⟩ / ⟨Δh,Δh⟩, ⟨a,b⟩ = Σ_i a_i b_i / feq_i (H-теорема) +# f_post = f − β(2Δs + γΔh), β = 1/(2τ) +# γ — энтропийный стабилизатор: подстраивает диссипацию неhydro-мод под энтропийное ограничение +# (поэтому KBC устойчив при τ→1/2). Сдвиг-моменты (вязкость) релаксируют с правильным 2β = 1/τ, +# то есть физическая вязкость задаётся только τ — стабилизатор её не меняет. +# +# Порядок шагов дословно совпадает с алгоритмом статьи (Bösch/Chikatamarla/Karlin, PRE 92, +# 043309 (2015), разд. III, листинг после ур.39): ρ,u → feq → Δs → Δh = f − feq − Δs → γ → релаксация. +# Вырожденный случай ⟨Δh|Δh⟩→0 отсекается ОТНОСИТЕЛЬНЫМ порогом B.GREL (см. backend.py): +# абсолютный порог здесь недопустим — den квадратична по неравновесию и физически мала. +import backend as B +import lattice as L + +cp = B.cp; xp = B.xp +Q = L.Q; Ps = L.Ps; GREL = B.GREL; ONE = B.ONE; TWO = B.TWO + +def _project_shift(dfn): + """Δs = Ps·Δ без cuBLAS (gemm при CUDA-graph capture тащит alpha/beta host→device). + Реализовано как Σ_k Ps[i,k]·Δ[k] через broadcast+редукцию — только обычные ядра.""" + dfn2d = dfn.reshape(Q, -1) # (Q, N) + return (Ps[:, :, None] * dfn2d[None]).sum(1).reshape(dfn.shape) + +def kbc_collide(f, fe, beta): + dfn = f - fe + ds = _project_shift(dfn) + dh = dfn - ds; inv = 1.0 / fe + num = (ds*dh*inv).sum(0); den = (dh*dh*inv).sum(0) + nrm = (dfn*dfn*inv).sum(0) # ‖Δ‖² — масштаб неравновесия узла + ok = den > GREL*nrm # относительный порог, не абсолютный + den_safe = xp.where(ok, den, ONE) # избегаем 0/0 (обе ветки where считаются) + binv = 1.0 / beta + g = xp.where(ok, binv - (2.0 - binv)*num/den_safe, TWO) + return f - beta*(2.0*ds + g[None]*dh) + +# единственный оператор столкновения модели +collide = kbc_collide diff --git a/docs/theory/solver_2x_sdf/config.py b/docs/theory/solver_2x_sdf/config.py new file mode 100644 index 0000000..a4fa572 --- /dev/null +++ b/docs/theory/solver_2x_sdf/config.py @@ -0,0 +1,138 @@ +# Конфигурация модели 2×+SDF. Всё в одном месте, чтобы математику/режимы было легко менять. +# Единицы — решёточные (lu — длина воксель, ts — шаг по времени). +import os +from dataclasses import dataclass +from typing import Optional + +@dataclass +class Config: + # --- сетка / геометрия L0 (умеренно расширены: меньше блокировка + больше следа) --- + Nx: int = 174 # домен по x (цилиндр на 40 → ~8.4D вниз по потоку до выхода) + Ny: int = 90 # домен по y (стенки free-slip; блокировка β=D/Ny — варьируется серией) + D: int = 16 # диаметр цилиндра на грубом уровне L0 + cx: int = 40 + cy: Optional[int] = None # центр по вертикали; по умолчанию Ny//2 (см. __post_init__) + + # --- физика --- + U: float = 0.07 # скорость набегающего потока + Re: float = 150.0 # число Рейнольдса по D и U + + # --- время --- + steps: int = 100000 + ramp: int = 1000 # smoothstep-разгон входной скорости (гасит импульсный старт) + frame_every: int = 34 # период сохранения кадров для гифки + + # --- патч уровня L1 (в координатах L0); refine=2 → разрешение Δx/2 --- + ax1: Optional[int] = None # по умолчанию cx − 1.5D (запас перед телом; см. __post_init__) + bx1: Optional[int] = None # по умолчанию cx + 6.25D (расширен в след) + ay1: Optional[int] = None # по умолчанию cy − 2D (центрирован по cy) + by1: Optional[int] = None # по умолчанию cy + 2D + refine: int = 2 # коэффициент измельчения L1 (модель «2×» рассчитана на 2) + + # --- зонд скорости в следе: px = cx + probe_dx*D, py = cy (берётся с тонкой сетки L1) --- + probe_dx: int = 3 + + # --- стартовое возмущение (триггер вихревой дорожки): поперечный sin-импульс входа --- + pert_amp: float = 0.1 # амплитуда u_y входа, доля от U (0 — выключить) + pert_dur: int = 300 # длительность импульса в шагах; окно [ramp, ramp+pert_dur] + + # --- кросс-чек силы: интеграл тензора напряжений σ·n по окружности R1+δ на L1 (forces_stress.py) --- + stress_every: int = 50 # период выборки в шагах L0 (0 — выключить кросс-чек) + stress_ntheta: int = 256 # число точек контура по углу + stress_delta: float = 2.0 # отступ контура от поверхности (в тонких ячейках L1); + # δ=2 → билинейный стенсиль не трогает Bouzidi-зону (q_max≈0.98) + + # --- ГУ выхода: режим поперечной скорости на Zou-He давление-выходе --- + # "zero" — классика: uy=0 на выходе (жёстко; отражает вихри дорожки) + # "extrapolate" — uy берётся из соседнего столбца (нуль-градиент); ρ-якорь сохраняется + outlet_uy: str = "zero" + + # --- губка (absorbing layer) перед выходом: плавный рост вязкости в последних sponge_len + # столбцах L0 (smoothstep, ν → ν·sponge_nu_mult). Гасит вихри И акустику до прихода на + # давление-выход. Зачем: канал «вход-скорость + выход-давление» — недодемпфированный + # акустический резонатор (затухание моды ∝ ν(π/Nx)²); на длинных доменах мода раскачивается + # стартовым транзиентом → смещённый режим ⟨ρ⟩≈1.66 или взрыв (факторное исследование, + # эксперимент №1: F1/F2/F3/F5). 0 — выключена. + sponge_len: int = 0 + sponge_nu_mult: float = 30.0 + + # --- исполнение --- + use_cuda_graph: bool = True + + def __post_init__(self): + # производная геометрия по вертикали: центр и патч следуют за Ny (для серии по блокировке) + if self.cy is None: + self.cy = self.Ny // 2 + if self.ay1 is None: + self.ay1 = self.cy - 2 * self.D + if self.by1 is None: + self.by1 = self.cy + 2 * self.D + # производная геометрия по горизонтали: патч следует за cx (для факторов вход/выход) + if self.ax1 is None: + self.ax1 = self.cx - (3 * self.D) // 2 + if self.bx1 is None: + self.bx1 = self.cx + (25 * self.D) // 4 + assert 1 <= self.ay1 < self.by1 <= self.Ny - 2, ( + f"патч L1 [{self.ay1},{self.by1}] должен лежать строго внутри (0,{self.Ny-1}) — " + f"specular-ряды стенок не накрывать; минимально допустимое Ny ≈ {4*self.D + 6}") + assert 2 <= self.ax1 < self.cx < self.bx1 <= self.Nx - 2, ( + f"патч L1 [{self.ax1},{self.bx1}] должен лежать строго внутри (1,{self.Nx-1}) " + f"и накрывать тело (cx={self.cx})") + assert self.outlet_uy in ("zero", "extrapolate"), self.outlet_uy + if self.sponge_len: + assert self.Nx - 1 - self.sponge_len > self.bx1, ( + f"губка (последние {self.sponge_len} столбцов) не должна накрывать патч L1 " + f"(bx1={self.bx1}, Nx={self.Nx})") + + # ---------- производные величины ---------- + @property + def nu(self): return self.U * self.D / self.Re # кинематическая вязкость (lu²/ts) + @property + def tau0(self): return self.nu / (1.0/3.0) + 0.5 # время релаксации на L0 (cs²=1/3) + @property + def tau1(self): # связка τ при измельчении в r раз: ν одна и та же ⇒ τ_f = r(τ_c − ½) + ½ + return self.refine * (self.tau0 - 0.5) + 0.5 + @property + def beta0(self): return 1.0 / (2.0 * self.tau0) # β = 1/(2τ) для KBC/BGK на L0 + @property + def beta1(self): return 1.0 / (2.0 * self.tau1) # β на L1 + @property + def R01(self): # масштаб неравновесной части грубый→тонкий: f^neq ∝ τ·δt ⇒ (τ_f/τ_c)/r + return self.tau1 / (self.refine * self.tau0) + @property + def Rf01(self): return 1.0 / self.R01 # тонкий→грубый + @property + def DL(self): return self.refine * self.D # эффективный диаметр у тела (на L1) + @property + def px(self): return self.cx + self.probe_dx * self.D + @property + def py(self): return self.cy + +def from_env(**overrides): + """Создать Config с учётом переменных окружения и явных overrides. + Геометрия (AMR_NY/AMR_NX/AMR_CX) попадает в overrides ДО конструктора — + производные cy/ay1/by1/ax1/bx1 строятся в __post_init__.""" + if "Ny" not in overrides and os.environ.get("AMR_NY"): + overrides["Ny"] = int(os.environ["AMR_NY"]) + if "Nx" not in overrides and os.environ.get("AMR_NX"): + overrides["Nx"] = int(os.environ["AMR_NX"]) + if "cx" not in overrides and os.environ.get("AMR_CX"): + overrides["cx"] = int(os.environ["AMR_CX"]) + if "outlet_uy" not in overrides and os.environ.get("AMR_OUTLET_UY"): + overrides["outlet_uy"] = os.environ["AMR_OUTLET_UY"] + if "sponge_len" not in overrides and os.environ.get("AMR_SPONGE_LEN"): + overrides["sponge_len"] = int(os.environ["AMR_SPONGE_LEN"]) + if "sponge_nu_mult" not in overrides and os.environ.get("AMR_SPONGE_NU"): + overrides["sponge_nu_mult"] = float(os.environ["AMR_SPONGE_NU"]) + cfg = Config(**overrides) + if os.environ.get("AMR_STEPS"): + cfg.steps = int(os.environ["AMR_STEPS"]) + if "AMR_CUDAGRAPH" in os.environ: + cfg.use_cuda_graph = (os.environ["AMR_CUDAGRAPH"] != "0") + if os.environ.get("AMR_STRESS_EVERY"): + cfg.stress_every = int(os.environ["AMR_STRESS_EVERY"]) + if os.environ.get("AMR_STRESS_NTHETA"): + cfg.stress_ntheta = int(os.environ["AMR_STRESS_NTHETA"]) + if os.environ.get("AMR_STRESS_DELTA"): + cfg.stress_delta = float(os.environ["AMR_STRESS_DELTA"]) + return cfg diff --git a/docs/theory/solver_2x_sdf/diagnostics.py b/docs/theory/solver_2x_sdf/diagnostics.py new file mode 100644 index 0000000..16b08fd --- /dev/null +++ b/docs/theory/solver_2x_sdf/diagnostics.py @@ -0,0 +1,140 @@ +# Диагностика по собранным рядам сил/скорости. numpy здесь — только host-постобработка малых рядов +# (FFT/статистика), это НЕ вычислительный бэкенд солвера. +import numpy as np +import backend as B + +def strouhal(uy_host, D, U, pad=8192): + """Число Струхаля из ряда поперечной скорости в следе. + УЛУЧШЕНО: параболическая (3-точечная) интерполяция пика спектра → суб-биновая точность. + (Раньше брался ближайший FFT-бин: шаг по St ≈ D/(U·pad) ≈ 0.028, из-за чего St 'застревал'.)""" + sig = uy_host[len(uy_host)//2:] # установившийся режим — вторая половина + sig = sig - sig.mean() + amp = np.abs(np.fft.rfft(sig, n=pad)) + if len(amp) <= 3: + return 0.0, np.fft.rfftfreq(pad, 1.0), amp + k = 1 + int(np.argmax(amp[1:])) # индекс пика (без DC) + if 1 <= k < len(amp) - 1: # параболическая интерполяция вершины + a0, a1, a2 = amp[k-1], amp[k], amp[k+1] + denom = (a0 - 2*a1 + a2) + delta = 0.5*(a0 - a2)/denom if denom != 0 else 0.0 + else: + delta = 0.0 + f_peak = (k + delta) / pad + return f_peak * D / U, np.fft.rfftfreq(pad, 1.0), amp + +def analyze(res, cfg): + Fx = B.to_cpu(res["Fx"]); Fy = B.to_cpu(res["Fy"]); uy = B.to_cpu(res["uy"]) + DL, U, D = res["DL"], cfg.U, cfg.D + n = len(uy); h = slice(n//2, n) + Cd = 2.0*Fx/(U**2*DL); Cl = 2.0*Fy/(U**2*DL) + St, freqs, amp = strouhal(uy, D, U) + a = dict(Cd=float(Cd[h].mean()), Clrms=float(Cl[h].std()), St=float(St), + uyrms=float(uy[h].std()), Cd_s=Cd, Cl_s=Cl, uy=uy, freqs=freqs, amp=amp, h0=n//2) + if "Tz" in res: # момент: Cm = 2Tz/(U²·DL²); для цилиндра ⟨Cm⟩≈0 + Cm = 2.0*B.to_cpu(res["Tz"])/(U**2*DL*DL) + a["Cm"] = float(Cm[h].mean()); a["Cmrms"] = float(Cm[h].std()); a["Cm_s"] = Cm + K = int(res.get("stress_every", 0) or 0) # кросс-чек σ·n (редкая сетка по времени) + if K and len(res.get("Fx_st", ())) > 3: + Fxs = B.to_cpu(res["Fx_st"]); Fys = B.to_cpu(res["Fy_st"]); Tzs = B.to_cpu(res["Tz_st"]) + m = len(Fxs); hs = slice(m//2, m) + Cds = 2.0*Fxs/(U**2*DL); Cls = 2.0*Fys/(U**2*DL); Cms = 2.0*Tzs/(U**2*DL*DL) + a.update(Cd_st=float(Cds[hs].mean()), Clrms_st=float(Cls[hs].std()), + Cm_st=float(Cms[hs].mean()), Cd_st_s=Cds, Cl_st_s=Cls, stress_every=K) + return a + +def print_table(a, cfg): + # поправка на блокировку канала (приведение к скорости в зазоре U/(1−β)): + # St — кинематическая → ×(1−β); Cd, rms Cl ~ скорость² → ×(1−β)² + beta = cfg.D / cfg.Ny + St_c = a['St'] * (1 - beta) + Cd_c = a['Cd'] * (1 - beta)**2 + Cl_c = a['Clrms'] * (1 - beta)**2 + cm = a.get('Cm') + cms = f"{cm:>10.5f}" if cm is not None else f"{'—':>10}" + print("\n=== Модель 2×+SDF — установившийся режим ===") + print(f"{'версия':18}{'D у тела':>9}{'St':>8}{'':>9}{'rms Cl':>9}{'':>10}{'rms u_y':>9}") + print(f"{'2×+SDF (raw)':18}{cfg.DL:>9}{a['St']:>8.3f}{a['Cd']:>9.3f}{a['Clrms']:>9.4f}{cms}{a['uyrms']:>9.4f}") + print(f"{'2×+SDF (×блок.)':18}{cfg.DL:>9}{St_c:>8.3f}{Cd_c:>9.3f}{Cl_c:>9.4f}{'—':>10}{'—':>9}") + print(f"{'лит. Re≈150':18}{'—':>9}{0.183:>8.3f}{1.330:>9.3f}{'~0.3':>9}{0.0:>10.1f}{'':>9}") + print(f"(блокировка β=D/Ny={beta:.3f}; поправка: St×(1−β), Cd/rmsCl×(1−β)². " + "Лит. — безграничный цилиндр; ⟨Cm⟩≈0 — контроль симметрии; см. README)") + +def print_crosscheck(a): + """Сравнение двух НЕЗАВИСИМЫХ считываний силы: GMEM (обмен импульсом по линкам) vs ∮σ·n ds + (интеграл тензора напряжений по контуру R+δ). Сходство — прямое свидетельство корректности + считывания; сравниваем средние (мгновенные ряды σ·n сдвинуты по фазе кольцом R..R+δ).""" + if "Cd_st" not in a: + print("\n[кросс-чек σ·n: выключен (stress_every=0) или слишком мало точек]") + return + dcd = abs(a["Cd_st"] - a["Cd"]) / max(abs(a["Cd"]), 1e-12) + dcl = abs(a["Clrms_st"] - a["Clrms"]) / max(abs(a["Clrms"]), 1e-12) + cm = a.get("Cm", float("nan")) + print("\n=== Кросс-чек считывания силы: GMEM vs ∮σ·n ds (установившийся режим) ===") + print(f"{'метод':26}{'':>9}{'rms Cl':>9}{'':>10}") + print(f"{'GMEM (обмен импульсом)':26}{a['Cd']:>9.3f}{a['Clrms']:>9.4f}{cm:>10.5f}") + print(f"{'∮σ·n ds (контур R+δ)':26}{a['Cd_st']:>9.3f}{a['Clrms_st']:>9.4f}{a['Cm_st']:>10.5f}") + verdict = "СОГЛАСОВАНО" if (dcd < 0.05 and dcl < 0.10) else "ПРОВЕРИТЬ" + print(f"расхождение: dCd={dcd*100:.1f}% (порог 5%), d(rmsCl)={dcl*100:.1f}% (порог 10%) → {verdict}") + +def fit_blockage(betas, vals): + """Экстраполяция величины серии к β→0 двумя моделями: val ≈ a + b·β и val ≈ a + b·β². + (Теория solid-blockage даёт ведущий член O(β²), практика поправки (1−β)² содержит и линейный.) + Спред интерсептов |a_lin − a_quad| — оценка модельной неопределённости экстраполяции.""" + b = np.asarray(betas, float); v = np.asarray(vals, float) + sl, al = np.polyfit(b, v, 1) + sq, aq = np.polyfit(b**2, v, 1) + return dict(lin=(float(al), float(sl)), quad=(float(aq), float(sq)), + spread=float(abs(al - aq))) + +def print_blockage_table(rows, fits): + """Сводка серии по блокировке. rows — список dict(Ny, beta, St, Cd, Clrms, Cm, Cd_st); + fits — dict('Cd'/'Clrms'/'St' → результат fit_blockage).""" + print("\n=== Серия по блокировке: D фикс., Ny варьируется ===") + print(f"{'Ny':>5}{'β=D/Ny':>9}{'St':>8}{'St(1−β)':>9}{'':>9}{'rms Cl':>9}{'':>10}{'Cd σ·n':>9}") + for r in rows: + cdst = f"{r['Cd_st']:>9.3f}" if r.get("Cd_st") is not None else f"{'—':>9}" + print(f"{r['Ny']:>5}{r['beta']:>9.3f}{r['St']:>8.3f}{r['St']*(1-r['beta']):>9.3f}" + f"{r['Cd']:>9.3f}{r['Clrms']:>9.4f}{r['Cm']:>10.5f}{cdst}") + print("экстраполяция β→0 (интерсепт лин. фита / квадр. фита; спред — неопределённость):") + print(f" Cd(0) = {fits['Cd']['lin'][0]:.3f} / {fits['Cd']['quad'][0]:.3f} " + f"(спред {fits['Cd']['spread']:.3f}; лит. безгранич. 1.33)") + print(f" rms Cl(0) = {fits['Clrms']['lin'][0]:.3f} / {fits['Clrms']['quad'][0]:.3f} " + f"(спред {fits['Clrms']['spread']:.3f}; лит. ~0.3)") + print(f" St(0) = {fits['St']['lin'][0]:.3f} / {fits['St']['quad'][0]:.3f} " + f"(спред {fits['St']['spread']:.3f}; лит. 0.183)") + +def convergence_report(res, cfg, nwin=10): + """Эволюция по окнам времени: видно, НАСЫЩЕНО ли решение или ДРЕЙФУЕТ. + Ключевое: ⟨ρ⟩ (средняя плотность) и Cd, нормированный на реальную ⟨ρ⟩ (дрейф-устойчивый Cd). + Если ⟨ρ⟩ уплывает от 1 — это дрейф массы из-за ГУ входа/выхода, а Cd_raw искажён нормировкой на ρ=1.""" + Fx = B.to_cpu(res["Fx"]); Fy = B.to_cpu(res["Fy"]); uy = B.to_cpu(res["uy"]); rho = B.to_cpu(res["rho"]) + n = len(Fx); U = cfg.U; DL = res["DL"] + if n < nwin * 2: + return + Cd = 2.0*Fx/(U**2*DL); Cl = 2.0*Fy/(U**2*DL) + w = n // nwin + print("\n=== Сходимость по времени / дрейф (по окнам) ===") + print(f"{'окно':>4}{'шаги':>16}{'<ρ>':>8}{'raw':>9}{'/ρ':>9}{'rms Cl':>9}{'rms u_y':>9}") + rows = [] + for k in range(nwin): + s = slice(k*w, (k+1)*w if k < nwin-1 else n) + rm = float(rho[s].mean()); cdr = float(Cd[s].mean()) + cdn = cdr / rm if rm != 0 else float("nan") + clr = float(Cl[s].std()); uyr = float(uy[s].std()) + rows.append((rm, cdr, cdn, clr, uyr)) + print(f"{k+1:>4}{f'{k*w}-{(k+1)*w}':>16}{rm:>8.3f}{cdr:>9.3f}{cdn:>9.3f}{clr:>9.4f}{uyr:>9.4f}") + # вердикт по последним двум окнам + (rm1, cdr1, cdn1, clr1, _), (rm0, _, _, clr0, _) = rows[-1], rows[-2] + drho = rm1 - rm0; dcl = clr1 - clr0 + verdict = [] + if abs(rm1 - 1.0) > 0.02: + # «стабильна, но не там»: система села на смещённую ветвь (акустическая накачка массы; + # ⟨Cd⟩/Cl на ней НЕвалидны для сравнения с литературой) — см. факторное исследование + verdict.append(f"плотность: ⟨ρ⟩={rm1:.3f} → РЕЖИМ СМЕЩЁН (⟨ρ⟩ далеко от 1; прогон невалиден)") + else: + verdict.append(f"плотность: ⟨ρ⟩={rm1:.3f}, Δ за окно={drho:+.4f} → " + + ("ДРЕЙФ массы (правь ГУ выхода: давление/Zou-He)" if abs(drho) > 1e-3 else "стабильна")) + verdict.append(f"rms Cl: Δ за окно={dcl:+.4f} → " + + ("ещё растёт (не насыщено)" if dcl > 1e-3 else "насыщено/стабильно")) + verdict.append(f"дрейф-устойчивый Cd (⟨Cd⟩/ρ) в последнем окне = {cdn1:.3f}") + print("вердикт: " + "; ".join(verdict)) diff --git a/docs/theory/solver_2x_sdf/equilibrium.py b/docs/theory/solver_2x_sdf/equilibrium.py new file mode 100644 index 0000000..c485b77 --- /dev/null +++ b/docs/theory/solver_2x_sdf/equilibrium.py @@ -0,0 +1,45 @@ +# Равновесие и макропеременные. +# +# Используется ЭНТРОПИЙНОЕ равновесие в product-form (как в KBC), а не усечённый полином: +# feq_i = w_i · ρ · Π_d (2 − sqrt(1+3 u_d²)) · ((2 u_d + sqrt(1+3 u_d²))/(1 − u_d))^{c_{i,d}} +# Показатели c_{i,d} ∈ {−1,0,+1}, поэтому степень НЕ нужна — берём q или 1/q (быстрее и совместимо +# с CUDA-graph: нет pow и нет host→device для границ clip). +import backend as B +import lattice as L + +cp = B.cp; xp = B.xp +CXa = L.CXa; CYa = L.CYa + +def _feq9_body(rho, ux, uy): + ux = cp.minimum(cp.maximum(ux, -0.95), 0.95) # clip скоростей литералами (запекается в кернел) + uy = cp.minimum(cp.maximum(uy, -0.95), 0.95) + sx = cp.sqrt(1.0 + 3.0*ux*ux); sy = cp.sqrt(1.0 + 3.0*uy*uy) + base = rho * (2.0 - sx) * (2.0 - sy) + qx = (2.0*ux + sx) / (1.0 - ux); qy = (2.0*uy + sy) / (1.0 - uy) + ix = 1.0/qx; iy = 1.0/qy + return (base*(4.0/9.0), # ( 0, 0) + base*(1.0/9.0)*qx, base*(1.0/9.0)*qy, # (+1,0) (0,+1) + base*(1.0/9.0)*ix, base*(1.0/9.0)*iy, # (-1,0) (0,-1) + base*(1.0/36.0)*qx*qy, base*(1.0/36.0)*ix*qy, # (+1,+1) (-1,+1) + base*(1.0/36.0)*ix*iy, base*(1.0/36.0)*qx*iy) # (-1,-1) (+1,-1) + +_feq9 = cp.fuse()(_feq9_body) # одно слитное ядро (если cp.fuse доступен) +_FUSE_OK = [True] + +def feq(rho, u): + """Равновесные популяции (Q,Ny,Nx) по плотности rho и скорости u (индексируется [0],[1]). + Сборка через B.pack (без cupy.stack) — иначе H2D ломает CUDA-graph capture.""" + if _FUSE_OK[0]: + try: + return B.pack(_feq9(rho, u[0], u[1])) + except Exception as e: # откат на не-fused (тоже без pow), один раз + print(f"[equilibrium] cp.fuse отключён ({type(e).__name__}: {e}); обычный путь") + _FUSE_OK[0] = False + return B.pack(_feq9_body(rho, u[0], u[1])) + +def macros(f): + """Макропеременные: ρ = Σ_i f_i, u = (Σ_i c_i f_i)/ρ. Возвращает (rho, u=(2,Ny,Nx)).""" + r = f.sum(0) + ux = (CXa[:, None, None] * f).sum(0) / r + uy = (CYa[:, None, None] * f).sum(0) / r + return r, B.pack((ux, uy)) diff --git a/docs/theory/solver_2x_sdf/forces.py b/docs/theory/solver_2x_sdf/forces.py new file mode 100644 index 0000000..69e75d9 --- /dev/null +++ b/docs/theory/solver_2x_sdf/forces.py @@ -0,0 +1,52 @@ +# СИЛА и МОМЕНТ на теле — галилей-инвариантный обмен импульсом (GMEM, Wen et al. 2014). +# +# Для каждого линка жидкость→тело по направлению i (маска cl): +# ΔF = (c_i − u_w)·f_i^{после столкновения}(x_f) − (c_ī − u_w)·f_ī^{после стриминга}(x_f) +# где u_w — скорость стенки на линке (для неподвижного цилиндра = 0). Т.к. c_ī = −c_i, по компонентам: +# F_x += (Cx_i − u_wx)·f_i + (Cx_i + u_wx)·f_ī +# F_y += (Cy_i − u_wy)·f_i + (Cy_i + u_wy)·f_ī +# +# МОМЕНТ (торк) вокруг центра тела: T_z = Σ_links (r_w × ΔF)_z, где точка приложения — +# ПЕРЕСЕЧЕНИЕ линка со стенкой r_w = r_f + q·c_i (q — Bouzidi-доля, уже лежит в bc). +# Узел жидкости дал бы ошибку плеча до 1 ячейки; q бесплатен. Для кругового цилиндра +# ⟨Cm⟩ ≈ 0 — это контроль симметрии считывания; для подвижных/вращающихся тел (цель SimV4) — +# рабочая величина. +# +# Свойства: +# * f_i — популяция, уходящая в стенку (после столкновения); f_ī — вернувшаяся (после стриминга/Bouzidi). +# f_ī берётся из поля ПОСЛЕ стриминга — иначе ведущий симметричный член ~2ρw_i сокращается и Cd врёт. +# * При u_w=0 сводится к классическому Σ c_i (f_i + f_ī); члены с u_w делают оценку галилей-инвариантной +# и ГОТОВОЙ к подвижным/вращающимся телам (цель проекта SimV4) — туда передаётся u_w на линке. +# +# Независимый кросс-чек этой оценки — интегрирование тензора напряжений по контуру вокруг тела: +# см. forces_stress.py (σ = −p′·I + σ^v из неравновесных моментов; вызывается редко, вне CUDA-графа). +import backend as B +import lattice as L + +xp = B.xp; ZERO = B.ZERO +Cx = L.Cx; Cy = L.Cy + +def force_gmem(fpost, fnew, bc, rxy=None, u_wall=(0.0, 0.0)): + """GMEM по линкам тела (маска cl). Возвращает (Fx, Fy, Tz) — device-скаляры. + rxy=(rx,ry) — координаты узлов решётки относительно центра тела (для торка); None → Tz=0. + u_wall — скорость стенки. Graph-safe: только where/арифметика с литералами.""" + uwx, uwy = u_wall + Fx = ZERO; Fy = ZERO; Tz = ZERO + if rxy is not None: + rx, ry = rxy + for (i, ib, mask, q, xff, cl) in bc: + fi = fpost[i]; fib = fnew[ib] + dFx = xp.where(cl, (Cx[i] - uwx)*fi + (Cx[i] + uwx)*fib, ZERO) + dFy = xp.where(cl, (Cy[i] - uwy)*fi + (Cy[i] + uwy)*fib, ZERO) + Fx = Fx + dFx.sum(); Fy = Fy + dFy.sum() + if rxy is not None: # плечо до точки пересечения линка со стенкой + Tz = Tz + ((rx + q*Cx[i])*dFy - (ry + q*Cy[i])*dFx).sum() + return Fx, Fy, Tz + +def coefficients(Fx, Fy, U, DL, Tz=None): + """Безразмерные коэффициенты: Cd = 2Fx/(U²·DL), Cl = 2Fy/(U²·DL), Cm = 2Tz/(U²·DL²). + DL — диаметр у тела (на L1); сила/плечо тоже в единицах L1, так что нормировка согласована.""" + Cd = 2.0*Fx/(U**2*DL); Cl = 2.0*Fy/(U**2*DL) + if Tz is None: + return Cd, Cl + return Cd, Cl, 2.0*Tz/(U**2*DL*DL) diff --git a/docs/theory/solver_2x_sdf/forces_stress.py b/docs/theory/solver_2x_sdf/forces_stress.py new file mode 100644 index 0000000..23a9c16 --- /dev/null +++ b/docs/theory/solver_2x_sdf/forces_stress.py @@ -0,0 +1,80 @@ +# НЕЗАВИСИМЫЙ КРОСС-ЧЕК силы/момента: баланс импульса контрольного объёма, ограниченного +# замкнутым контуром (окружностью) вокруг тела на тонком уровне L1. +# +# F_тела = ∮ [σ·n − ρ·u·(u·n)] ds − d/dt ∫_кольцо ρu dV, σ = −p′·I + σ^v +# +# * давление: p = ρ·c_s²; интегрируем p′ = (ρ − ⟨ρ⟩_контур)·c_s² — константа давления по замкнутому +# контуру даёт ∮ p0·n ds ≡ 0, а вычитание убирает катастрофическое сокращение в float32; +# * вязкая часть из неравновесных моментов (Чепмен–Энског): σ^v_αβ = −(1 − 1/(2τ))·Π^neq_αβ, +# Π^neq_αβ = Σ_i c_iα c_iβ (f_i − f_i^eq). +# ВАЖНО (KBC): след Π^neq релаксирует не с 1/τ, а с γβ (поле-зависимый стабилизатор), поэтому +# берём строго ДЕВИАТОРНУЮ проекцию (след исключён) — сдвиг-моменты в KBC релаксируют с точным +# 2β = 1/τ, для них префактор корректен. Bulk-часть в силу трения и не входит. +# * КОНВЕКТИВНЫЙ член −ρu(u·n): поток импульса через контур. Зануляется только при δ→0 (no-slip +# на поверхности); при δ=2 скорость на контуре уже заметна, и без этого члена кросс-чек давал +# систематический сдвиг +4% по ⟨Cd⟩ на всех сетках (факторное исследование, эксперимент №0). +# * член d/dt ∫ρu dV по кольцу R..R1+δ НЕ считается: в среднем по времени он зануляется, +# на мгновенных рядах даёт малый сдвиг фазы → кросс-чек ведётся по средним (⟨Cd⟩, rms Cl). +# * контур — окружность радиуса R1+δ (δ = cfg.stress_delta тонких ячеек, по умолчанию 2): +# билинейный стенсиль выборки не задевает первое жидкое кольцо у стенки, где популяции +# реконструированы Bouzidi (q_max ≈ 0.98 < 1). +# +# Вызывается РЕДКО (каждые cfg.stress_every шагов) в Solver.run() ВНЕ step()/CUDA-графа. +import math +import backend as B +import lattice as L +import equilibrium as E + +cp = B.cp; xp = B.xp; DTYPE = B.DTYPE +CS2 = L.CS2 + +def build_probe(cfg): + """Прекомпьют контура (один раз, вне захвата): N=stress_ntheta точек на окружности R1+δ + вокруг центра тела на L1; индексы/веса билинейной интерполяции, нормали, плечи, элемент дуги.""" + r = cfg.refine + R1 = r * float(cfg.D) / 2.0 # радиус цилиндра на L1 (тонкие ячейки) + Rp = R1 + float(cfg.stress_delta) + ccx = (cfg.cx - cfg.ax1) * r; ccy = (cfg.cy - cfg.ay1) * r + N = int(cfg.stress_ntheta) + th = (2.0 * math.pi / N) * cp.arange(N) + nx = cp.cos(th).astype(DTYPE); ny = cp.sin(th).astype(DTYPE) + px = ccx + Rp * nx; py = ccy + Rp * ny + x0 = cp.floor(px).astype(cp.int64); y0 = cp.floor(py).astype(cp.int64) + # контур обязан лежать внутри патча L1 (он центрирован вокруг тела — выполняется с запасом) + Nfx = (cfg.bx1 - cfg.ax1) * r + 1; Nfy = (cfg.by1 - cfg.ay1) * r + 1 + assert int(x0.min()) >= 0 and int(x0.max()) + 1 <= Nfx - 1, "контур σ·n вышел за патч L1 по x" + assert int(y0.min()) >= 0 and int(y0.max()) + 1 <= Nfy - 1, "контур σ·n вышел за патч L1 по y" + return dict(x0=x0, y0=y0, x1=x0 + 1, y1=y0 + 1, + tx=(px - x0).astype(DTYPE), ty=(py - y0).astype(DTYPE), + nx=nx, ny=ny, rx=(Rp * nx), ry=(Rp * ny), ds=2.0 * math.pi * Rp / N) + +def _sample(fld, pr): + """Билинейная выборка 2D-поля в точках контура (аналог amr.pint, но по 1D-набору точек).""" + return (fld[pr["y0"], pr["x0"]] * (1 - pr["tx"]) * (1 - pr["ty"]) + + fld[pr["y0"], pr["x1"]] * pr["tx"] * (1 - pr["ty"]) + + fld[pr["y1"], pr["x0"]] * (1 - pr["tx"]) * pr["ty"] + + fld[pr["y1"], pr["x1"]] * pr["tx"] * pr["ty"]) + +def force_stress(F1, pr, tau1): + """Сила/момент на тело из баланса импульса ∮[σ·n − ρu(u·n)]ds по контуру pr на состоянии F1 + (L1, после стриминга). Возвращает (Fx, Fy, Tz) — device-скаляры. tau1 — релаксация на L1.""" + rho, u = E.macros(F1) + fneq = F1 - E.feq(rho, u) + CX = L.CXa[:, None, None]; CY = L.CYa[:, None, None] + Pxx = (CX * CX * fneq).sum(0) + Pyy = (CY * CY * fneq).sum(0) + Pxy = (CX * CY * fneq).sum(0) + rho_s = _sample(rho, pr) + ux_s = _sample(u[0], pr); uy_s = _sample(u[1], pr) + Pxx_s = _sample(Pxx, pr); Pyy_s = _sample(Pyy, pr); Pxy_s = _sample(Pxy, pr) + p = (rho_s - rho_s.mean()) * CS2 # p′: давление без константы (см. шапку) + pref = 1.0 - 1.0 / (2.0 * tau1) + tr = 0.5 * (Pxx_s + Pyy_s) # девиаторная проекция (след исключён) + sxx = -pref * (Pxx_s - tr); syy = -pref * (Pyy_s - tr); sxy = -pref * Pxy_s + un = ux_s * pr["nx"] + uy_s * pr["ny"] # нормальная скорость на контуре + flux = rho_s * un # ρ(u·n): конвективный вынос импульса + tx = (-p + sxx) * pr["nx"] + sxy * pr["ny"] - flux * ux_s # t = σ·n − ρu(u·n) + ty = sxy * pr["nx"] + (-p + syy) * pr["ny"] - flux * uy_s + Fx = tx.sum() * pr["ds"]; Fy = ty.sum() * pr["ds"] + Tz = (pr["rx"] * ty - pr["ry"] * tx).sum() * pr["ds"] # давление в торк не входит (n ∥ r) + return Fx, Fy, Tz diff --git a/docs/theory/solver_2x_sdf/geometry.py b/docs/theory/solver_2x_sdf/geometry.py new file mode 100644 index 0000000..d77b13d --- /dev/null +++ b/docs/theory/solver_2x_sdf/geometry.py @@ -0,0 +1,47 @@ +# Геометрия: маски тела/стенок и знаковое поле расстояний (SDF) для L0 и патча L1. +# Чистый CuPy. Соглашение по SDF: phi>0 в жидкости, phi<0 в теле; |phi| ≈ расстоянию до границы. +import backend as B +import lattice as L +import amr + +cp = B.cp; xp = B.xp; DTYPE = B.DTYPE + +def _cmask(NX, NY, ccx, ccy, R): + """Булева маска круга радиуса R (центр ccx,ccy) на сетке (NY,NX).""" + Y, X = cp.meshgrid(cp.arange(NY), cp.arange(NX), indexing="ij") + return (X - ccx)**2 + (Y - ccy)**2 <= R*R + +def _csdf(NX, NY, ccx, ccy, R): + """SDF круга: sqrt((x−ccx)²+(y−ccy)²) − R (отрицательно внутри).""" + Y, X = cp.meshgrid(cp.arange(NY), cp.arange(NX), indexing="ij") + return cp.sqrt((X - ccx).astype(DTYPE)**2 + (Y - ccy).astype(DTYPE)**2) - R + +class Geometry: + """Контейнер масок/SDF/патча. Поля *_np — host-копии для визуализации.""" + pass + +def build(cfg): + Nx, Ny, D, cx, cy = cfg.Nx, cfg.Ny, cfg.D, cfg.cx, cfg.cy + r = cfg.refine + ax1, bx1, ay1, by1 = cfg.ax1, cfg.bx1, cfg.ay1, cfg.by1 + g = Geometry() + + # --- L0: только цилиндр как твёрдое тело (стенки канала верх/низ — free-slip, не solid) --- + g.cyl0 = _cmask(Nx, Ny, cx, cy, D/2.0) + g.solid0 = g.cyl0 # стенки обрабатываются specular-отражением, см. boundary.free_slip_walls + g.phi0 = _csdf(Nx, Ny, cx, cy, D/2.0) # SDF только цилиндра (для Bouzidi тела) + + # --- патч L1 (измельчение r) над областью [ax1,bx1]×[ay1,by1] --- + g.P1 = amr.patch(Nx, Ny, ax1, bx1, ay1, by1, r) + Nfx, Nfy = g.P1["Nfx"], g.P1["Nfy"] + # цилиндр на L1: центр и радиус масштабируются на r (диаметр r·D → радиус r·D/2) + R1 = r * D / 2.0 + g.solid1 = _cmask(Nfx, Nfy, (cx - ax1)*r, (cy - ay1)*r, R1) + g.phi1 = _csdf(Nfx, Nfy, (cx - ax1)*r, (cy - ay1)*r, R1) + + # маска жидких узлов для рестрикции L1→L0 (внутренняя часть патча на L0) + g.fl1 = ~g.solid0[ay1+1:by1, ax1+1:bx1] + + # host-копии для визуализации + g.solid0_np = B.to_cpu(g.solid0); g.solid1_np = B.to_cpu(g.solid1) + return g diff --git a/docs/theory/solver_2x_sdf/lattice.py b/docs/theory/solver_2x_sdf/lattice.py new file mode 100644 index 0000000..67720c6 --- /dev/null +++ b/docs/theory/solver_2x_sdf/lattice.py @@ -0,0 +1,34 @@ +# Решётка D2Q9 и KBC-проектор. Чистый CuPy; всё считается один раз при импорте. +# +# Скорости e_i и веса w_i (стандартная нумерация D2Q9): +# 0:( 0, 0) 1:(+1,0) 2:(0,+1) 3:(-1,0) 4:(0,-1) +# 5:(+1,+1) 6:(-1,+1) 7:(-1,-1) 8:(+1,-1) +# OPP[i] — индекс противоположного направления. +import backend as B + +cp = B.cp; xp = B.xp; DTYPE = B.DTYPE + +Q = 9 +Cx = [0, 1, 0, -1, 0, 1, -1, -1, 1] # python-инты (для roll/индексации) +Cy = [0, 0, 1, 0, -1, 1, 1, -1, -1] +OPP = [0, 3, 4, 1, 2, 7, 8, 5, 6] +_Wlist = [4/9, 1/9, 1/9, 1/9, 1/9, 1/36, 1/36, 1/36, 1/36] +CS2 = 1.0 / 3.0 # квадрат скорости звука решётки + +# device-векторы +Wa = cp.asarray(_Wlist, DTYPE) +CXa = cp.asarray(Cx, DTYPE) +CYa = cp.asarray(Cy, DTYPE) + +def _build_projector(): + """Проектор Ps на сдвиг-моменты {cx²−cy², cx·cy} (ядро KBC-N1). + Ps = M⁻¹ · diag(оставить только эти 2 момента) · M, где M — моментный базис.""" + cxv = cp.asarray(Cx, cp.float64); cyv = cp.asarray(Cy, cp.float64) + M = cp.zeros((Q, Q), cp.float64) + M[0] = 1.0; M[1] = cxv; M[2] = cyv; M[3] = 3.0*(cxv**2 + cyv**2) - 2.0 + M[4] = cxv**2 - cyv**2; M[5] = cxv*cyv + M[6] = cxv**2*cyv; M[7] = cxv*cyv**2; M[8] = cxv**2*cyv**2 + Dm = cp.zeros((Q, Q), cp.float64); Dm[4, 4] = Dm[5, 5] = 1.0 + return (cp.linalg.inv(M) @ Dm @ M) + +Ps = _build_projector().astype(DTYPE) # (Q,Q) проектор на сдвиг diff --git a/docs/theory/solver_2x_sdf/run.py b/docs/theory/solver_2x_sdf/run.py new file mode 100644 index 0000000..08d4bb2 --- /dev/null +++ b/docs/theory/solver_2x_sdf/run.py @@ -0,0 +1,53 @@ +# Точка входа модели 2×+SDF. Запуск из этой папки: +# python run.py +# AMR_STEPS=2000 python run.py # короткий прогон +# AMR_CUDAGRAPH=0 python run.py # без CUDA-графов +# AMR_FP64=1 python run.py # двойная точность +import os, time +import config as C +import backend as B +import solver as S +import diagnostics as Diag +import visualization as Viz + +HERE = os.path.dirname(os.path.abspath(__file__)) +OUT = os.path.join(HERE, "out"); os.makedirs(OUT, exist_ok=True) + +def main(): + cfg = C.from_env() + print(f"[2×+SDF] backend={B.BACKEND}; домен {cfg.Nx}x{cfg.Ny}; D={cfg.D}; steps={cfg.steps}; " + f"collision=kbc; force=gmem; " + f"graphs={'on' if cfg.use_cuda_graph else 'off'}; " + f"L1 {cfg.refine}× = {(cfg.bx1-cfg.ax1)*cfg.refine+1}x{(cfg.by1-cfg.ay1)*cfg.refine+1}; " + f"вход {cfg.cx/cfg.D:.1f}D / выход {(cfg.Nx-1-cfg.cx)/cfg.D:.1f}D; outlet_uy={cfg.outlet_uy}") + + t0 = time.perf_counter() + sim = S.Solver(cfg) + res = sim.run(Viz.make_progress("2x+sdf")) + print(" время:", round(time.perf_counter() - t0, 1), "s") + + a = Diag.analyze(res, cfg) + Diag.print_table(a, cfg) + Diag.print_crosscheck(a) + Diag.convergence_report(res, cfg) + + Viz.save_gif(res, sim.geo, cfg, os.path.join(OUT, "cyl_2x_sdf.gif")) + Viz.save_series_panel(res, a, cfg, os.path.join(OUT, "series_2x_sdf.png")) + import numpy as np + np.savez(os.path.join(OUT, "probe_2x_sdf.npz"), + # сводные числа (самоописываемость для ноутбука: он только читает артефакты) + St=a["St"], Cd=a["Cd"], Clrms=a["Clrms"], uyrms=a["uyrms"], + Cm=a.get("Cm", float("nan")), + Cd_st=a.get("Cd_st", float("nan")), Clrms_st=a.get("Clrms_st", float("nan")), + Cm_st=a.get("Cm_st", float("nan")), + Ny=cfg.Ny, beta=cfg.D/cfg.Ny, D=cfg.D, U=cfg.U, Re=cfg.Re, steps=cfg.steps, + Nx=cfg.Nx, cx=cfg.cx, outlet_uy=cfg.outlet_uy, + stress_every=res["stress_every"], + # ряды + Cl=a["Cl_s"], uy=a["uy"], Fx=B.to_cpu(res["Fx"]), Fy=B.to_cpu(res["Fy"]), + Tz=B.to_cpu(res["Tz"]), rho=B.to_cpu(res["rho"]), + Fx_st=B.to_cpu(res["Fx_st"]), Fy_st=B.to_cpu(res["Fy_st"]), Tz_st=B.to_cpu(res["Tz_st"])) + print("DONE (2×+SDF)") + +if __name__ == "__main__": + main() diff --git a/docs/theory/solver_2x_sdf/run_blockage.py b/docs/theory/solver_2x_sdf/run_blockage.py new file mode 100644 index 0000000..486e701 --- /dev/null +++ b/docs/theory/solver_2x_sdf/run_blockage.py @@ -0,0 +1,95 @@ +# Серия по блокировке: D фиксирован, Ny растёт → β=D/Ny падает; экстраполяция β→0 даёт +# прямое сравнение с БЕЗГРАНИЧНОЙ литературой (Re=150: Cd≈1.33, St≈0.183, rms Cl≈0.3) +# без ручной поправки (1−β)². Запуск из этой папки: +# python run_blockage.py +# AMR_NY_LIST=90,128,180 python run_blockage.py # свой список Ny +# AMR_STEPS=20000 AMR_NY_LIST=128 python run_blockage.py # смоук +# Стоимость прогона ≈ как у run.py: патч L1 (основная работа) от Ny не зависит (высота 4D фикс.). +import os, time +import numpy as np +import config as C +import backend as B +import solver as S +import diagnostics as Diag +import visualization as Viz + +HERE = os.path.dirname(os.path.abspath(__file__)) +OUT = os.path.join(HERE, "out"); os.makedirs(OUT, exist_ok=True) + +LIT = dict(Cd=1.33, Clrms=0.3, St=0.183) # безграничный цилиндр, Re≈150 + +def run_one(Ny): + cfg = C.from_env(Ny=Ny, frame_every=0) # серия без кадров/гифок (только ряды) + print(f"\n[блокировка] Ny={cfg.Ny} (β={cfg.D/cfg.Ny:.3f}); домен {cfg.Nx}x{cfg.Ny}; " + f"патч y=[{cfg.ay1},{cfg.by1}]; steps={cfg.steps}") + t0 = time.perf_counter() + sim = S.Solver(cfg) + res = sim.run(Viz.make_progress(f"Ny={cfg.Ny}")) + print(" время:", round(time.perf_counter() - t0, 1), "s") + a = Diag.analyze(res, cfg) + Diag.print_table(a, cfg) + Diag.print_crosscheck(a) + Diag.convergence_report(res, cfg) + np.savez(os.path.join(OUT, f"probe_blockage_Ny{cfg.Ny}.npz"), + St=a["St"], Cd=a["Cd"], Clrms=a["Clrms"], uyrms=a["uyrms"], + Cm=a.get("Cm", float("nan")), + Cd_st=a.get("Cd_st", float("nan")), Clrms_st=a.get("Clrms_st", float("nan")), + Ny=cfg.Ny, beta=cfg.D/cfg.Ny, D=cfg.D, U=cfg.U, Re=cfg.Re, steps=cfg.steps, + Cl=a["Cl_s"], uy=a["uy"], rho=B.to_cpu(res["rho"]), + Fx=B.to_cpu(res["Fx"]), Fy=B.to_cpu(res["Fy"]), Tz=B.to_cpu(res["Tz"])) + row = dict(Ny=cfg.Ny, beta=cfg.D/cfg.Ny, St=a["St"], Cd=a["Cd"], Clrms=a["Clrms"], + Cm=a.get("Cm", float("nan")), Cd_st=a.get("Cd_st")) + # освободить VRAM перед следующим прогоном (буферы, BC, захваченный CUDA-граф) + del sim, res, a + B.cp.get_default_memory_pool().free_all_blocks() + return row + +def save_extrapolation_figure(rows, fits, path): + import matplotlib; matplotlib.use("Agg") + import matplotlib.pyplot as plt + betas = np.array([r["beta"] for r in rows]); bb = np.linspace(0, betas.max()*1.05, 100) + panels = [("Cd", "⟨Cd⟩", LIT["Cd"], "лит. 1.33"), + ("Clrms", "rms Cl", LIT["Clrms"], "лит. ~0.3"), + ("St", "St", LIT["St"], "лит. 0.183")] + fig, axs = plt.subplots(1, 3, figsize=(13.5, 4.2), dpi=110) + for ax, (key, lab, lit, litlab) in zip(axs, panels): + vals = np.array([r[key] for r in rows]); ft = fits[key] + ax.plot(betas, vals, "o", ms=7, color="#d32f2f", label="серия (raw)") + al, sl = ft["lin"]; aq, sq = ft["quad"] + ax.plot(bb, al + sl*bb, "-", lw=1.2, color="#1976d2", label=f"a+b·β → {al:.3f}") + ax.plot(bb, aq + sq*bb**2, "--", lw=1.2, color="#388e3c", label=f"a+b·β² → {aq:.3f}") + ax.axhline(lit, color="gray", lw=1.0, ls=":", label=litlab) + if key == "St": # для St полезен и кинематически поправленный вид + ax.plot(betas, vals*(1-betas), "s", ms=6, mfc="none", color="#7b1fa2", label="St·(1−β)") + ax.set_xlabel("β = D/Ny"); ax.set_ylabel(lab); ax.set_xlim(0, bb[-1]) + ax.legend(fontsize=8); ax.set_title(f"{lab}(β): экстраполяция β→0", fontsize=10) + fig.suptitle("Серия по блокировке: стеснение каналом — свойство ПОСТАНОВКИ, не считывания силы", + fontsize=11) + fig.tight_layout(rect=(0, 0, 1, 0.93)) + fig.savefig(path, bbox_inches="tight"); plt.close(fig) + print("saved", os.path.basename(path)) + +def main(): + ny_list = [int(s) for s in os.environ.get("AMR_NY_LIST", "90,128,180").split(",")] + print(f"[серия по блокировке] backend={B.BACKEND}; Ny={ny_list}") + rows = [run_one(Ny) for Ny in ny_list] + if len(rows) < 2: + print("\n(одна точка — фит/экстраполяция пропущены)") + return + betas = [r["beta"] for r in rows] + fits = {key: Diag.fit_blockage(betas, [r[key] for r in rows]) for key in ("Cd", "Clrms", "St")} + Diag.print_blockage_table(rows, fits) + np.savez(os.path.join(OUT, "blockage_summary.npz"), + Ny=np.array([r["Ny"] for r in rows]), beta=np.array(betas), + St=np.array([r["St"] for r in rows]), Cd=np.array([r["Cd"] for r in rows]), + Clrms=np.array([r["Clrms"] for r in rows]), Cm=np.array([r["Cm"] for r in rows]), + Cd_st=np.array([r["Cd_st"] if r["Cd_st"] is not None else np.nan for r in rows]), + Cd0_lin=fits["Cd"]["lin"][0], Cd0_quad=fits["Cd"]["quad"][0], + Cl0_lin=fits["Clrms"]["lin"][0], Cl0_quad=fits["Clrms"]["quad"][0], + St0_lin=fits["St"]["lin"][0], St0_quad=fits["St"]["quad"][0], + lit_Cd=LIT["Cd"], lit_Clrms=LIT["Clrms"], lit_St=LIT["St"]) + save_extrapolation_figure(rows, fits, os.path.join(OUT, "blockage_extrapolation.png")) + print("DONE (серия по блокировке)") + +if __name__ == "__main__": + main() diff --git a/docs/theory/solver_2x_sdf/run_factors.py b/docs/theory/solver_2x_sdf/run_factors.py new file mode 100644 index 0000000..5844b33 --- /dev/null +++ b/docs/theory/solver_2x_sdf/run_factors.py @@ -0,0 +1,184 @@ +# ФАКТОРНОЕ ИССЛЕДОВАНИЕ постановки: какие границы расчётной области отвечают за завышение +# Cd / rms Cl относительно безграничной литературы (Re=150: Cd≈1.33, rms Cl≈0.3, St≈0.183). +# +# Контекст (эксперимент №0 — серия по боковой блокировке, см. ноутбук, раздел 23): Cd(β) +# немонотонен (1.80 → 1.77 → 1.87 при β = 0.178 → 0.125 → 0.089) → боковое стеснение НЕ +# доминирующий фактор. Подозреваемые — продольные границы, которые серия держала константой: +# вход 2.5D (жёсткий равномерный профиль), выход 8.3D (Zou-He давление с жёстким uy=0, +# отражает вихри дорожки), и их связка. +# +# Здесь каждый фактор варьируется ОТДЕЛЬНО при фиксированной боковой блокировке (Ny=90): +# изоляция вклада входа, выхода и выходного ГУ. Все результаты накапливаются в out/factors.csv +# (одна строка на прогон, с полной конфигурацией) — реестр для документирования исследования. +# +# Запуск: python run_factors.py +# AMR_FACTORS=B0_baseline,F4_outlet_uy python run_factors.py # подмножество факторов +# AMR_STEPS=20000 python run_factors.py # смоук +import os, csv, time +import numpy as np +import config as C +import backend as B +import solver as S +import diagnostics as Diag +import visualization as Viz + +HERE = os.path.dirname(os.path.abspath(__file__)) +OUT = os.path.join(HERE, "out"); os.makedirs(OUT, exist_ok=True) +LIT = dict(Cd=1.33, Clrms=0.3, St=0.183) + +# (имя, overrides конфига, что изолирует) +# Эксперимент №1 (B0–F5, прогнан 2026-06-10): итоги — мягкий uy-выход (F4) выигрывает по всем +# метрикам; ВСЕ длинные домены без демпфера уходят в смещённый режим ⟨ρ⟩≈1.66 (акустический +# резонатор «вход-скорость/выход-давление» + накачка массы входом) или взрываются (F5). +# Эксперимент №2 (F6–F8): губка перед выходом — лечит акустику, открывает длинные домены. +FACTORS = [ + ("B0_baseline", dict(), + "база 174x90: вход 2.5D, выход 8.3D, uy=0 (контроль; кросс-чек уже с конвективным членом)"), + ("F1_outlet_far", dict(Nx=300), + "выход 8.3D -> 16.2D (вход 2.5D как в базе) — изолирует близость выхода"), + ("F2_inlet_far", dict(Nx=230, cx=96), + "вход 2.5D -> 6.0D (выход 8.3D как в базе) — изолирует близость входа"), + ("F3_inout_far", dict(Nx=390, cx=96), + "вход 6.0D + выход 18.3D — оба продольных фактора вместе"), + ("F4_outlet_uy", dict(outlet_uy="extrapolate"), + "мягкий выход: uy нуль-градиент вместо uy=0 (геометрия базовая) — изолирует отражение вихрей"), + ("F5_combo", dict(Nx=390, cx=96, outlet_uy="extrapolate"), + "вход 6.0D + выход 18.3D + мягкий uy-выход — всё вместе"), + # --- эксперимент №2: губка (absorbing layer) --- + ("F6_sponge", dict(outlet_uy="extrapolate", sponge_len=32), + "база 174x90 + мягкий uy + ГУБКА 32 столбца (nu x30) — валидация губки против F4"), + ("F7_long_sponge", dict(Nx=390, cx=96, outlet_uy="extrapolate", sponge_len=32), + "вход 6D + выход 18.3D + мягкий uy + губка — целевая «чистая» постановка"), + ("F8_long_sp_uy0", dict(Nx=390, cx=96, sponge_len=32), + "длинный домен + губка, но ЖЁСТКОЕ uy=0 — изолирует вклад губки от uy-режима"), +] + +CSV_FIELDS = ["when", "name", "status", "steps", "Nx", "Ny", "cx", "in_D", "out_D", "outlet_uy", + "sponge_len", "beta", "St", "St_corr", "Cd", "Clrms", "Cm", "Cd_st", "Clrms_st", + "dCd_pct", "dCl_pct", "rho_last", "cd_win_std", "cl_win_std", "wall_s", "desc"] + +def window_stats(res, cfg, nwin=10): + """Срединная изменчивость: std оконных средних Cd и оконных rms Cl (окна 2..nwin, + первое окно с разгоном пропускается). Метрика низкочастотной модуляции дорожки.""" + Fx = B.to_cpu(res["Fx"]); Fy = B.to_cpu(res["Fy"]) + Cd = 2.0*Fx/(cfg.U**2*res["DL"]); Cl = 2.0*Fy/(cfg.U**2*res["DL"]) + n = len(Cd); w = n // nwin + cds = [float(Cd[k*w:(k+1)*w].mean()) for k in range(1, nwin)] + cls = [float(Cl[k*w:(k+1)*w].std()) for k in range(1, nwin)] + return float(np.std(cds)), float(np.std(cls)) + +def run_factor(name, overrides, desc): + cfg = C.from_env(frame_every=0, **overrides) + in_D = cfg.cx / cfg.D; out_D = (cfg.Nx - 1 - cfg.cx) / cfg.D + print(f"\n=== Фактор {name}: {desc}") + print(f" домен {cfg.Nx}x{cfg.Ny}; вход {in_D:.1f}D / выход {out_D:.1f}D; " + f"outlet_uy={cfg.outlet_uy}; губка={cfg.sponge_len or '—'}; " + f"патч x=[{cfg.ax1},{cfg.bx1}] y=[{cfg.ay1},{cfg.by1}]; steps={cfg.steps}") + t0 = time.perf_counter() + sim = S.Solver(cfg) + res = sim.run(Viz.make_progress(name[:8])) + wall = time.perf_counter() - t0 + print(" время:", round(wall, 1), "s") + status = "ok" if len(res["Fx"]) == cfg.steps + 1 else f"BLEW_UP@{len(res['Fx'])}" + a = Diag.analyze(res, cfg) + Diag.print_table(a, cfg) + Diag.print_crosscheck(a) + Diag.convergence_report(res, cfg) + cd_ws, cl_ws = window_stats(res, cfg) + rho_last = float(B.to_cpu(res["rho"])[-1]) + np.savez(os.path.join(OUT, f"factor_{name}.npz"), + St=a["St"], Cd=a["Cd"], Clrms=a["Clrms"], uyrms=a["uyrms"], + Cm=a.get("Cm", float("nan")), + Cd_st=a.get("Cd_st", float("nan")), Clrms_st=a.get("Clrms_st", float("nan")), + Nx=cfg.Nx, Ny=cfg.Ny, cx=cfg.cx, D=cfg.D, U=cfg.U, Re=cfg.Re, steps=cfg.steps, + outlet_uy=cfg.outlet_uy, beta=cfg.D/cfg.Ny, + Cl=a["Cl_s"], uy=a["uy"], rho=B.to_cpu(res["rho"]), + Fx=B.to_cpu(res["Fx"]), Fy=B.to_cpu(res["Fy"]), Tz=B.to_cpu(res["Tz"])) + beta = cfg.D / cfg.Ny + dcd = abs(a.get("Cd_st", float("nan")) - a["Cd"]) / a["Cd"] * 100.0 + dcl = abs(a.get("Clrms_st", float("nan")) - a["Clrms"]) / max(a["Clrms"], 1e-12) * 100.0 + row = dict(when=time.strftime("%Y-%m-%d %H:%M:%S"), name=name, status=status, steps=cfg.steps, + Nx=cfg.Nx, Ny=cfg.Ny, cx=cfg.cx, in_D=round(in_D, 2), out_D=round(out_D, 2), + outlet_uy=cfg.outlet_uy, sponge_len=cfg.sponge_len, beta=round(beta, 4), + St=round(a["St"], 4), St_corr=round(a["St"]*(1-beta), 4), + Cd=round(a["Cd"], 4), Clrms=round(a["Clrms"], 4), + Cm=round(a.get("Cm", float("nan")), 6), + Cd_st=round(a.get("Cd_st", float("nan")), 4), + Clrms_st=round(a.get("Clrms_st", float("nan")), 4), + dCd_pct=round(dcd, 2), dCl_pct=round(dcl, 2), + rho_last=round(rho_last, 5), cd_win_std=round(cd_ws, 4), + cl_win_std=round(cl_ws, 4), wall_s=round(wall, 1), desc=desc) + del sim, res, a + B.cp.get_default_memory_pool().free_all_blocks() + return row + +def append_csv(rows): + path = os.path.join(OUT, "factors.csv") + if os.path.exists(path): + with open(path, encoding="utf-8") as fh: + header = fh.readline().strip() + if header != ",".join(CSV_FIELDS): + # схема реестра изменилась — старый файл сохраняем (история не теряется) + k = 1 + while os.path.exists(os.path.join(OUT, f"factors_v{k}.csv")): + k += 1 + os.rename(path, os.path.join(OUT, f"factors_v{k}.csv")) + print(f"[реестр] схема CSV изменилась — прежний файл сохранён как factors_v{k}.csv") + new = not os.path.exists(path) + with open(path, "a", newline="", encoding="utf-8") as fh: + wr = csv.DictWriter(fh, fieldnames=CSV_FIELDS) + if new: + wr.writeheader() + for r in rows: + wr.writerow(r) + print("CSV:", path, f"(+{len(rows)} строк)") + +def save_summary_figure(rows, path): + import matplotlib; matplotlib.use("Agg") + import matplotlib.pyplot as plt + names = [r["name"] for r in rows] + xs = np.arange(len(rows)) + fig, axs = plt.subplots(1, 3, figsize=(15, 4.6)) + ax = axs[0] + ax.bar(xs, [r["Cd"] for r in rows], color="#1f6feb", label="⟨Cd⟩ GMEM") + ax.plot(xs, [r["Cd_st"] for r in rows], "o", color="#ff8f00", label="⟨Cd⟩ ∮[σ·n−ρu(u·n)]ds") + ax.axhline(LIT["Cd"], color="#d1495b", ls="--", label=f"лит. безгранич. {LIT['Cd']}") + ax.set_ylabel("⟨Cd⟩"); ax.set_title("Сопротивление по факторам") + ax = axs[1] + ax.bar(xs, [r["Clrms"] for r in rows], color="#2e7d32") + ax.axhline(LIT["Clrms"], color="#d1495b", ls="--", label=f"лит. ~{LIT['Clrms']}") + ax.set_ylabel("rms Cl"); ax.set_title("Амплитуда подъёмной силы") + ax = axs[2] + ax.bar(xs, [r["cd_win_std"] for r in rows], color="#7b1fa2") + ax.set_ylabel("std оконных ⟨Cd⟩"); ax.set_title("НЧ-модуляция (меньше — стабильнее)") + for ax in axs: + ax.set_xticks(xs) + ax.set_xticklabels([f"{r['name']}\nвх {r['in_D']}D / вых {r['out_D']}D\n" + f"uy:{r['outlet_uy']} губ:{r['sponge_len']}" for r in rows], fontsize=7) + ax.legend(fontsize=8) + fig.suptitle("Факторное исследование постановки (Ny=90, β=0.178 фикс., 100k шагов)", fontsize=12) + fig.tight_layout(rect=(0, 0, 1, 0.94)) + fig.savefig(path, bbox_inches="tight"); plt.close(fig) + print("saved", os.path.basename(path)) + +def main(): + sel = os.environ.get("AMR_FACTORS") + todo = FACTORS if not sel else [f for f in FACTORS if f[0] in sel.split(",")] + print(f"[факторы] backend={B.BACKEND}; прогонов: {len(todo)}") + rows = [run_factor(*f) for f in todo] + print("\n=== Сводка факторного исследования ===") + hdr = (f"{'фактор':15}{'вх,D':>6}{'вых,D':>7}{'uy':>12}{'губка':>6}{'St':>7}{'':>8}" + f"{'rms Cl':>8}{'Cd σ·n':>8}{'dCd%':>6}{'<ρ>фин':>8}{'модул.':>8} статус") + print(hdr) + for r in rows: + print(f"{r['name']:15}{r['in_D']:>6}{r['out_D']:>7}{r['outlet_uy']:>12}{r['sponge_len']:>6}" + f"{r['St']:>7.3f}{r['Cd']:>8.3f}{r['Clrms']:>8.4f}{r['Cd_st']:>8.3f}{r['dCd_pct']:>6.1f}" + f"{r['rho_last']:>8.4f}{r['cd_win_std']:>8.4f} {r['status']}") + print(f"{'лит. безгранич.':15}{'':>6}{'':>7}{'':>12}{'':>6}{LIT['St']:>7.3f}{LIT['Cd']:>8.3f}{LIT['Clrms']:>8.4f}") + append_csv(rows) + if len(rows) > 1: + save_summary_figure(rows, os.path.join(OUT, "factors_summary.png")) + print("DONE (факторы)") + +if __name__ == "__main__": + main() diff --git a/docs/theory/solver_2x_sdf/solver.py b/docs/theory/solver_2x_sdf/solver.py new file mode 100644 index 0000000..9679c2e --- /dev/null +++ b/docs/theory/solver_2x_sdf/solver.py @@ -0,0 +1,191 @@ +# Оркестратор модели 2×+SDF: держит persistent-буферы, собирает один шаг из компонентов и гоняет цикл. +# Один шаг = замкнутая step() над фикс. буферами без host→device (готова к захвату в CUDA-граф). +import math +import backend as B +import lattice as L +import geometry as G +import equilibrium as E +import collision as Coll +import streaming as Strm +import boundary as Bnd +import forces as Fz +import forces_stress as FzS +import amr as Amr + +cp = B.cp; xp = B.xp; DTYPE = B.DTYPE; to_cpu = B.to_cpu +CYa = L.CYa + +def _capture(step_fn): + """Захват одного шага в CUDA-граф. При сбое гарантированно выводит поток из режима записи.""" + cp.cuda.Device().synchronize() + s = cp.cuda.Stream(non_blocking=True) + with s: + s.begin_capture() + try: + step_fn() + except Exception: + try: s.end_capture() + except Exception: pass + raise + return s.end_capture() + +class Solver: + def __init__(self, cfg): + self.cfg = cfg + self.collide = Coll.collide # KBC-N1 (единственный оператор столкновения) + self.force = Fz.force_gmem # галилей-инвариантный обмен импульсом + self.geo = G.build(cfg) + self.P1 = self.geo.P1 + self.beta1 = cfg.beta1 + if cfg.sponge_len: + # губка: τ(x) = τ0 + (mult−1)·ν·s(x)/cs², s — smoothstep 0→1 в последних sponge_len + # столбцах. β становится ПОЛЕМ (Nx,) → broadcast в kbc_collide; патч L1 губки не видит + # (гарантировано assert'ом в config), там остаётся скалярный beta1. + xs = cp.arange(cfg.Nx, dtype=DTYPE) + s = cp.clip((xs - (cfg.Nx - 1 - cfg.sponge_len)) / float(cfg.sponge_len), 0.0, 1.0) + s = s*s*(3.0 - 2.0*s) + tau_x = cfg.tau0 + (cfg.sponge_nu_mult - 1.0) * cfg.nu / (1.0/3.0) * s + self.beta0 = (1.0 / (2.0 * tau_x)).astype(DTYPE)[None, :] # (1,Nx) → broadcast по y + else: + self.beta0 = cfg.beta0 + self.R01 = cfg.R01; self.Rf01 = cfg.Rf01 + self.refine = cfg.refine + # ЗОНД скорости в следе: физическая точка (px,py) в координатах L0. + # Берём её с ТОНКОЙ сетки L1 (меньше численного размытия вихрей → чище St / rms u_y), + # если точка внутри патча; иначе fallback на L0. Индексы фиксированы → graph-safe. + self.probe_l1 = (cfg.ax1 <= cfg.px <= cfg.bx1) and (cfg.ay1 <= cfg.py <= cfg.by1) + if self.probe_l1: + self.pfx = (cfg.px - cfg.ax1) * cfg.refine + self.pfy = (cfg.py - cfg.ay1) * cfg.refine + else: + self.pfx = cfg.px; self.pfy = cfg.py + # ГУ (SDF/Bouzidi) на L0 (цилиндр+стенки) и L1 (цилиндр) + self.BC0 = Bnd.build_bc(self.geo.solid0, self.geo.phi0, self.geo.cyl0) + self.BC1 = Bnd.build_bc(self.geo.solid1, self.geo.phi1, self.geo.solid1) + self.fl1 = self.geo.fl1 + # persistent-состояние + Ny, Nx = cfg.Ny, cfg.Nx; Nfy, Nfx = self.P1["Nfy"], self.P1["Nfx"] + self.F0 = E.feq(xp.ones((Ny, Nx), DTYPE), xp.zeros((2, Ny, Nx), DTYPE)).copy() + self.F1 = E.feq(xp.ones((Nfy, Nfx), DTYPE), xp.zeros((2, Nfy, Nfx), DTYPE)).copy() + self.onecol = xp.ones((Ny, 1), DTYPE) + self.uin = xp.zeros((2, Ny, 1), DTYPE) # вход; обновляется СНАРУЖИ захвата + self.Fx_s = xp.zeros((), DTYPE); self.Fy_s = xp.zeros((), DTYPE); self.uy_s = xp.zeros((), DTYPE) + self.Tz_s = xp.zeros((), DTYPE) + # координаты узлов L1 относительно центра тела — плечи торка (прекомпьют вне захвата) + ccx1 = (cfg.cx - cfg.ax1) * cfg.refine; ccy1 = (cfg.cy - cfg.ay1) * cfg.refine + Yf, Xf = cp.meshgrid(cp.arange(Nfy), cp.arange(Nfx), indexing="ij") + self.rxy1 = ((Xf - ccx1).astype(DTYPE), (Yf - ccy1).astype(DTYPE)) + # контур кросс-чека силы σ·n (forces_stress; считается редко, вне CUDA-графа) + self.sprobe = FzS.build_probe(cfg) if cfg.stress_every else None + # разгон входа на device: U*smoothstep(t/ramp) + ts = cp.minimum(cp.arange(cfg.steps + 1) / cfg.ramp, 1.0) + self.ramp_u = (cfg.U * (ts*ts*(3 - 2*ts))).astype(DTYPE) + # стартовое возмущение: поперечный sin-импульс u_y входа в окне [ramp, ramp+pert_dur] (триггер схода) + uyp = cp.zeros(cfg.steps + 1, DTYPE) + if cfg.pert_dur > 0 and cfg.pert_amp != 0.0: + k = cp.arange(cfg.steps + 1) + inw = (k >= cfg.ramp) & (k < cfg.ramp + cfg.pert_dur) + ph = (k - cfg.ramp).astype(DTYPE) / float(cfg.pert_dur) + uyp = cp.where(inw, (cfg.pert_amp * cfg.U) * cp.sin(math.pi * ph), 0.0).astype(DTYPE) + self.ramp_uy = uyp + # ⟨ρ⟩ — диагностика дрейфа массы. Считать ТОЛЬКО по жидкости: узлы внутри цилиндра — + # фиктивные (их популяции не имеют физического смысла, ГУ их не трогает), а их плотность + # уезжает независимо. При D=12 на 120×60 это 1.6% узлов и смещение ⟨ρ⟩ на −5.4e-4 — + # ровно тот разряд, в котором ⟨ρ⟩ и цитируется в отчётах (1.0000 / 1.001). + self.fluid0 = (~self.geo.solid0).astype(DTYPE) + self._ncells = float(self.fluid0.sum()) + + def step(self): + F0 = self.F0; F1 = self.F1; P1 = self.P1 + feq = E.feq; macros = E.macros; stream = Strm.stream + # ----- уровень 0 ----- + rho, u0 = macros(F0) + pre = F0.copy() + post0 = self.collide(F0, feq(rho, u0), self.beta0) + f0 = stream(post0); f0 = Bnd.apply_bc(f0, post0, self.BC0) + # порядок важен: стенки снимают y-заворот roll, затем Zou-He закрывает x-заворот НА ВЕСЬ + # столбец, включая угловые узлы (иначе вход и выход связаны напрямую — см. boundary.py) + f0 = Bnd.free_slip_walls(f0) # верх/низ — скользящие стенки (specular) + f0 = Bnd.channel_bc(f0, self.uin, outlet_uy=self.cfg.outlet_uy) # Zou-He вход/выход + # ----- уровень 1: refine подшагов по времени с временно́й интерполяцией ghost ----- + g1o = Amr.ghost(pre, P1, self.R01); g1n = Amr.ghost(f0, P1, self.R01) + f1 = F1 + # сила/момент: меряем на КАЖДОМ подшаге L1 и усредняем (анти-алиасинг; раньше — мгновенная + # на последнем подшаге). Средний Cd не меняется, ряды становятся глаже. + fxa = B.ZERO; fya = B.ZERO; tza = B.ZERO + for s1 in range(self.refine): + r1, u1 = macros(f1); post1 = self.collide(f1, feq(r1, u1), self.beta1) + f1 = stream(post1); f1 = Bnd.apply_bc(f1, post1, self.BC1) + fx, fy, tz = self.force(post1, f1, self.BC1, self.rxy1) + fxa = fxa + fx; fya = fya + fy; tza = tza + tz + w = (s1 + 1) / self.refine # временна́я интерполяция ghost: o→n + f1 = Amr.fill(f1, (1 - w)*g1o + w*g1n) + self.Fx_s[...] = fxa / self.refine; self.Fy_s[...] = fya / self.refine + self.Tz_s[...] = tza / self.refine + f0 = Amr.restrict(f1, f0, P1, self.Rf01, self.fl1) + F1[...] = f1 + # зонд скорости в следе (с тонкой сетки L1, если точка внутри патча) + запись состояния + psrc = f1 if self.probe_l1 else f0 + col = psrc[:, self.pfy, self.pfx]; self.uy_s[...] = (CYa*col).sum() / col.sum() + F0[...] = f0 + + def run(self, progress=None): + cfg = self.cfg + Fx = xp.zeros(cfg.steps + 1, DTYPE); Fy = xp.zeros(cfg.steps + 1, DTYPE); uy = xp.zeros(cfg.steps + 1, DTYPE) + Tz = xp.zeros(cfg.steps + 1, DTYPE) # момент (торк) вокруг центра тела + rho = xp.zeros(cfg.steps + 1, DTYPE) # ⟨ρ⟩(t) — диагностика дрейфа массы + # кросс-чек σ·n: редкая выборка (каждые stress_every шагов), вне CUDA-графа + nst = (cfg.steps // cfg.stress_every + 1) if cfg.stress_every else 0 + Fx_st = xp.zeros(nst, DTYPE); Fy_st = xp.zeros(nst, DTYPE); Tz_st = xp.zeros(nst, DTYPE) + kst = 0 + frames = [] + graph = None; graph_failed = False + def snap(): return (self.F0.copy(), self.F1.copy()) + def restore(s): self.F0[...] = s[0]; self.F1[...] = s[1] + def maxdiff(s): return max(float(xp.abs(s[0] - self.F0).max()), float(xp.abs(s[1] - self.F1).max())) + for t in range(cfg.steps + 1): + self.uin[0, :, 0] = self.ramp_u[t] + self.uin[1, :, 0] = self.ramp_uy[t] # поперечный импульс-триггер (0 вне окна возмущения) + did = False + if t == 1 and cfg.use_cuda_graph and not graph_failed: + # захват + РАНТАЙМ-САМОПРОВЕРКА (граф vs eager на одном шаге); при расхождении — откат + try: + graph = _capture(self.step) + before = snap(); graph.launch(); gres = snap() + restore(before); self.step() + d = maxdiff(gres) + if d > 1e-3: + print(f"\n[graph] self-check разошёлся (Δ={d:.2e}) — отключаю графы, работаю eager") + graph = None; graph_failed = True + else: + print(f"\n[graph] self-check OK (Δ={d:.2e}) — CUDA graphs активны") + did = True + except Exception as e: + print(f"\n[graph] недоступны ({type(e).__name__}: {e}) — работаю eager") + import traceback as _tb; _tb.print_exc() + graph = None; graph_failed = True + try: cp.cuda.Device().synchronize() + except Exception: pass + if not did: + if graph is not None and t >= 1: + graph.launch() + else: + self.step() + Fx[t] = self.Fx_s; Fy[t] = self.Fy_s; Tz[t] = self.Tz_s; uy[t] = self.uy_s + rho[t] = (self.F0.sum(0) * self.fluid0).sum() / self._ncells # ⟨ρ⟩ по жидкости (дрейф массы) + if cfg.stress_every and t % cfg.stress_every == 0: + # eager-вычисление на текущем F1 после launch/step — упорядочено на стриме, + # сам захваченный граф не трогаем (паттерн как у rho[t] выше) + sfx, sfy, stz = FzS.force_stress(self.F1, self.sprobe, cfg.tau1) + Fx_st[kst] = sfx; Fy_st[kst] = sfy; Tz_st[kst] = stz; kst += 1 + if progress is not None: + progress(t, cfg.steps) + if t % 500 == 0 and not bool(xp.isfinite(self.F0).all()): + print("BLEW UP", t) + Fx = Fx[:t]; Fy = Fy[:t]; Tz = Tz[:t]; uy = uy[:t]; rho = rho[:t] + Fx_st = Fx_st[:kst]; Fy_st = Fy_st[:kst]; Tz_st = Tz_st[:kst] + break + if cfg.frame_every and t % cfg.frame_every == 0: + frames.append((t, to_cpu(E.macros(self.F0)[1]), to_cpu(E.macros(self.F1)[1]))) + return dict(Fx=Fx, Fy=Fy, Tz=Tz, uy=uy, rho=rho, frames=frames, DL=cfg.DL, + Fx_st=Fx_st, Fy_st=Fy_st, Tz_st=Tz_st, stress_every=cfg.stress_every) diff --git a/docs/theory/solver_2x_sdf/streaming.py b/docs/theory/solver_2x_sdf/streaming.py new file mode 100644 index 0000000..b4851e6 --- /dev/null +++ b/docs/theory/solver_2x_sdf/streaming.py @@ -0,0 +1,17 @@ +# ПЕРЕНОС (streaming): f_i(x, t+1) = f_i(x − c_i, t). +# Реализован пул-схемой через cp.roll по осям (y, x). 9 сдвигов в новый буфер. +# +# Заметка для ревизии: roll создаёт по ядру на направление (9 ядер). Это НЕ влияет на физику, +# только на число запусков ядер. Главный способ убрать накладные расходы — CUDA-graph (см. solver.py), +# а не переписывание переноса. Альтернатива (один gather-кернел по предвыч. индексам) — точка расширения. +import backend as B +import lattice as L + +xp = B.xp +Q = L.Q; Cx = L.Cx; Cy = L.Cy + +def stream(f): + fs = xp.empty_like(f) + for i in range(Q): + fs[i] = xp.roll(f[i], (Cy[i], Cx[i]), (0, 1)) + return fs diff --git a/docs/theory/solver_2x_sdf/visualization.py b/docs/theory/solver_2x_sdf/visualization.py new file mode 100644 index 0000000..7d8c291 --- /dev/null +++ b/docs/theory/solver_2x_sdf/visualization.py @@ -0,0 +1,92 @@ +# Визуализация (host): гифка |ω| с наложением тонкого патча L1 и прогресс-бар. +# matplotlib/PIL работают только с host-массивами — кадры уже перенесены на host в solver.run(). +import os +import time as _time +import numpy as np + +def make_progress(label, width=32, every=0.1): + """ASCII-шкала прогресса по выполненным шагам из заданных (обновление на месте через \\r).""" + st = {"t0": _time.perf_counter(), "last": 0.0} + def cb(t, total): + now = _time.perf_counter(); done = (t >= total) + if not done and (now - st["last"] < every): + return + st["last"] = now; frac = (t + 1) / (total + 1) + filled = int(round(width * frac)); bar = "#"*filled + "-"*(width - filled) + el = now - st["t0"]; eta = (el/frac - el) if frac > 0 else 0.0 + print(f"\r {label:8}[{bar}] {frac*100:5.1f}% ({t}/{total}) {el:5.1f}s ETA {eta:5.1f}s", + end=("\n" if done else ""), flush=True) + return cb + +def _vort(u): + return (np.roll(u[1], -1, 1) - np.roll(u[1], 1, 1))*0.5 - (np.roll(u[0], -1, 0) - np.roll(u[0], 1, 0))*0.5 + +def save_series_panel(res, a, cfg, path): + """Готовая png-панель для ноутбука (он код не исполняет — только вставляет картинки): + (1) ряды Cd(t)/Cl(t) + редкие точки кросс-чека ∮σ·n ds; (2) Cm(t) — контроль симметрии; + (3) спектр зонда u_y с пиком St; (4) ⟨ρ⟩(t) — контроль дрейфа массы.""" + import backend as B + import matplotlib; matplotlib.use("Agg") + import matplotlib.pyplot as plt + Cd = a["Cd_s"]; Cl = a["Cl_s"]; n = len(Cd); h0 = a["h0"]; t = np.arange(n) + fig, axs = plt.subplots(2, 2, figsize=(12.5, 7.2), dpi=110) + ax = axs[0, 0] + ax.plot(t, Cd, lw=0.7, color="#d32f2f", label=f"Cd (GMEM), ⟨Cd⟩={a['Cd']:.3f}") + ax.plot(t, Cl, lw=0.7, color="#1976d2", label=f"Cl (GMEM), rms={a['Clrms']:.3f}") + if "Cd_st_s" in a: + K = a["stress_every"]; ts = np.arange(len(a["Cd_st_s"])) * K + ax.plot(ts, a["Cd_st_s"], ".", ms=3, color="#ff8f00", label=f"Cd ∮σ·n, ⟨⟩={a['Cd_st']:.3f}") + ax.plot(ts, a["Cl_st_s"], ".", ms=3, color="#4fc3f7", label="Cl ∮σ·n") + ax.axvline(h0, color="gray", lw=0.8, ls="--") + ax.set_xlabel("шаг L0"); ax.set_ylabel("Cd, Cl"); ax.legend(fontsize=8, loc="upper right") + ax.set_title("Сила: GMEM (линии) vs ∮σ·n ds (точки)", fontsize=10) + ax = axs[0, 1] + if "Cm_s" in a: + ax.plot(t, a["Cm_s"], lw=0.7, color="#388e3c") + ax.axhline(0.0, color="gray", lw=0.8) + ax.set_title(f"Cm(t): ⟨Cm⟩={a['Cm']:.5f} (контроль симметрии, ожид. ≈0)", fontsize=10) + ax.set_xlabel("шаг L0"); ax.set_ylabel("Cm") + ax = axs[1, 0] + ax.plot(a["freqs"]*cfg.D/cfg.U, a["amp"], lw=0.9, color="#7b1fa2") + ax.axvline(a["St"], color="#d32f2f", lw=1.0, ls="--", label=f"St={a['St']:.3f}") + ax.set_xlim(0, 0.6); ax.set_xlabel("St = f·D/U"); ax.set_ylabel("|FFT(u_y)|") + ax.legend(fontsize=9); ax.set_title("Спектр зонда в следе (вторая половина ряда)", fontsize=10) + ax = axs[1, 1] + rho = B.to_cpu(res["rho"]) if not isinstance(res["rho"], np.ndarray) else res["rho"] + ax.plot(np.arange(len(rho)), rho, lw=0.9, color="#5d4037") + ax.axhline(1.0, color="gray", lw=0.8) + ax.set_xlabel("шаг L0"); ax.set_ylabel("⟨ρ⟩") + ax.set_title(f"⟨ρ⟩(t): дрейф массы (финально {float(rho[-1]):.4f})", fontsize=10) + fig.suptitle(f"2×+SDF · Ny={cfg.Ny} (β={cfg.D/cfg.Ny:.3f}) · Re={cfg.Re:g} · {len(rho)-1} шагов", + fontsize=11) + fig.tight_layout(rect=(0, 0, 1, 0.96)) + os.makedirs(os.path.dirname(path), exist_ok=True) + fig.savefig(path, bbox_inches="tight"); plt.close(fig) + print("saved", os.path.basename(path)) + +def save_gif(res, geo, cfg, path, fps=24): + import matplotlib; matplotlib.use("Agg") + import matplotlib.pyplot as plt, matplotlib.patches as mpatches + from PIL import Image + s0 = geo.solid0_np; s1 = geo.solid1_np + Nx, Ny = cfg.Nx, cfg.Ny; ax1, bx1, ay1, by1 = cfg.ax1, cfg.bx1, cfg.ay1, cfg.by1 + frames = res["frames"] + vm = np.nanpercentile(np.abs(np.where(s0, np.nan, _vort(frames[len(frames)//2][1]))), 99.0) + cm = plt.get_cmap("inferno").copy(); cm.set_bad("white"); pil = [] + for (t, u0, u1) in frames: + fig = plt.figure(figsize=(11.2, 5.7), dpi=96); ax = fig.add_subplot(111) + ax.imshow(np.abs(np.where(s0, np.nan, _vort(u0))), origin="lower", cmap=cm, vmin=0, vmax=vm, + extent=(0, Nx, 0, Ny), interpolation="nearest") + ax.imshow(np.abs(np.where(s1, np.nan, _vort(u1)))[1:-1, 1:-1], origin="lower", cmap=cm, vmin=0, vmax=vm, + extent=(ax1+0.5, bx1-0.5, ay1+0.5, by1-0.5), interpolation="nearest") + ax.add_patch(mpatches.Rectangle((0.2, 0.2), Nx-0.4, Ny-0.4, fill=False, edgecolor="#4fc3f7", lw=1.6)) + ax.text(1.5, Ny-4, "L0: Δx", color="#4fc3f7", fontsize=9, weight="bold") + ax.add_patch(mpatches.Rectangle((ax1, ay1), bx1-ax1, by1-ay1, fill=False, edgecolor="#aed581", lw=2.2)) + ax.text(ax1+1, by1-3.5, "L1: Δx/2 (тело+след)", color="#aed581", fontsize=9, weight="bold") + ax.set_title(f"2×+SDF · |\\omega| · t={t}", fontsize=11) + ax.set_xlabel("x [lu]"); ax.set_ylabel("y [lu]"); ax.set_xlim(0, Nx); ax.set_ylim(0, Ny) + buf = __import__("io").BytesIO(); fig.savefig(buf, format="png", bbox_inches="tight"); buf.seek(0); plt.close(fig) + pil.append(Image.open(buf).convert("RGB").convert("P", palette=Image.ADAPTIVE)) + os.makedirs(os.path.dirname(path), exist_ok=True) + pil[0].save(path, save_all=True, append_images=pil[1:], duration=int(1000/fps), loop=0, optimize=True) + print("saved", os.path.basename(path), len(frames), "кадров") diff --git a/extern/.gitkeep b/extern/.gitkeep new file mode 100644 index 0000000..e69de29 diff --git a/run.bat b/run.bat new file mode 100644 index 0000000..17430e6 --- /dev/null +++ b/run.bat @@ -0,0 +1,22 @@ +@echo off +REM Portable launcher for SimVulcan. Resolves the exe path relative to this +REM script so the project folder can be moved without breaking the shortcut. +setlocal +set "SCRIPT_DIR=%~dp0" +set "EXE_DIR=%SCRIPT_DIR%build\vs2022\src\app\Release" +set "EXE=%EXE_DIR%\SimVulcan.exe" + +if not exist "%EXE%" ( + echo [ERROR] SimVulcan.exe not found at: + echo %EXE% + echo. + echo Build the project first: + echo cmake --preset windows-msvc-release + echo cmake --build --preset windows-msvc-release + pause + exit /b 1 +) + +cd /d "%EXE_DIR%" +start "" "%EXE%" +endlocal diff --git a/shaders/CMakeLists.txt b/shaders/CMakeLists.txt new file mode 100644 index 0000000..eb075ff --- /dev/null +++ b/shaders/CMakeLists.txt @@ -0,0 +1,17 @@ +# Collect all shader sources and feed them to the simv_shaders custom target. +file(GLOB_RECURSE SHADER_SOURCES CONFIGURE_DEPENDS + "${CMAKE_CURRENT_SOURCE_DIR}/editor/*.vert" + "${CMAKE_CURRENT_SOURCE_DIR}/editor/*.frag" +) + +if(SHADER_SOURCES) + # INCLUDE root is `shaders/` so that #include "common/foo.glsl" would resolve + # to shaders/common/foo.glsl if a shader needs a shared helper. + simv_compile_shaders(simv_shaders + ${SHADER_SOURCES} + INCLUDES "${CMAKE_CURRENT_SOURCE_DIR}" + ) +else() + # Empty placeholder so dependent targets don't break when no shaders exist yet. + add_custom_target(simv_shaders ALL COMMAND ${CMAKE_COMMAND} -E true) +endif() diff --git a/shaders/editor/grid.frag b/shaders/editor/grid.frag new file mode 100644 index 0000000..619d614 --- /dev/null +++ b/shaders/editor/grid.frag @@ -0,0 +1,8 @@ +#version 460 + +layout(location = 0) in vec3 vColor; +layout(location = 0) out vec4 outColor; + +void main() { + outColor = vec4(vColor, 1.0); +} diff --git a/shaders/editor/grid.vert b/shaders/editor/grid.vert new file mode 100644 index 0000000..8b152f4 --- /dev/null +++ b/shaders/editor/grid.vert @@ -0,0 +1,16 @@ +#version 460 +// Reference-grid / axis lines: per-vertex colour, transformed by the MVP. + +layout(location = 0) in vec3 inPos; +layout(location = 1) in vec3 inColor; + +layout(push_constant) uniform PC { + mat4 mvp; +} pc; + +layout(location = 0) out vec3 vColor; + +void main() { + vColor = inColor; + gl_Position = pc.mvp * vec4(inPos, 1.0); +} diff --git a/shaders/editor/mesh.frag b/shaders/editor/mesh.frag new file mode 100644 index 0000000..572f56b --- /dev/null +++ b/shaders/editor/mesh.frag @@ -0,0 +1,28 @@ +#version 460 +// Flat shading: the per-face normal is reconstructed from screen-space +// derivatives of the model-space position, so the vertex stream needs no +// normals. color.a selects shaded (1) vs constant colour (0, for wireframe). + +layout(location = 0) in vec3 vModelPos; +layout(location = 0) out vec4 outColor; + +layout(push_constant) uniform PC { + mat4 mvp; + vec4 color; +} pc; + +void main() { + vec3 dx = dFdx(vModelPos); + vec3 dy = dFdy(vModelPos); + vec3 c = cross(dx, dy); + float len = length(c); + vec3 n = (len > 1e-8) ? c / len : vec3(0.0, 0.0, 1.0); + + const vec3 L = normalize(vec3(0.4, 0.85, 0.55)); + float diff = abs(dot(n, L)); // two-sided + float shade = clamp(0.25 + 0.8 * diff, 0.0, 1.0); + + vec3 base = pc.color.rgb; + vec3 rgb = mix(base, base * shade, pc.color.a); + outColor = vec4(rgb, 1.0); +} diff --git a/shaders/editor/mesh.vert b/shaders/editor/mesh.vert new file mode 100644 index 0000000..2dea64c --- /dev/null +++ b/shaders/editor/mesh.vert @@ -0,0 +1,17 @@ +#version 460 +// Transforms model vertices by the MVP push constant. The model-space position +// is passed through so the fragment shader can derive a flat normal from it. + +layout(location = 0) in vec3 inPos; + +layout(push_constant) uniform PC { + mat4 mvp; + vec4 color; // .rgb base colour, .a = lit flag (1 = shaded, 0 = flat) +} pc; + +layout(location = 0) out vec3 vModelPos; + +void main() { + vModelPos = inPos; + gl_Position = pc.mvp * vec4(inPos, 1.0); +} diff --git a/src/app/CMakeLists.txt b/src/app/CMakeLists.txt new file mode 100644 index 0000000..742c4a2 --- /dev/null +++ b/src/app/CMakeLists.txt @@ -0,0 +1,27 @@ +add_executable(SimVulcan + main.cpp +) +target_link_libraries(SimVulcan PRIVATE + simv_core simv_vk simv_mesh simv_editor + glm::glm spdlog::spdlog +) +add_dependencies(SimVulcan simv_shaders) +simv_set_warnings(SimVulcan) + +# Copy assets next to the executable. +add_custom_command(TARGET SimVulcan POST_BUILD + COMMAND ${CMAKE_COMMAND} -E rm -rf "$/assets" + COMMAND ${CMAKE_COMMAND} -E copy_directory + "${CMAKE_SOURCE_DIR}/assets" + "$/assets" + COMMENT "Copying assets to output directory" +) + +# Copy compiled SPIR-V next to the executable. +add_custom_command(TARGET SimVulcan POST_BUILD + COMMAND ${CMAKE_COMMAND} -E make_directory "${CMAKE_BINARY_DIR}/spirv" + COMMAND ${CMAKE_COMMAND} -E copy_directory + "${CMAKE_BINARY_DIR}/spirv" + "$/spirv" + COMMENT "Copying SPIR-V shaders to output directory" +) diff --git a/src/app/main.cpp b/src/app/main.cpp new file mode 100644 index 0000000..13c0499 --- /dev/null +++ b/src/app/main.cpp @@ -0,0 +1,85 @@ +// SimVulcan editor: a 3D viewport with an orbit camera, three reference grid +// planes through the origin, and .obj model loading/visualisation. + +#include "core/App.h" +#include "core/Logger.h" + +#include "vk/Renderer.h" + +#include "mesh/Mesh.h" +#include "mesh/MeshDecimator.h" + +#include "editor/Camera.h" +#include "editor/CameraInput.h" +#include "editor/EditorUI.h" +#include "editor/MeshLoadPanel.h" + +#include +#include + +#include + +#include +#include +#include + +int main(int /*argc*/, char** /*argv*/) { + try { + simv::core::Logger::Instance().Init(); + + simv::core::App app; + simv::vk::Renderer& renderer = app.Renderer(); + + simv::editor::Camera camera; + simv::editor::EditorUI editorUI; + simv::editor::MeshLoadPanel meshPanel; + + // Locate assets/meshes by probing a few ancestor directories (the binary + // runs from build//src/app, with assets/ copied alongside it). + std::filesystem::path meshDir; + for (const auto& candidate : { "../../../../../assets/meshes", + "../../../../assets/meshes", + "../../../assets/meshes", + "../../assets/meshes", + "assets/meshes" }) { + if (std::filesystem::exists(candidate)) { + meshDir = std::filesystem::canonical(candidate); + break; + } + } + if (meshDir.empty()) meshDir = "assets/meshes"; + meshPanel.SetMeshDirectory(meshDir); + + meshPanel.SetOnLoaded([&](simv::mesh::Mesh m) { + simv::mesh::WeldVertices(m, 1e-4f); + simv::core::LogFmt(simv::core::LogCategory::MeshIO, + simv::core::LogLevel::Info, + "Mesh ready: {} verts, {} tris", + m.VertexCount(), m.TriangleCount()); + renderer.SetMeshCpu(m); + // Frame the camera to the model's size (it is recentred on the origin). + const float radius = 0.5f * glm::length(m.bboxMax - m.bboxMin); + if (radius > 0.0f) camera.SetDistance(radius * 2.5f); + }); + + app.SetUiCallback([&]() { + editorUI.Draw(camera); + meshPanel.Draw(); + simv::editor::ApplyMouseInput(camera); + renderer.SetRenderMode(static_cast(editorUI.RenderMode())); + renderer.SetGridVisible(editorUI.GridVisible()); + renderer.SetViewProj(camera.ViewProj(renderer.AspectRatio())); + }); + + const int rc = app.Run(); + simv::core::Logger::Instance().Shutdown(); + return rc; + } catch (const std::exception& e) { + spdlog::critical("Fatal: {}", e.what()); + std::fprintf(stderr, "Fatal: %s\n", e.what()); + return 1; + } catch (...) { + std::fprintf(stderr, "Fatal: unknown exception\n"); + return 1; + } +} diff --git a/src/core/App.cpp b/src/core/App.cpp new file mode 100644 index 0000000..3eb3e38 --- /dev/null +++ b/src/core/App.cpp @@ -0,0 +1,33 @@ +#include "App.h" +#include "Window.h" + +#include "vk/Renderer.h" + +#include + +namespace simv::core { + +App::App() { + _window = std::make_unique(WindowDesc{}); + _renderer = std::make_unique(*_window); +} + +App::~App() { + if (_renderer) _renderer->WaitIdle(); +} + +void App::SetUiCallback(UiCallback cb) { + _renderer->SetUiCallback(std::move(cb)); +} + +int App::Run() { + spdlog::info("SimVulcan running. Close the window to exit."); + while (!_window->ShouldClose()) { + _window->PollEvents(); + _renderer->DrawFrame(); + } + _renderer->WaitIdle(); + return 0; +} + +} // namespace simv::core diff --git a/src/core/App.h b/src/core/App.h new file mode 100644 index 0000000..1266b4c --- /dev/null +++ b/src/core/App.h @@ -0,0 +1,36 @@ +#pragma once + +#include +#include + +namespace simv::vk { class Renderer; } + +namespace simv::core { + +class Window; + +// Top-level lifetime owner. Creates the window and the Vulkan renderer, runs the +// frame loop, and forwards the UI callback. Contains no Vulkan code itself — all +// of that lives behind simv::vk::Renderer. +class App { +public: + App(); + ~App(); + + App(const App&) = delete; + App& operator=(const App&) = delete; + + // ImGui panels are drawn from this callback each frame. + using UiCallback = std::function; + void SetUiCallback(UiCallback cb); + + [[nodiscard]] simv::vk::Renderer& Renderer() noexcept { return *_renderer; } + + int Run(); + +private: + std::unique_ptr _window; + std::unique_ptr _renderer; +}; + +} // namespace simv::core diff --git a/src/core/CMakeLists.txt b/src/core/CMakeLists.txt new file mode 100644 index 0000000..ac83724 --- /dev/null +++ b/src/core/CMakeLists.txt @@ -0,0 +1,14 @@ +add_library(simv_core STATIC + Logger.h + Logger.cpp + Window.h + Window.cpp + App.h + App.cpp +) +target_include_directories(simv_core PUBLIC ${CMAKE_CURRENT_SOURCE_DIR}/..) +target_link_libraries(simv_core + PUBLIC spdlog::spdlog + PRIVATE simv_vk glfw +) +simv_set_warnings(simv_core) diff --git a/src/core/Logger.cpp b/src/core/Logger.cpp new file mode 100644 index 0000000..4889599 --- /dev/null +++ b/src/core/Logger.cpp @@ -0,0 +1,129 @@ +#include "Logger.h" + +#include + +#include +#include +#include +#include + +namespace simv::core { + +namespace { + +constexpr std::array kCategoryNames = {{ + "core", "vk", "mesh", "ui", "test", +}}; +static_assert(kCategoryNames.size() == LogCategoryCount, + "kCategoryNames must have one entry per LogCategory"); + +struct CategoryEntry { + bool enabled {true}; + LogLevel minLevel {LogLevel::Info}; + double throttleSec{0.5}; + std::atomic lastLogMs {INT64_MIN}; +}; + +struct LoggerImpl { + std::array entries{}; + std::shared_ptr sink; + std::chrono::steady_clock::time_point epoch{std::chrono::steady_clock::now()}; + std::mutex initMutex; + bool initialized{false}; +}; + +LoggerImpl& Impl() { + static LoggerImpl impl; + return impl; +} + +spdlog::level::level_enum ToSpd(LogLevel l) noexcept { + switch (l) { + case LogLevel::Trace: return spdlog::level::trace; + case LogLevel::Debug: return spdlog::level::debug; + case LogLevel::Info: return spdlog::level::info; + case LogLevel::Warn: return spdlog::level::warn; + case LogLevel::Error: return spdlog::level::err; + case LogLevel::Critical: return spdlog::level::critical; + default: return spdlog::level::off; + } +} + +std::int64_t NowMs() noexcept { + using namespace std::chrono; + return duration_cast(steady_clock::now() - Impl().epoch).count(); +} + +} // namespace + +const char* CategoryName(LogCategory cat) noexcept { + const auto idx = static_cast(cat); + return idx < LogCategoryCount ? kCategoryNames[idx] : "?"; +} + +Logger& Logger::Instance() noexcept { + static Logger inst; + return inst; +} + +void Logger::Init() { + auto& impl = Impl(); + std::lock_guard lk(impl.initMutex); + if (impl.initialized) return; + + impl.sink = spdlog::stdout_color_mt("simv"); + impl.sink->set_pattern("[%H:%M:%S.%e] [%^%l%$] %v"); + impl.sink->set_level(spdlog::level::trace); + + impl.initialized = true; +} + +void Logger::Shutdown() { + auto& impl = Impl(); + std::lock_guard lk(impl.initMutex); + if (!impl.initialized) return; + impl.sink.reset(); + spdlog::drop("simv"); + impl.initialized = false; +} + +void Logger::SetMinLevel(LogCategory cat, LogLevel lvl) noexcept { + const auto idx = static_cast(cat); + if (idx < LogCategoryCount) Impl().entries[idx].minLevel = lvl; +} + +void Logger::SetThrottle(LogCategory cat, double seconds) noexcept { + const auto idx = static_cast(cat); + if (idx < LogCategoryCount) Impl().entries[idx].throttleSec = seconds; +} + +void Logger::SetEnabled(LogCategory cat, bool enabled) noexcept { + const auto idx = static_cast(cat); + if (idx < LogCategoryCount) Impl().entries[idx].enabled = enabled; +} + +void Logger::LogRaw(LogCategory cat, LogLevel lvl, std::string_view msg) noexcept { + auto& impl = Impl(); + if (!impl.initialized) Init(); + + const auto idx = static_cast(cat); + if (idx >= LogCategoryCount) return; + auto& e = impl.entries[idx]; + if (!e.enabled) return; + if (static_cast(lvl) < static_cast(e.minLevel)) return; + + // Warnings/errors bypass throttling. + const bool important = (lvl == LogLevel::Warn) || (lvl == LogLevel::Error) + || (lvl == LogLevel::Critical); + if (!important && e.throttleSec > 0.0) { + const std::int64_t nowMs = NowMs(); + const std::int64_t throttle = static_cast(e.throttleSec * 1000.0); + std::int64_t lastMs = e.lastLogMs.load(std::memory_order_relaxed); + if (lastMs != INT64_MIN && (nowMs - lastMs) < throttle) return; + e.lastLogMs.store(nowMs, std::memory_order_relaxed); + } + + impl.sink->log(ToSpd(lvl), "[{}] {}", CategoryName(cat), msg); +} + +} // namespace simv::core diff --git a/src/core/Logger.h b/src/core/Logger.h new file mode 100644 index 0000000..78fb1b9 --- /dev/null +++ b/src/core/Logger.h @@ -0,0 +1,57 @@ +#pragma once + +#include +#include + +#include +#include + +namespace simv::core { + +enum class LogLevel : std::uint8_t { + Trace, Debug, Info, Warn, Error, Critical, Off, +}; + +enum class LogCategory : std::uint8_t { + Core, + Vulkan, + MeshIO, + UI, + Test, + Count_, // sentinel +}; + +constexpr std::size_t LogCategoryCount = static_cast(LogCategory::Count_); + +const char* CategoryName(LogCategory cat) noexcept; + +// Throttled, category-aware logger. +class Logger { +public: + static Logger& Instance() noexcept; + + void Init(); // safe to call multiple times; first call wins + void Shutdown(); + + void SetMinLevel(LogCategory cat, LogLevel lvl) noexcept; + void SetThrottle(LogCategory cat, double minIntervalSeconds) noexcept; + void SetEnabled(LogCategory cat, bool enabled) noexcept; + + void LogRaw(LogCategory cat, LogLevel lvl, std::string_view msg) noexcept; + +private: + Logger() = default; + ~Logger() = default; + Logger(const Logger&) = delete; + Logger& operator=(const Logger&) = delete; +}; + +template +void LogFmt(LogCategory cat, LogLevel lvl, + fmt::format_string fmtStr, Args&&... args) +{ + Logger::Instance().LogRaw(cat, lvl, + fmt::format(fmtStr, std::forward(args)...)); +} + +} // namespace simv::core diff --git a/src/core/Window.cpp b/src/core/Window.cpp new file mode 100644 index 0000000..e852be3 --- /dev/null +++ b/src/core/Window.cpp @@ -0,0 +1,72 @@ +#include "Window.h" + +#include +#include + +namespace simv::core { + +namespace { + int s_glfwRefCount = 0; + + void GlfwErrorCallback(int code, const char* description) { + std::fprintf(stderr, "[GLFW] error %d: %s\n", code, description); + } + + void EnsureGlfwInit() { + if (s_glfwRefCount++ == 0) { + glfwSetErrorCallback(GlfwErrorCallback); + if (glfwInit() != GLFW_TRUE) { + throw std::runtime_error("glfwInit failed"); + } + } + } + + void ReleaseGlfw() { + if (--s_glfwRefCount == 0) { + glfwTerminate(); + } + } +} // namespace + +Window::Window(const WindowDesc& desc) { + EnsureGlfwInit(); + glfwWindowHint(GLFW_CLIENT_API, GLFW_NO_API); + glfwWindowHint(GLFW_RESIZABLE, desc.resizable ? GLFW_TRUE : GLFW_FALSE); + + _handle = glfwCreateWindow(desc.width, desc.height, desc.title.c_str(), + nullptr, nullptr); + if (!_handle) { + ReleaseGlfw(); + throw std::runtime_error("glfwCreateWindow failed"); + } +} + +Window::~Window() { + if (_handle) glfwDestroyWindow(_handle); + ReleaseGlfw(); +} + +bool Window::ShouldClose() const noexcept { + return glfwWindowShouldClose(_handle) == GLFW_TRUE; +} + +void Window::PollEvents() const noexcept { + glfwPollEvents(); +} + +void Window::GetFramebufferSize(int& w, int& h) const noexcept { + glfwGetFramebufferSize(_handle, &w, &h); +} + +std::vector Window::RequiredInstanceExtensions() { + EnsureGlfwInit(); // glfwGetRequiredInstanceExtensions needs GLFW initialised + std::uint32_t count = 0; + const char** raw = glfwGetRequiredInstanceExtensions(&count); + std::vector out(raw, raw + count); + ReleaseGlfw(); + return out; +} + +// Need to expose _handle storage — declared inline in header would also work, +// kept here so the GLFW header dependency stays in the .cpp. +} // namespace simv::core diff --git a/src/core/Window.h b/src/core/Window.h new file mode 100644 index 0000000..6d8ac70 --- /dev/null +++ b/src/core/Window.h @@ -0,0 +1,43 @@ +#pragma once + +#include +#include +#include + +struct GLFWwindow; + +namespace simv::core { + +struct WindowDesc { + std::string title {"SimVulcan"}; + std::int32_t width {1280}; + std::int32_t height {720}; + bool resizable{true}; +}; + +// Thin GLFW wrapper. Holds the window and exposes the bits we need to wire up +// Vulkan (required instance extensions, surface creation) and ImGui. +class Window { +public: + explicit Window(const WindowDesc& desc); + ~Window(); + + Window(const Window&) = delete; + Window& operator=(const Window&) = delete; + Window(Window&&) = delete; + Window& operator=(Window&&) = delete; + + [[nodiscard]] bool ShouldClose() const noexcept; + void PollEvents() const noexcept; + [[nodiscard]] GLFWwindow* Raw() const noexcept { return _handle; } + + void GetFramebufferSize(int& w, int& h) const noexcept; + + // Required Vulkan instance extensions for GLFW surface integration. + static std::vector RequiredInstanceExtensions(); + +private: + GLFWwindow* _handle {nullptr}; +}; + +} // namespace simv::core diff --git a/src/editor/CMakeLists.txt b/src/editor/CMakeLists.txt new file mode 100644 index 0000000..ed01d1a --- /dev/null +++ b/src/editor/CMakeLists.txt @@ -0,0 +1,15 @@ +add_library(simv_editor STATIC + Camera.h + Camera.cpp + CameraInput.h + CameraInput.cpp + EditorUI.h + EditorUI.cpp + MeshLoadPanel.h + MeshLoadPanel.cpp +) +target_include_directories(simv_editor PUBLIC ${CMAKE_CURRENT_SOURCE_DIR}/..) +target_link_libraries(simv_editor PUBLIC + simv_core simv_mesh imgui glm::glm +) +simv_set_warnings(simv_editor) diff --git a/src/editor/Camera.cpp b/src/editor/Camera.cpp new file mode 100644 index 0000000..b9703ad --- /dev/null +++ b/src/editor/Camera.cpp @@ -0,0 +1,58 @@ +#define GLM_FORCE_DEPTH_ZERO_TO_ONE +#include "Camera.h" + +#include + +#include +#include + +namespace simv::editor { + +namespace { +constexpr float kPi = 3.14159265358979323846f; +constexpr float kPitchLimit = 1.55334f; // ~89°, avoids the lookAt singularity +constexpr float kMinDist = 0.5f; +constexpr float kMaxDist = 200.0f; +} + +void Camera::Orbit(float dYaw, float dPitch) { + _yaw += dYaw; + _pitch = std::clamp(_pitch + dPitch, -kPitchLimit, kPitchLimit); +} + +void Camera::Zoom(float delta) { + _distance = std::clamp(_distance * std::exp(-delta * 0.15f), kMinDist, kMaxDist); +} + +void Camera::SetDistance(float d) { + _distance = std::clamp(d, kMinDist, kMaxDist); +} + +void Camera::AlignToPlane(int axis) { + switch (axis) { + case 1: _yaw = 0.0f; _pitch = kPitchLimit; break; // Top (down -Y, XZ) + case 2: _yaw = kPi * 0.5f; _pitch = 0.0f; break; // Side (down -X, YZ) + default: _yaw = 0.0f; _pitch = 0.0f; break; // Front(down -Z, XY) + } +} + +glm::mat4 Camera::View() const { + const glm::vec3 target(0.0f); + const glm::vec3 eye = target + _distance * glm::vec3( + std::cos(_pitch) * std::sin(_yaw), + std::sin(_pitch), + std::cos(_pitch) * std::cos(_yaw)); + return glm::lookAt(eye, target, glm::vec3(0.0f, 1.0f, 0.0f)); +} + +glm::mat4 Camera::Proj(float aspect) const { + glm::mat4 p = glm::perspective(glm::radians(45.0f), aspect, 0.05f, 500.0f); + p[1][1] *= -1.0f; // Vulkan's clip space has +Y down + return p; +} + +glm::mat4 Camera::ViewProj(float aspect) const { + return Proj(aspect) * View(); +} + +} // namespace simv::editor diff --git a/src/editor/Camera.h b/src/editor/Camera.h new file mode 100644 index 0000000..5b124af --- /dev/null +++ b/src/editor/Camera.h @@ -0,0 +1,34 @@ +#pragma once + +#include + +namespace simv::editor { + +// Orbit camera fixed on the world origin. Yaw/pitch place the eye on a sphere of +// the given radius around (0,0,0); the view always looks at the centre. Pure glm +// math — no Vulkan dependency. +class Camera { +public: + // Rotate around the target (radians). + void Orbit(float dYaw, float dPitch); + + // Dolly in/out. Positive `delta` (e.g. scroll up) moves closer. + void Zoom(float delta); + + // Snap to look squarely at one of the three principal planes: + // 0 = Front (down -Z, XY plane), 1 = Top (down -Y, XZ), 2 = Side (down -X, YZ). + void AlignToPlane(int axis); + + void SetDistance(float d); + + [[nodiscard]] glm::mat4 View() const; + [[nodiscard]] glm::mat4 Proj(float aspect) const; // Vulkan clip space + [[nodiscard]] glm::mat4 ViewProj(float aspect) const; + +private: + float _yaw {0.6f}; // radians around +Y + float _pitch {0.5f}; // radians above the XZ plane + float _distance {8.0f}; +}; + +} // namespace simv::editor diff --git a/src/editor/CameraInput.cpp b/src/editor/CameraInput.cpp new file mode 100644 index 0000000..606044c --- /dev/null +++ b/src/editor/CameraInput.cpp @@ -0,0 +1,21 @@ +#include "CameraInput.h" +#include "Camera.h" + +#include + +namespace simv::editor { + +void ApplyMouseInput(Camera& camera) { + const ImGuiIO& io = ImGui::GetIO(); + if (io.WantCaptureMouse) return; // pointer is over a panel + + if (ImGui::IsMouseDragging(ImGuiMouseButton_Left)) { + constexpr float kOrbitSpeed = 0.01f; // radians per pixel + camera.Orbit(io.MouseDelta.x * kOrbitSpeed, -io.MouseDelta.y * kOrbitSpeed); + } + if (io.MouseWheel != 0.0f) { + camera.Zoom(io.MouseWheel * 0.5f); + } +} + +} // namespace simv::editor diff --git a/src/editor/CameraInput.h b/src/editor/CameraInput.h new file mode 100644 index 0000000..b23396e --- /dev/null +++ b/src/editor/CameraInput.h @@ -0,0 +1,12 @@ +#pragma once + +namespace simv::editor { + +class Camera; + +// Maps mouse input (ImGui IO) to camera orbit/zoom. Ignored while the pointer is +// over an ImGui window so panel interaction doesn't move the view. Call once per +// frame after ImGui::NewFrame. +void ApplyMouseInput(Camera& camera); + +} // namespace simv::editor diff --git a/src/editor/EditorUI.cpp b/src/editor/EditorUI.cpp new file mode 100644 index 0000000..74eaa3d --- /dev/null +++ b/src/editor/EditorUI.cpp @@ -0,0 +1,32 @@ +#include "EditorUI.h" +#include "Camera.h" + +#include + +namespace simv::editor { + +void EditorUI::Draw(Camera& camera) { + ImGui::SetNextWindowSize(ImVec2(280.0f, 200.0f), ImGuiCond_FirstUseEver); + if (!ImGui::Begin("Viewport")) { ImGui::End(); return; } + + ImGui::TextDisabled("Camera"); + if (ImGui::Button("Front")) camera.AlignToPlane(0); + ImGui::SameLine(); + if (ImGui::Button("Top")) camera.AlignToPlane(1); + ImGui::SameLine(); + if (ImGui::Button("Side")) camera.AlignToPlane(2); + ImGui::TextDisabled("Drag to orbit · wheel to zoom"); + + ImGui::Separator(); + ImGui::TextDisabled("Model display"); + ImGui::RadioButton("Solid", &_renderMode, 0); + ImGui::RadioButton("Wireframe", &_renderMode, 1); + ImGui::RadioButton("Solid+Wire", &_renderMode, 2); + + ImGui::Separator(); + ImGui::Checkbox("Show grid", &_gridVisible); + + ImGui::End(); +} + +} // namespace simv::editor diff --git a/src/editor/EditorUI.h b/src/editor/EditorUI.h new file mode 100644 index 0000000..1389618 --- /dev/null +++ b/src/editor/EditorUI.h @@ -0,0 +1,23 @@ +#pragma once + +namespace simv::editor { + +class Camera; + +// Small editor control panel: camera plane-alignment buttons, model display mode +// (0=Solid, 1=Wireframe, 2=Solid+Wireframe), and grid visibility. Holds the +// chosen state; the app reads it each frame and forwards it to the renderer. +class EditorUI { +public: + // Call between ImGui::NewFrame and ImGui::Render. + void Draw(Camera& camera); + + [[nodiscard]] int RenderMode() const noexcept { return _renderMode; } + [[nodiscard]] bool GridVisible() const noexcept { return _gridVisible; } + +private: + int _renderMode {0}; + bool _gridVisible {true}; +}; + +} // namespace simv::editor diff --git a/src/editor/MeshLoadPanel.cpp b/src/editor/MeshLoadPanel.cpp new file mode 100644 index 0000000..9050d4f --- /dev/null +++ b/src/editor/MeshLoadPanel.cpp @@ -0,0 +1,85 @@ +#include "MeshLoadPanel.h" + +#include "mesh/ObjLoader.h" + +#include + +#include +#include +#include +#include + +namespace simv::editor { + +MeshLoadPanel::MeshLoadPanel() { RescanFiles(); } + +void MeshLoadPanel::RescanFiles() { + _objFiles.clear(); + if (!std::filesystem::exists(_meshDir)) return; + auto isObjExt = [](const std::filesystem::path& p) { + // case-insensitive — `Cube.obj`, `cube.OBJ`, `Plane.Obj` all count. + std::string ext = p.extension().string(); + for (auto& c : ext) c = static_cast(std::tolower(static_cast(c))); + return ext == ".obj"; + }; + for (const auto& e : std::filesystem::directory_iterator(_meshDir)) { + if (!e.is_regular_file()) continue; + if (isObjExt(e.path())) { + _objFiles.push_back(e.path().filename().string()); + } + } + std::sort(_objFiles.begin(), _objFiles.end()); +} + +void MeshLoadPanel::Draw() { + if (!_open) return; + + // Drain pending future on the main thread. + if (_pending.valid()) { + const auto status = _pending.wait_for(std::chrono::milliseconds(0)); + if (status == std::future_status::ready) { + try { + auto m = _pending.get(); + if (_onLoaded) _onLoaded(std::move(m)); + _statusMsg = "Loaded."; + } catch (const std::exception& e) { + _statusMsg = std::string("Error: ") + e.what(); + } + } + } + + ImGui::SetNextWindowSize(ImVec2(360.0f, 240.0f), ImGuiCond_FirstUseEver); + if (!ImGui::Begin("Mesh", &_open)) { ImGui::End(); return; } + + ImGui::TextDisabled("Source: %s", _meshDir.string().c_str()); + if (ImGui::SmallButton("Rescan")) RescanFiles(); + ImGui::Separator(); + + if (ImGui::BeginListBox("##objs", ImVec2(-1.0f, 120.0f))) { + for (int i = 0; i < static_cast(_objFiles.size()); ++i) { + const bool selected = (i == _selected); + if (ImGui::Selectable(_objFiles[i].c_str(), selected)) _selected = i; + if (selected) ImGui::SetItemDefaultFocus(); + } + ImGui::EndListBox(); + } + + ImGui::BeginDisabled(_selected < 0 || _pending.valid()); + if (ImGui::Button("Load (async)")) { + _statusMsg = "Loading..."; + _pending = simv::mesh::LoadObjAsync(_meshDir / _objFiles[_selected]); + } + ImGui::EndDisabled(); + + if (_pending.valid()) { + ImGui::SameLine(); + ImGui::TextDisabled("(loading...)"); + } + if (!_statusMsg.empty()) { + ImGui::Separator(); + ImGui::TextWrapped("%s", _statusMsg.c_str()); + } + ImGui::End(); +} + +} // namespace simv::editor diff --git a/src/editor/MeshLoadPanel.h b/src/editor/MeshLoadPanel.h new file mode 100644 index 0000000..dfc012c --- /dev/null +++ b/src/editor/MeshLoadPanel.h @@ -0,0 +1,40 @@ +#pragma once + +#include "mesh/Mesh.h" + +#include +#include +#include +#include +#include + +namespace simv::editor { + +// Lists *.obj files under a directory and lets the user kick off an async load. +// When the future is ready, fires the supplied callback on the main thread from +// Draw(). No Vulkan dependency — produces a CPU mesh for the renderer to upload. +class MeshLoadPanel { +public: + using OnLoadedFn = std::function; + + MeshLoadPanel(); + + void SetMeshDirectory(std::filesystem::path dir) { _meshDir = std::move(dir); RescanFiles(); } + void SetOnLoaded(OnLoadedFn cb) { _onLoaded = std::move(cb); } + + // Call between ImGui::NewFrame and ImGui::Render. + void Draw(); + +private: + void RescanFiles(); + + std::filesystem::path _meshDir {"assets/meshes"}; + std::vector _objFiles; + int _selected {-1}; + std::string _statusMsg; + std::future _pending; + OnLoadedFn _onLoaded; + bool _open {true}; +}; + +} // namespace simv::editor diff --git a/src/mesh/CMakeLists.txt b/src/mesh/CMakeLists.txt new file mode 100644 index 0000000..191cc32 --- /dev/null +++ b/src/mesh/CMakeLists.txt @@ -0,0 +1,13 @@ +add_library(simv_mesh STATIC + Mesh.h + Mesh.cpp + ObjLoader.h + ObjLoader.cpp + MeshDecimator.h + MeshDecimator.cpp +) +target_include_directories(simv_mesh PUBLIC ${CMAKE_CURRENT_SOURCE_DIR}/..) +target_link_libraries(simv_mesh PUBLIC + glm::glm tinyobjloader simv_core +) +simv_set_warnings(simv_mesh) diff --git a/src/mesh/Mesh.cpp b/src/mesh/Mesh.cpp new file mode 100644 index 0000000..501cf8f --- /dev/null +++ b/src/mesh/Mesh.cpp @@ -0,0 +1,26 @@ +#include "Mesh.h" + +#include +#include + +#include // glm::min / glm::max for vec3 + +namespace simv::mesh { + +void Mesh::RecalculateBounds() noexcept { + if (positions.empty()) { + bboxMin = glm::vec3{0.0f}; + bboxMax = glm::vec3{0.0f}; + return; + } + glm::vec3 lo{ std::numeric_limits::max() }; + glm::vec3 hi{ std::numeric_limits::lowest() }; + for (const auto& p : positions) { + lo = glm::min(lo, p); + hi = glm::max(hi, p); + } + bboxMin = lo; + bboxMax = hi; +} + +} // namespace simv::mesh diff --git a/src/mesh/Mesh.h b/src/mesh/Mesh.h new file mode 100644 index 0000000..73b089b --- /dev/null +++ b/src/mesh/Mesh.h @@ -0,0 +1,23 @@ +#pragma once + +#include +#include +#include + +namespace simv::mesh { + +// CPU-side triangle soup. Loaded by ObjLoader, optionally decimated, then uploaded to GpuMesh. +struct Mesh { + std::vector positions; + std::vector indices; // 3 per triangle + glm::vec3 bboxMin {0.0f}; + glm::vec3 bboxMax {0.0f}; + + [[nodiscard]] std::size_t VertexCount() const noexcept { return positions.size(); } + [[nodiscard]] std::size_t TriangleCount() const noexcept { return indices.size() / 3; } + [[nodiscard]] bool Empty() const noexcept { return positions.empty() || indices.empty(); } + + void RecalculateBounds() noexcept; +}; + +} // namespace simv::mesh diff --git a/src/mesh/MeshDecimator.cpp b/src/mesh/MeshDecimator.cpp new file mode 100644 index 0000000..99d2e30 --- /dev/null +++ b/src/mesh/MeshDecimator.cpp @@ -0,0 +1,88 @@ +#include "MeshDecimator.h" + +#include +#include +#include + +namespace simv::mesh { + +namespace { + +struct CellKey { + std::int32_t x, y, z; + bool operator==(const CellKey& o) const noexcept { + return x == o.x && y == o.y && z == o.z; + } +}; + +struct CellHash { + std::size_t operator()(const CellKey& k) const noexcept { + // FNV-1a-style mix on three int32. Cheap and good for this density. + std::uint64_t h = 0xcbf29ce484222325ULL; + auto mix = [&](std::int32_t v) { + h ^= static_cast(static_cast(v)); + h *= 0x100000001b3ULL; + }; + mix(k.x); mix(k.y); mix(k.z); + return static_cast(h); + } +}; + +// Round-to-nearest grouping: any two points within `tolerance` of each other +// are guaranteed to map to the same cell when both are within tolerance of a +// shared grid node. floor()-based bucketing breaks at cell boundaries when +// floats land on either side; round() is the standard fix for spatial-hash +// welding. +inline CellKey ToCell(const glm::vec3& p, float tolerance) noexcept { + const double t = static_cast(tolerance); + return { + static_cast(std::lround(static_cast(p.x) / t)), + static_cast(std::lround(static_cast(p.y) / t)), + static_cast(std::lround(static_cast(p.z) / t)), + }; +} + +} // namespace + +void WeldVertices(Mesh& mesh, float tolerance) { + if (mesh.positions.empty() || tolerance <= 0.0f) return; + + std::unordered_map cellToVertex; + cellToVertex.reserve(mesh.positions.size()); + + std::vector welded; + std::vector remap(mesh.positions.size()); + welded.reserve(mesh.positions.size()); + + for (std::size_t i = 0; i < mesh.positions.size(); ++i) { + const auto cell = ToCell(mesh.positions[i], tolerance); + auto it = cellToVertex.find(cell); + if (it == cellToVertex.end()) { + const auto idx = static_cast(welded.size()); + cellToVertex.emplace(cell, idx); + welded.push_back(mesh.positions[i]); + remap[i] = idx; + } else { + remap[i] = it->second; + } + } + + // Rewrite indices and drop degenerate triangles (where >= 2 verts collapsed). + std::vector newIndices; + newIndices.reserve(mesh.indices.size()); + for (std::size_t i = 0; i + 2 < mesh.indices.size(); i += 3) { + const auto a = remap[mesh.indices[i]]; + const auto b = remap[mesh.indices[i + 1]]; + const auto c = remap[mesh.indices[i + 2]]; + if (a == b || b == c || a == c) continue; + newIndices.push_back(a); + newIndices.push_back(b); + newIndices.push_back(c); + } + + mesh.positions = std::move(welded); + mesh.indices = std::move(newIndices); + mesh.RecalculateBounds(); +} + +} // namespace simv::mesh diff --git a/src/mesh/MeshDecimator.h b/src/mesh/MeshDecimator.h new file mode 100644 index 0000000..91eb7fd --- /dev/null +++ b/src/mesh/MeshDecimator.h @@ -0,0 +1,14 @@ +#pragma once + +#include "Mesh.h" + +#include + +namespace simv::mesh { + +// Spatial-hash vertex welding. Collapses positions that fall within `tolerance` +// of each other into a single canonical vertex, rewrites the indices, drops any +// triangle that becomes degenerate, and recomputes the bounds. +void WeldVertices(Mesh& mesh, float tolerance); + +} // namespace simv::mesh diff --git a/src/mesh/ObjLoader.cpp b/src/mesh/ObjLoader.cpp new file mode 100644 index 0000000..1ee95e7 --- /dev/null +++ b/src/mesh/ObjLoader.cpp @@ -0,0 +1,68 @@ +#include "ObjLoader.h" + +#include "core/Logger.h" + +#define TINYOBJLOADER_IMPLEMENTATION +#include + +#include + +namespace simv::mesh { + +Mesh LoadObj(const std::filesystem::path& path) { + tinyobj::ObjReaderConfig cfg; + cfg.triangulate = true; + cfg.vertex_color = false; + + tinyobj::ObjReader reader; + if (!reader.ParseFromFile(path.string(), cfg)) { + const auto& err = reader.Error(); + throw std::runtime_error("LoadObj: " + path.string() + ": " + err); + } + if (!reader.Warning().empty()) { + simv::core::LogFmt(simv::core::LogCategory::MeshIO, + simv::core::LogLevel::Warn, + "OBJ warnings ({}): {}", path.string(), reader.Warning()); + } + + const auto& attrib = reader.GetAttrib(); + const auto& shapes = reader.GetShapes(); + + Mesh m; + // Vertex positions are global (not per-shape). Reuse the same vector. + m.positions.reserve(attrib.vertices.size() / 3); + for (std::size_t i = 0; i + 2 < attrib.vertices.size(); i += 3) { + m.positions.emplace_back(attrib.vertices[i], + attrib.vertices[i + 1], + attrib.vertices[i + 2]); + } + + std::size_t triCount = 0; + for (const auto& s : shapes) triCount += s.mesh.indices.size() / 3; + m.indices.reserve(triCount * 3); + + for (const auto& s : shapes) { + const auto& idx = s.mesh.indices; + for (std::size_t i = 0; i + 2 < idx.size(); i += 3) { + m.indices.push_back(static_cast(idx[i].vertex_index)); + m.indices.push_back(static_cast(idx[i + 1].vertex_index)); + m.indices.push_back(static_cast(idx[i + 2].vertex_index)); + } + } + + m.RecalculateBounds(); + + simv::core::LogFmt(simv::core::LogCategory::MeshIO, + simv::core::LogLevel::Info, + "Loaded OBJ '{}': {} verts, {} tris", + path.filename().string(), m.VertexCount(), m.TriangleCount()); + return m; +} + +std::future LoadObjAsync(std::filesystem::path path) { + return std::async(std::launch::async, [p = std::move(path)] { + return LoadObj(p); + }); +} + +} // namespace simv::mesh diff --git a/src/mesh/ObjLoader.h b/src/mesh/ObjLoader.h new file mode 100644 index 0000000..64ade20 --- /dev/null +++ b/src/mesh/ObjLoader.h @@ -0,0 +1,17 @@ +#pragma once + +#include "Mesh.h" + +#include +#include +#include + +namespace simv::mesh { + +// Synchronous loader (small files, tests). +Mesh LoadObj(const std::filesystem::path& path); + +// Async loader — runs on a worker thread. Caller owns the future. +std::future LoadObjAsync(std::filesystem::path path); + +} // namespace simv::mesh diff --git a/src/vk/Buffer.cpp b/src/vk/Buffer.cpp new file mode 100644 index 0000000..014c4d6 --- /dev/null +++ b/src/vk/Buffer.cpp @@ -0,0 +1,130 @@ +#include "Buffer.h" +#include "Context.h" + +#include + +#include +#include +#include + +namespace simv::vk { + +namespace { +VkBufferUsageFlags ToVkUsage(BufferUsage u) noexcept { + VkBufferUsageFlags f = 0; + if (Has(u, BufferUsage::Storage)) f |= VK_BUFFER_USAGE_STORAGE_BUFFER_BIT; + if (Has(u, BufferUsage::Uniform)) f |= VK_BUFFER_USAGE_UNIFORM_BUFFER_BIT; + if (Has(u, BufferUsage::Index)) f |= VK_BUFFER_USAGE_INDEX_BUFFER_BIT; + if (Has(u, BufferUsage::Vertex)) f |= VK_BUFFER_USAGE_VERTEX_BUFFER_BIT; + if (Has(u, BufferUsage::Indirect)) f |= VK_BUFFER_USAGE_INDIRECT_BUFFER_BIT; + if (Has(u, BufferUsage::TransferSrc)) f |= VK_BUFFER_USAGE_TRANSFER_SRC_BIT; + if (Has(u, BufferUsage::TransferDst)) f |= VK_BUFFER_USAGE_TRANSFER_DST_BIT; + return f; +} +} // namespace + +Buffer::Buffer(Context& ctx, VkDeviceSize size, BufferUsage usage, MemoryLocation loc, + bool persistentMapped) + : _ctx(&ctx), _size(size) +{ + VkBufferCreateInfo bi{}; + bi.sType = VK_STRUCTURE_TYPE_BUFFER_CREATE_INFO; + bi.size = size; + bi.usage = ToVkUsage(usage); + bi.sharingMode = VK_SHARING_MODE_EXCLUSIVE; + + VmaAllocationCreateInfo ai{}; + switch (loc) { + case MemoryLocation::DeviceLocal: + ai.usage = VMA_MEMORY_USAGE_AUTO_PREFER_DEVICE; + break; + case MemoryLocation::HostVisible: + ai.usage = VMA_MEMORY_USAGE_AUTO_PREFER_HOST; + ai.flags = VMA_ALLOCATION_CREATE_HOST_ACCESS_SEQUENTIAL_WRITE_BIT; + break; + case MemoryLocation::HostReadback: + ai.usage = VMA_MEMORY_USAGE_AUTO_PREFER_HOST; + ai.flags = VMA_ALLOCATION_CREATE_HOST_ACCESS_RANDOM_BIT; + break; + } + if (persistentMapped) { + ai.flags |= VMA_ALLOCATION_CREATE_MAPPED_BIT; + } + + VmaAllocationInfo info{}; + if (vmaCreateBuffer(_ctx->Allocator(), &bi, &ai, &_handle, &_alloc, &info) != VK_SUCCESS) { + throw std::runtime_error("vmaCreateBuffer failed"); + } + if (persistentMapped) _mapped = info.pMappedData; +} + +Buffer::~Buffer() { Free(); } + +Buffer::Buffer(Buffer&& other) noexcept + : _ctx(other._ctx), _handle(other._handle), _alloc(other._alloc), + _size(other._size), _mapped(other._mapped) +{ + other._ctx = nullptr; + other._handle = VK_NULL_HANDLE; + other._alloc = nullptr; + other._size = 0; + other._mapped = nullptr; +} + +Buffer& Buffer::operator=(Buffer&& other) noexcept { + if (this != &other) { + Free(); + _ctx = other._ctx; + _handle = other._handle; + _alloc = other._alloc; + _size = other._size; + _mapped = other._mapped; + other._ctx = nullptr; + other._handle = VK_NULL_HANDLE; + other._alloc = nullptr; + other._size = 0; + other._mapped = nullptr; + } + return *this; +} + +void Buffer::Free() { + if (_handle && _ctx) { + if (_mapped) { + // VMA tracks mapping count; only unmap if persistent. + // For persistent-mapped allocations the mapping is destroyed by vmaDestroyBuffer. + _mapped = nullptr; + } + vmaDestroyBuffer(_ctx->Allocator(), _handle, _alloc); + } + _ctx = nullptr; _handle = VK_NULL_HANDLE; _alloc = nullptr; _size = 0; +} + +void* Buffer::Map() { + assert(_alloc); + if (_mapped) return _mapped; + void* p = nullptr; + if (vmaMapMemory(_ctx->Allocator(), _alloc, &p) != VK_SUCCESS) { + throw std::runtime_error("vmaMapMemory failed"); + } + return p; +} + +void Buffer::Unmap() { + if (!_mapped && _alloc) { + vmaUnmapMemory(_ctx->Allocator(), _alloc); + } +} + +void Buffer::Write(const void* src, VkDeviceSize size, VkDeviceSize dstOffset) { + assert(src && size && _alloc); + if (_mapped) { + std::memcpy(static_cast(_mapped) + dstOffset, src, size); + } else { + void* p = Map(); + std::memcpy(static_cast(p) + dstOffset, src, size); + Unmap(); + } +} + +} // namespace simv::vk diff --git a/src/vk/Buffer.h b/src/vk/Buffer.h new file mode 100644 index 0000000..e623799 --- /dev/null +++ b/src/vk/Buffer.h @@ -0,0 +1,73 @@ +#pragma once + +#include +#include +#include + +struct VmaAllocation_T; +using VmaAllocation = VmaAllocation_T*; + +namespace simv::vk { + +class Context; + +enum class BufferUsage : std::uint32_t { + Storage = 1u << 0, // VK_BUFFER_USAGE_STORAGE_BUFFER_BIT + Uniform = 1u << 1, + Index = 1u << 2, + Vertex = 1u << 3, + Indirect = 1u << 4, + TransferSrc = 1u << 5, + TransferDst = 1u << 6, +}; + +inline BufferUsage operator|(BufferUsage a, BufferUsage b) noexcept { + return static_cast(static_cast(a) | static_cast(b)); +} +inline bool Has(BufferUsage v, BufferUsage flag) noexcept { + return (static_cast(v) & static_cast(flag)) != 0u; +} + +enum class MemoryLocation : std::uint8_t { + DeviceLocal, // GPU-only (fastest); reach via staging + HostVisible, // CPU-mappable (staging, small UBOs) + HostReadback, // host-visible + cached (read after GPU write) +}; + +// Move-only RAII over a VMA-allocated VkBuffer. +class Buffer { +public: + Buffer() = default; + Buffer(Context& ctx, VkDeviceSize size, BufferUsage usage, MemoryLocation loc, + bool persistentMapped = false); + ~Buffer(); + + Buffer(const Buffer&) = delete; + Buffer& operator=(const Buffer&) = delete; + Buffer(Buffer&& other) noexcept; + Buffer& operator=(Buffer&& other) noexcept; + + void Free(); + + [[nodiscard]] VkBuffer Handle() const noexcept { return _handle; } + [[nodiscard]] VmaAllocation Allocation() const noexcept { return _alloc; } + [[nodiscard]] VkDeviceSize Size() const noexcept { return _size; } + [[nodiscard]] void* MappedPtr() const noexcept { return _mapped; } + [[nodiscard]] bool IsValid() const noexcept { return _handle != VK_NULL_HANDLE; } + + // Non-mapped buffers can still be temporarily mapped via Map/Unmap. + void* Map(); + void Unmap(); + + // Convenience: copy `size` bytes into the buffer (host-visible only). + void Write(const void* src, VkDeviceSize size, VkDeviceSize dstOffset = 0); + +private: + Context* _ctx {nullptr}; + VkBuffer _handle {VK_NULL_HANDLE}; + VmaAllocation _alloc {nullptr}; + VkDeviceSize _size {0}; + void* _mapped {nullptr}; +}; + +} // namespace simv::vk diff --git a/src/vk/CMakeLists.txt b/src/vk/CMakeLists.txt new file mode 100644 index 0000000..dfed115 --- /dev/null +++ b/src/vk/CMakeLists.txt @@ -0,0 +1,30 @@ +add_library(simv_vk STATIC + Context.h + Context.cpp + Buffer.h + Buffer.cpp + Image.h + Image.cpp + Shader.h + Shader.cpp + Swapchain.h + Swapchain.cpp + GpuMesh.h + GpuMesh.cpp + RenderMode.h + MeshRenderer.h + MeshRenderer.cpp + GridRenderer.h + GridRenderer.cpp + Renderer.h + Renderer.cpp +) +target_include_directories(simv_vk PUBLIC ${CMAKE_CURRENT_SOURCE_DIR}/..) +target_link_libraries(simv_vk PUBLIC + Vulkan::Headers volk vk-bootstrap::vk-bootstrap + GPUOpen::VulkanMemoryAllocator + glfw glm::glm spdlog::spdlog + PRIVATE imgui +) +target_compile_definitions(simv_vk PUBLIC VK_NO_PROTOTYPES) +simv_set_warnings(simv_vk) diff --git a/src/vk/Context.cpp b/src/vk/Context.cpp new file mode 100644 index 0000000..3e5a868 --- /dev/null +++ b/src/vk/Context.cpp @@ -0,0 +1,213 @@ +#include "Context.h" + +#include "core/Window.h" + +#include + +#define VMA_IMPLEMENTATION +#define VMA_STATIC_VULKAN_FUNCTIONS 0 +#define VMA_DYNAMIC_VULKAN_FUNCTIONS 1 +#include + +#include +#include + +#include +#include +#include +#include + +namespace simv::vk { + +namespace { + +VKAPI_ATTR VkBool32 VKAPI_CALL DebugUtilsCallback( + VkDebugUtilsMessageSeverityFlagBitsEXT severity, + VkDebugUtilsMessageTypeFlagsEXT /*type*/, + const VkDebugUtilsMessengerCallbackDataEXT* data, + void* /*user*/) +{ + if (severity & VK_DEBUG_UTILS_MESSAGE_SEVERITY_ERROR_BIT_EXT) { + spdlog::error("[VK] {}", data->pMessage); + } else if (severity & VK_DEBUG_UTILS_MESSAGE_SEVERITY_WARNING_BIT_EXT) { + spdlog::warn("[VK] {}", data->pMessage); + } else if (severity & VK_DEBUG_UTILS_MESSAGE_SEVERITY_INFO_BIT_EXT) { + spdlog::info("[VK] {}", data->pMessage); + } + return VK_FALSE; +} + +} // namespace + +Context::Context(simv::core::Window& window, const ContextOptions& opts) { + if (volkInitialize() != VK_SUCCESS) { + throw std::runtime_error("volkInitialize failed — Vulkan loader not found"); + } + + // ----- Instance ----- + vkb::InstanceBuilder ib; + ib.set_app_name("SimVulcan") + .set_engine_name("simv") + .require_api_version(1, 3, 0); + + if (opts.enableValidation) ib.request_validation_layers(true); + if (opts.enableDebugUtils) { + ib.set_debug_callback(DebugUtilsCallback) + .set_debug_messenger_severity( + VK_DEBUG_UTILS_MESSAGE_SEVERITY_ERROR_BIT_EXT + | VK_DEBUG_UTILS_MESSAGE_SEVERITY_WARNING_BIT_EXT) + .set_debug_messenger_type( + VK_DEBUG_UTILS_MESSAGE_TYPE_GENERAL_BIT_EXT + | VK_DEBUG_UTILS_MESSAGE_TYPE_VALIDATION_BIT_EXT + | VK_DEBUG_UTILS_MESSAGE_TYPE_PERFORMANCE_BIT_EXT); + } + + auto instRes = ib.build(); + if (!instRes) { + throw std::runtime_error("vkb::InstanceBuilder::build failed: " + instRes.error().message()); + } + auto inst = instRes.value(); + _instance = inst.instance; + _debugMessenger = inst.debug_messenger; + _validationEnabled = opts.enableValidation; + volkLoadInstance(_instance); + + // ----- Surface (GLFW) ----- + if (glfwCreateWindowSurface(_instance, window.Raw(), nullptr, &_surface) != VK_SUCCESS) { + throw std::runtime_error("glfwCreateWindowSurface failed"); + } + + // ----- Physical device + features ----- + VkPhysicalDeviceVulkan13Features feat13{}; + feat13.sType = VK_STRUCTURE_TYPE_PHYSICAL_DEVICE_VULKAN_1_3_FEATURES; + feat13.synchronization2 = VK_TRUE; + feat13.dynamicRendering = VK_TRUE; + + VkPhysicalDeviceVulkan12Features feat12{}; + feat12.sType = VK_STRUCTURE_TYPE_PHYSICAL_DEVICE_VULKAN_1_2_FEATURES; + feat12.timelineSemaphore = VK_TRUE; + feat12.descriptorIndexing = VK_TRUE; + feat12.bufferDeviceAddress = VK_TRUE; + feat12.shaderSubgroupExtendedTypes = VK_TRUE; + feat12.scalarBlockLayout = VK_TRUE; + feat12.runtimeDescriptorArray = VK_TRUE; + + // fillModeNonSolid: required for the wireframe (line polygon mode) pipeline. + VkPhysicalDeviceFeatures feat10{}; + feat10.fillModeNonSolid = VK_TRUE; + + vkb::PhysicalDeviceSelector ps(inst); + ps.set_surface(_surface) + .set_minimum_version(1, 3) + .set_required_features(feat10) + .set_required_features_13(feat13) + .set_required_features_12(feat12); + + auto pdRes = ps.select(); + if (!pdRes) { + throw std::runtime_error("vkb PhysicalDeviceSelector failed: " + pdRes.error().message()); + } + auto pd = pdRes.value(); + _phys = pd.physical_device; + + // ----- Logical device ----- + vkb::DeviceBuilder db(pd); + auto devRes = db.build(); + if (!devRes) { + throw std::runtime_error("vkb::DeviceBuilder::build failed: " + devRes.error().message()); + } + auto dev = devRes.value(); + _device = dev.device; + volkLoadDevice(_device); + + // ----- Queues (graphics, compute, transfer; fall back to graphics if dedicated unavailable) ----- + auto pickQueue = [&](vkb::QueueType t, std::uint32_t& outFamily, VkQueue& outHandle) { + auto qRes = dev.get_queue(t); + auto fRes = dev.get_queue_index(t); + if (qRes && fRes) { outHandle = qRes.value(); outFamily = fRes.value(); return true; } + return false; + }; + + if (!pickQueue(vkb::QueueType::graphics, _graphicsFamily, _graphicsQueue)) { + throw std::runtime_error("No graphics queue available"); + } + if (!opts.requireAsyncCompute || !pickQueue(vkb::QueueType::compute, _computeFamily, _computeQueue)) { + _computeQueue = _graphicsQueue; _computeFamily = _graphicsFamily; + spdlog::warn("[VK] No dedicated compute queue - using graphics queue."); + } + if (!opts.requireAsyncTransfer || !pickQueue(vkb::QueueType::transfer, _transferFamily, _transferQueue)) { + _transferQueue = _graphicsQueue; _transferFamily = _graphicsFamily; + spdlog::warn("[VK] No dedicated transfer queue - using graphics queue."); + } + + // ----- VMA allocator (dynamic function pointers via volk) ----- + VmaVulkanFunctions vfn{}; + vfn.vkGetInstanceProcAddr = vkGetInstanceProcAddr; + vfn.vkGetDeviceProcAddr = vkGetDeviceProcAddr; + + VmaAllocatorCreateInfo aci{}; + aci.flags = VMA_ALLOCATOR_CREATE_BUFFER_DEVICE_ADDRESS_BIT; + aci.physicalDevice = _phys; + aci.device = _device; + aci.instance = _instance; + aci.vulkanApiVersion = VK_API_VERSION_1_3; + aci.pVulkanFunctions = &vfn; + + if (vmaCreateAllocator(&aci, &_allocator) != VK_SUCCESS) { + throw std::runtime_error("vmaCreateAllocator failed"); + } + + // ----- Persistent pipeline cache (disk-backed) ----- + // Saves pipeline-build time on warm starts by reusing vendor ISA. + std::vector cacheBlob; + std::filesystem::path cachePath = "pipeline_cache.bin"; + if (std::filesystem::exists(cachePath)) { + std::ifstream f(cachePath, std::ios::binary | std::ios::ate); + if (f) { + const auto sz = static_cast(f.tellg()); + cacheBlob.resize(sz); + f.seekg(0); + f.read(cacheBlob.data(), static_cast(sz)); + } + } + VkPipelineCacheCreateInfo pcci{ VK_STRUCTURE_TYPE_PIPELINE_CACHE_CREATE_INFO }; + pcci.initialDataSize = cacheBlob.size(); + pcci.pInitialData = cacheBlob.empty() ? nullptr : cacheBlob.data(); + if (vkCreatePipelineCache(_device, &pcci, nullptr, &_pipelineCache) != VK_SUCCESS) { + spdlog::warn("[VK] pipeline cache creation failed; pipelines will rebuild every run"); + } else { + spdlog::info("Vulkan pipeline cache loaded: {} bytes", cacheBlob.size()); + } + + spdlog::info("Vulkan context ready: {}", pd.name); +} + +Context::~Context() { + // Save the pipeline cache before tearing the device down. + if (_pipelineCache) { + std::size_t sz = 0; + if (vkGetPipelineCacheData(_device, _pipelineCache, &sz, nullptr) == VK_SUCCESS && sz > 0) { + std::vector blob(sz); + if (vkGetPipelineCacheData(_device, _pipelineCache, &sz, blob.data()) == VK_SUCCESS) { + std::ofstream f("pipeline_cache.bin", std::ios::binary | std::ios::trunc); + if (f) f.write(blob.data(), static_cast(sz)); + } + } + vkDestroyPipelineCache(_device, _pipelineCache, nullptr); + _pipelineCache = VK_NULL_HANDLE; + } + if (_allocator) { vmaDestroyAllocator(_allocator); _allocator = nullptr; } + if (_device) { vkDestroyDevice(_device, nullptr); _device = VK_NULL_HANDLE; } + if (_surface) { vkDestroySurfaceKHR(_instance, _surface, nullptr); _surface = VK_NULL_HANDLE; } + if (_debugMessenger && _validationEnabled) { + vkDestroyDebugUtilsMessengerEXT(_instance, _debugMessenger, nullptr); + _debugMessenger = VK_NULL_HANDLE; + } + if (_instance) { vkDestroyInstance(_instance, nullptr); _instance = VK_NULL_HANDLE; } +} + +void Context::WaitIdle() const noexcept { + if (_device) vkDeviceWaitIdle(_device); +} + +} // namespace simv::vk diff --git a/src/vk/Context.h b/src/vk/Context.h new file mode 100644 index 0000000..527d23f --- /dev/null +++ b/src/vk/Context.h @@ -0,0 +1,75 @@ +#pragma once + +#include +#include + +// Forward-declare VMA allocator to avoid pulling its header into every TU. +struct VmaAllocator_T; +using VmaAllocator = VmaAllocator_T*; + +namespace simv::core { class Window; } + +namespace simv::vk { + +struct ContextOptions { + bool enableValidation {true}; // VK_LAYER_KHRONOS_validation + bool enableDebugUtils {true}; // VK_EXT_debug_utils + bool requireAsyncCompute {true}; // dedicated compute queue family + bool requireAsyncTransfer {true}; // dedicated transfer queue family +}; + +// Vulkan 1.3 instance + physical/logical device + queues + VMA. +// Built on top of vk-bootstrap; volk is initialised exactly once. +// +// Owns: VkInstance, VkSurfaceKHR, VkDevice, VmaAllocator, debug messenger. +// Does NOT own: VkPhysicalDevice (lifetime of the instance). +class Context { +public: + Context(simv::core::Window& window, const ContextOptions& opts); + ~Context(); + + Context(const Context&) = delete; + Context& operator=(const Context&) = delete; + Context(Context&&) = delete; + Context& operator=(Context&&) = delete; + + [[nodiscard]] VkInstance Instance() const noexcept { return _instance; } + [[nodiscard]] VkPhysicalDevice PhysicalDevice() const noexcept { return _phys; } + [[nodiscard]] VkDevice Device() const noexcept { return _device; } + [[nodiscard]] VkSurfaceKHR Surface() const noexcept { return _surface; } + [[nodiscard]] VmaAllocator Allocator() const noexcept { return _allocator; } + + [[nodiscard]] VkQueue GraphicsQueue() const noexcept { return _graphicsQueue; } + [[nodiscard]] VkQueue ComputeQueue() const noexcept { return _computeQueue; } + [[nodiscard]] VkQueue TransferQueue() const noexcept { return _transferQueue; } + [[nodiscard]] std::uint32_t GraphicsFamily() const noexcept { return _graphicsFamily; } + [[nodiscard]] std::uint32_t ComputeFamily() const noexcept { return _computeFamily; } + [[nodiscard]] std::uint32_t TransferFamily() const noexcept { return _transferFamily; } + + // Persistent VkPipelineCache, serialised to disk so a cold start doesn't + // re-translate SPIR-V to vendor ISA every run. + [[nodiscard]] VkPipelineCache PipelineCache() const noexcept { return _pipelineCache; } + + void WaitIdle() const noexcept; + +private: + VkInstance _instance {VK_NULL_HANDLE}; + VkDebugUtilsMessengerEXT _debugMessenger {VK_NULL_HANDLE}; + VkSurfaceKHR _surface {VK_NULL_HANDLE}; + VkPhysicalDevice _phys {VK_NULL_HANDLE}; + VkDevice _device {VK_NULL_HANDLE}; + VmaAllocator _allocator {nullptr}; + + VkQueue _graphicsQueue {VK_NULL_HANDLE}; + VkQueue _computeQueue {VK_NULL_HANDLE}; + VkQueue _transferQueue {VK_NULL_HANDLE}; + std::uint32_t _graphicsFamily {0}; + std::uint32_t _computeFamily {0}; + std::uint32_t _transferFamily {0}; + + VkPipelineCache _pipelineCache {VK_NULL_HANDLE}; + + bool _validationEnabled {false}; +}; + +} // namespace simv::vk diff --git a/src/vk/GpuMesh.cpp b/src/vk/GpuMesh.cpp new file mode 100644 index 0000000..894565a --- /dev/null +++ b/src/vk/GpuMesh.cpp @@ -0,0 +1,183 @@ +#include "GpuMesh.h" + +#include "Context.h" +#include "mesh/Mesh.h" + +#include + +#include +#include + +namespace simv::vk { + +namespace { + +// Submit a one-time command buffer on the transfer queue and wait for it. +// Mesh uploads are rare (a model load), so a blocking copy is fine. +void OneShotCopy(Context& ctx, VkBuffer src, VkBuffer dst, VkDeviceSize size) { + VkCommandPool pool = VK_NULL_HANDLE; + VkCommandPoolCreateInfo cpi{ VK_STRUCTURE_TYPE_COMMAND_POOL_CREATE_INFO }; + cpi.flags = VK_COMMAND_POOL_CREATE_TRANSIENT_BIT; + cpi.queueFamilyIndex = ctx.TransferFamily(); + if (vkCreateCommandPool(ctx.Device(), &cpi, nullptr, &pool) != VK_SUCCESS) + throw std::runtime_error("OneShotCopy: vkCreateCommandPool failed"); + + VkCommandBuffer cmd = VK_NULL_HANDLE; + VkCommandBufferAllocateInfo cai{ VK_STRUCTURE_TYPE_COMMAND_BUFFER_ALLOCATE_INFO }; + cai.commandPool = pool; + cai.level = VK_COMMAND_BUFFER_LEVEL_PRIMARY; + cai.commandBufferCount = 1; + if (vkAllocateCommandBuffers(ctx.Device(), &cai, &cmd) != VK_SUCCESS) { + vkDestroyCommandPool(ctx.Device(), pool, nullptr); + throw std::runtime_error("OneShotCopy: vkAllocateCommandBuffers failed"); + } + + VkCommandBufferBeginInfo bi{ VK_STRUCTURE_TYPE_COMMAND_BUFFER_BEGIN_INFO }; + bi.flags = VK_COMMAND_BUFFER_USAGE_ONE_TIME_SUBMIT_BIT; + vkBeginCommandBuffer(cmd, &bi); + + VkBufferCopy region{}; + region.size = size; + vkCmdCopyBuffer(cmd, src, dst, 1, ®ion); + + vkEndCommandBuffer(cmd); + + VkFenceCreateInfo fci{ VK_STRUCTURE_TYPE_FENCE_CREATE_INFO }; + VkFence fence = VK_NULL_HANDLE; + if (vkCreateFence(ctx.Device(), &fci, nullptr, &fence) != VK_SUCCESS) { + vkFreeCommandBuffers(ctx.Device(), pool, 1, &cmd); + vkDestroyCommandPool(ctx.Device(), pool, nullptr); + throw std::runtime_error("OneShotCopy: vkCreateFence failed"); + } + + VkSubmitInfo si{ VK_STRUCTURE_TYPE_SUBMIT_INFO }; + si.commandBufferCount = 1; + si.pCommandBuffers = &cmd; + vkQueueSubmit(ctx.TransferQueue(), 1, &si, fence); + vkWaitForFences(ctx.Device(), 1, &fence, VK_TRUE, UINT64_MAX); + + vkDestroyFence(ctx.Device(), fence, nullptr); + vkFreeCommandBuffers(ctx.Device(), pool, 1, &cmd); + vkDestroyCommandPool(ctx.Device(), pool, nullptr); +} + +} // namespace + +GpuMesh::~GpuMesh() { Free(); } + +GpuMesh::GpuMesh(GpuMesh&& other) noexcept + : _ctx(other._ctx) + , _vertexBuf(other._vertexBuf), _indexBuf(other._indexBuf) + , _vertexAlloc(other._vertexAlloc), _indexAlloc(other._indexAlloc) + , _vertexCount(other._vertexCount), _indexCount(other._indexCount) +{ + other._ctx = nullptr; + other._vertexBuf = VK_NULL_HANDLE; + other._indexBuf = VK_NULL_HANDLE; + other._vertexAlloc = nullptr; + other._indexAlloc = nullptr; + other._vertexCount = 0; + other._indexCount = 0; +} + +GpuMesh& GpuMesh::operator=(GpuMesh&& other) noexcept { + if (this != &other) { + Free(); + _ctx = other._ctx; + _vertexBuf = other._vertexBuf; + _indexBuf = other._indexBuf; + _vertexAlloc = other._vertexAlloc; + _indexAlloc = other._indexAlloc; + _vertexCount = other._vertexCount; + _indexCount = other._indexCount; + other._ctx = nullptr; + other._vertexBuf = VK_NULL_HANDLE; + other._indexBuf = VK_NULL_HANDLE; + other._vertexAlloc = nullptr; + other._indexAlloc = nullptr; + other._vertexCount = 0; + other._indexCount = 0; + } + return *this; +} + +void GpuMesh::Upload(Context& ctx, const simv::mesh::Mesh& cpuMesh) { + Free(); + _ctx = &ctx; + _vertexCount = static_cast(cpuMesh.positions.size()); + _indexCount = static_cast(cpuMesh.indices.size()); + + if (_vertexCount == 0 || _indexCount == 0) { + throw std::runtime_error("GpuMesh::Upload: empty mesh"); + } + + const VkDeviceSize vertSize = sizeof(glm::vec3) * _vertexCount; + const VkDeviceSize idxSize = sizeof(std::uint32_t) * _indexCount; + + // ----- Device-local destination buffers ----- + auto makeDeviceBuffer = [&](VkDeviceSize sz, VkBufferUsageFlags usage, + VkBuffer& out, VmaAllocation& alloc) { + VkBufferCreateInfo bi{ VK_STRUCTURE_TYPE_BUFFER_CREATE_INFO }; + bi.size = sz; + bi.usage = VK_BUFFER_USAGE_TRANSFER_DST_BIT | usage; + bi.sharingMode = VK_SHARING_MODE_EXCLUSIVE; + VmaAllocationCreateInfo ai{}; + ai.usage = VMA_MEMORY_USAGE_AUTO_PREFER_DEVICE; + if (vmaCreateBuffer(ctx.Allocator(), &bi, &ai, &out, &alloc, nullptr) != VK_SUCCESS) { + throw std::runtime_error("GpuMesh: vmaCreateBuffer device-local failed"); + } + }; + makeDeviceBuffer(vertSize, VK_BUFFER_USAGE_VERTEX_BUFFER_BIT, + _vertexBuf, reinterpret_cast(_vertexAlloc)); + makeDeviceBuffer(idxSize, VK_BUFFER_USAGE_INDEX_BUFFER_BIT, + _indexBuf, reinterpret_cast(_indexAlloc)); + + // ----- Staging buffers, host-visible ----- + auto makeStaging = [&](VkDeviceSize sz, VkBuffer& out, VmaAllocation& alloc, void*& mapped) { + VkBufferCreateInfo bi{ VK_STRUCTURE_TYPE_BUFFER_CREATE_INFO }; + bi.size = sz; + bi.usage = VK_BUFFER_USAGE_TRANSFER_SRC_BIT; + bi.sharingMode = VK_SHARING_MODE_EXCLUSIVE; + VmaAllocationCreateInfo ai{}; + ai.usage = VMA_MEMORY_USAGE_AUTO_PREFER_HOST; + ai.flags = VMA_ALLOCATION_CREATE_HOST_ACCESS_SEQUENTIAL_WRITE_BIT + | VMA_ALLOCATION_CREATE_MAPPED_BIT; + VmaAllocationInfo info{}; + if (vmaCreateBuffer(ctx.Allocator(), &bi, &ai, &out, &alloc, &info) != VK_SUCCESS) { + throw std::runtime_error("GpuMesh: vmaCreateBuffer staging failed"); + } + mapped = info.pMappedData; + }; + + VkBuffer vertStage{}, idxStage{}; + VmaAllocation vertStageAlloc{}, idxStageAlloc{}; + void* vertMapped{}, *idxMapped{}; + makeStaging(vertSize, vertStage, vertStageAlloc, vertMapped); + makeStaging(idxSize, idxStage, idxStageAlloc, idxMapped); + + std::memcpy(vertMapped, cpuMesh.positions.data(), vertSize); + std::memcpy(idxMapped, cpuMesh.indices.data(), idxSize); + + OneShotCopy(ctx, vertStage, _vertexBuf, vertSize); + OneShotCopy(ctx, idxStage, _indexBuf, idxSize); + + vmaDestroyBuffer(ctx.Allocator(), vertStage, vertStageAlloc); + vmaDestroyBuffer(ctx.Allocator(), idxStage, idxStageAlloc); +} + +void GpuMesh::Free() { + if (_ctx) { + if (_vertexBuf) vmaDestroyBuffer(_ctx->Allocator(), _vertexBuf, + static_cast(_vertexAlloc)); + if (_indexBuf) vmaDestroyBuffer(_ctx->Allocator(), _indexBuf, + static_cast(_indexAlloc)); + } + _vertexBuf = VK_NULL_HANDLE; + _indexBuf = VK_NULL_HANDLE; + _vertexAlloc = nullptr; + _indexAlloc = nullptr; + _vertexCount = 0; + _indexCount = 0; +} + +} // namespace simv::vk diff --git a/src/vk/GpuMesh.h b/src/vk/GpuMesh.h new file mode 100644 index 0000000..fd87186 --- /dev/null +++ b/src/vk/GpuMesh.h @@ -0,0 +1,44 @@ +#pragma once + +#include +#include + +namespace simv::mesh { struct Mesh; } + +namespace simv::vk { + +class Context; + +// Vulkan-resident copy of a CPU mesh: a tight float3 vertex buffer plus a +// uint32 index buffer, both device-local and uploaded via a staging copy on +// the transfer queue. Used by MeshRenderer to draw the loaded model. +class GpuMesh { +public: + GpuMesh() = default; + ~GpuMesh(); + + GpuMesh(const GpuMesh&) = delete; + GpuMesh& operator=(const GpuMesh&) = delete; + GpuMesh(GpuMesh&&) noexcept; + GpuMesh& operator=(GpuMesh&&) noexcept; + + void Upload(Context& ctx, const simv::mesh::Mesh& cpuMesh); + void Free(); + + [[nodiscard]] VkBuffer VertexBuffer() const noexcept { return _vertexBuf; } + [[nodiscard]] VkBuffer IndexBuffer() const noexcept { return _indexBuf; } + [[nodiscard]] std::uint32_t VertexCount() const noexcept { return _vertexCount; } + [[nodiscard]] std::uint32_t IndexCount() const noexcept { return _indexCount; } + [[nodiscard]] bool IsValid() const noexcept { return _vertexBuf != VK_NULL_HANDLE; } + +private: + Context* _ctx {nullptr}; + VkBuffer _vertexBuf {VK_NULL_HANDLE}; + VkBuffer _indexBuf {VK_NULL_HANDLE}; + void* _vertexAlloc {nullptr}; // VmaAllocation, opaque + void* _indexAlloc {nullptr}; + std::uint32_t _vertexCount {0}; + std::uint32_t _indexCount {0}; +}; + +} // namespace simv::vk diff --git a/src/vk/GridRenderer.cpp b/src/vk/GridRenderer.cpp new file mode 100644 index 0000000..a3cb49d --- /dev/null +++ b/src/vk/GridRenderer.cpp @@ -0,0 +1,213 @@ +#include "GridRenderer.h" + +#include "Context.h" +#include "Shader.h" + +#include + +#include + +#include +#include +#include +#include + +namespace simv::vk { + +namespace { + +struct GridVertex { + glm::vec3 pos; + glm::vec3 color; +}; + +} // namespace + +GridRenderer::GridRenderer(Context& ctx) : _ctx(&ctx) { + BuildGeometry(); + + VkPushConstantRange pcr{}; + pcr.stageFlags = VK_SHADER_STAGE_VERTEX_BIT; + pcr.offset = 0; + pcr.size = sizeof(glm::mat4); + + VkPipelineLayoutCreateInfo pli{ VK_STRUCTURE_TYPE_PIPELINE_LAYOUT_CREATE_INFO }; + pli.pushConstantRangeCount = 1; + pli.pPushConstantRanges = &pcr; + if (vkCreatePipelineLayout(_ctx->Device(), &pli, nullptr, &_layout) != VK_SUCCESS) { + throw std::runtime_error("GridRenderer: vkCreatePipelineLayout failed"); + } +} + +GridRenderer::~GridRenderer() { + DestroyPipeline(); + if (_vbuf) vmaDestroyBuffer(_ctx->Allocator(), _vbuf, + static_cast(_vbufAlloc)); + if (_layout) vkDestroyPipelineLayout(_ctx->Device(), _layout, nullptr); +} + +void GridRenderer::BuildGeometry() { + constexpr int N = 10; // half-extent in cells + constexpr float S = 1.0f; // cell size + const glm::vec3 grid{ 0.30f, 0.31f, 0.35f }; + + std::vector verts; + verts.reserve(static_cast((2 * N + 1) * 6 * 2 + 6)); + + auto addLine = [&](glm::vec3 a, glm::vec3 b, glm::vec3 c) { + verts.push_back({ a, c }); + verts.push_back({ b, c }); + }; + + const float ext = N * S; + for (int i = -N; i <= N; ++i) { + const float t = i * S; + // XZ plane (y = 0) + addLine({ -ext, 0.0f, t }, { ext, 0.0f, t }, grid); + addLine({ t, 0.0f, -ext }, { t, 0.0f, ext }, grid); + // XY plane (z = 0) + addLine({ -ext, t, 0.0f }, { ext, t, 0.0f }, grid); + addLine({ t, -ext, 0.0f }, { t, ext, 0.0f }, grid); + // YZ plane (x = 0) + addLine({ 0.0f, -ext, t }, { 0.0f, ext, t }, grid); + addLine({ 0.0f, t, -ext }, { 0.0f, t, ext }, grid); + } + + // Coloured axes last so they overdraw the grey centre lines. + addLine({ -ext, 0.0f, 0.0f }, { ext, 0.0f, 0.0f }, { 0.85f, 0.25f, 0.25f }); // X red + addLine({ 0.0f, -ext, 0.0f }, { 0.0f, ext, 0.0f }, { 0.25f, 0.80f, 0.30f }); // Y green + addLine({ 0.0f, 0.0f, -ext }, { 0.0f, 0.0f, ext }, { 0.30f, 0.45f, 0.90f }); // Z blue + + _vertexCount = static_cast(verts.size()); + const VkDeviceSize size = sizeof(GridVertex) * verts.size(); + + // Host-visible vertex buffer: the geometry is static and tiny, so a mapped + // upload avoids a staging copy. Read directly by the vertex shader each frame. + VkBufferCreateInfo bi{ VK_STRUCTURE_TYPE_BUFFER_CREATE_INFO }; + bi.size = size; + bi.usage = VK_BUFFER_USAGE_VERTEX_BUFFER_BIT; + bi.sharingMode = VK_SHARING_MODE_EXCLUSIVE; + VmaAllocationCreateInfo ai{}; + ai.usage = VMA_MEMORY_USAGE_AUTO_PREFER_HOST; + ai.flags = VMA_ALLOCATION_CREATE_HOST_ACCESS_SEQUENTIAL_WRITE_BIT + | VMA_ALLOCATION_CREATE_MAPPED_BIT; + VmaAllocationInfo info{}; + VmaAllocation alloc{}; + if (vmaCreateBuffer(_ctx->Allocator(), &bi, &ai, &_vbuf, &alloc, &info) != VK_SUCCESS) { + throw std::runtime_error("GridRenderer: vmaCreateBuffer failed"); + } + _vbufAlloc = alloc; + std::memcpy(info.pMappedData, verts.data(), static_cast(size)); +} + +void GridRenderer::DestroyPipeline() { + if (_pipeline) { vkDestroyPipeline(_ctx->Device(), _pipeline, nullptr); _pipeline = VK_NULL_HANDLE; } +} + +void GridRenderer::EnsurePipeline(VkFormat colorFormat, VkFormat depthFormat) { + if (_pipeline && _colorFormat == colorFormat && _depthFormat == depthFormat) return; + DestroyPipeline(); + _colorFormat = colorFormat; + _depthFormat = depthFormat; + BuildPipeline(); +} + +void GridRenderer::BuildPipeline() { + // RAII modules: freed on scope exit, including the throw paths below. + const ShaderModule vert(*_ctx, FindSpvPath("editor/grid.vert.spv")); + const ShaderModule frag(*_ctx, FindSpvPath("editor/grid.frag.spv")); + + VkPipelineShaderStageCreateInfo stages[2]{}; + stages[0].sType = VK_STRUCTURE_TYPE_PIPELINE_SHADER_STAGE_CREATE_INFO; + stages[0].stage = VK_SHADER_STAGE_VERTEX_BIT; + stages[0].module = vert.Handle(); stages[0].pName = "main"; + stages[1].sType = VK_STRUCTURE_TYPE_PIPELINE_SHADER_STAGE_CREATE_INFO; + stages[1].stage = VK_SHADER_STAGE_FRAGMENT_BIT; + stages[1].module = frag.Handle(); stages[1].pName = "main"; + + VkVertexInputBindingDescription bind{}; + bind.binding = 0; + bind.stride = sizeof(GridVertex); + bind.inputRate = VK_VERTEX_INPUT_RATE_VERTEX; + std::array attrs{}; + attrs[0] = { 0, 0, VK_FORMAT_R32G32B32_SFLOAT, offsetof(GridVertex, pos) }; + attrs[1] = { 1, 0, VK_FORMAT_R32G32B32_SFLOAT, offsetof(GridVertex, color) }; + + VkPipelineVertexInputStateCreateInfo vi{ VK_STRUCTURE_TYPE_PIPELINE_VERTEX_INPUT_STATE_CREATE_INFO }; + vi.vertexBindingDescriptionCount = 1; + vi.pVertexBindingDescriptions = &bind; + vi.vertexAttributeDescriptionCount = static_cast(attrs.size()); + vi.pVertexAttributeDescriptions = attrs.data(); + + VkPipelineInputAssemblyStateCreateInfo ia{ VK_STRUCTURE_TYPE_PIPELINE_INPUT_ASSEMBLY_STATE_CREATE_INFO }; + ia.topology = VK_PRIMITIVE_TOPOLOGY_LINE_LIST; + + VkPipelineViewportStateCreateInfo vp{ VK_STRUCTURE_TYPE_PIPELINE_VIEWPORT_STATE_CREATE_INFO }; + vp.viewportCount = 1; vp.scissorCount = 1; + + VkPipelineRasterizationStateCreateInfo rs{ VK_STRUCTURE_TYPE_PIPELINE_RASTERIZATION_STATE_CREATE_INFO }; + rs.polygonMode = VK_POLYGON_MODE_FILL; // ignored for line topology + rs.cullMode = VK_CULL_MODE_NONE; + rs.lineWidth = 1.0f; + + VkPipelineMultisampleStateCreateInfo ms{ VK_STRUCTURE_TYPE_PIPELINE_MULTISAMPLE_STATE_CREATE_INFO }; + ms.rasterizationSamples = VK_SAMPLE_COUNT_1_BIT; + + VkPipelineDepthStencilStateCreateInfo dss{ VK_STRUCTURE_TYPE_PIPELINE_DEPTH_STENCIL_STATE_CREATE_INFO }; + dss.depthTestEnable = VK_TRUE; + dss.depthWriteEnable = VK_TRUE; + dss.depthCompareOp = VK_COMPARE_OP_LESS_OR_EQUAL; + dss.minDepthBounds = 0.0f; + dss.maxDepthBounds = 1.0f; + + VkPipelineColorBlendAttachmentState cb{}; + cb.colorWriteMask = VK_COLOR_COMPONENT_R_BIT | VK_COLOR_COMPONENT_G_BIT + | VK_COLOR_COMPONENT_B_BIT | VK_COLOR_COMPONENT_A_BIT; + VkPipelineColorBlendStateCreateInfo cbs{ VK_STRUCTURE_TYPE_PIPELINE_COLOR_BLEND_STATE_CREATE_INFO }; + cbs.attachmentCount = 1; + cbs.pAttachments = &cb; + + const std::array dyn{ VK_DYNAMIC_STATE_VIEWPORT, VK_DYNAMIC_STATE_SCISSOR }; + VkPipelineDynamicStateCreateInfo dynState{ VK_STRUCTURE_TYPE_PIPELINE_DYNAMIC_STATE_CREATE_INFO }; + dynState.dynamicStateCount = static_cast(dyn.size()); + dynState.pDynamicStates = dyn.data(); + + VkPipelineRenderingCreateInfo prc{ VK_STRUCTURE_TYPE_PIPELINE_RENDERING_CREATE_INFO }; + prc.colorAttachmentCount = 1; + prc.pColorAttachmentFormats = &_colorFormat; + prc.depthAttachmentFormat = _depthFormat; + + VkGraphicsPipelineCreateInfo gp{ VK_STRUCTURE_TYPE_GRAPHICS_PIPELINE_CREATE_INFO }; + gp.pNext = &prc; + gp.stageCount = 2; + gp.pStages = stages; + gp.pVertexInputState = &vi; + gp.pInputAssemblyState = &ia; + gp.pViewportState = &vp; + gp.pRasterizationState = &rs; + gp.pMultisampleState = &ms; + gp.pDepthStencilState = &dss; + gp.pColorBlendState = &cbs; + gp.pDynamicState = &dynState; + gp.layout = _layout; + + const VkResult r = vkCreateGraphicsPipelines(_ctx->Device(), _ctx->PipelineCache(), + 1, &gp, nullptr, &_pipeline); + if (r != VK_SUCCESS) { + throw std::runtime_error("GridRenderer: vkCreateGraphicsPipelines failed"); + } +} + +void GridRenderer::Draw(VkCommandBuffer cmd, const glm::mat4& mvp) { + if (!_pipeline || _vertexCount == 0) return; + + vkCmdBindPipeline(cmd, VK_PIPELINE_BIND_POINT_GRAPHICS, _pipeline); + vkCmdPushConstants(cmd, _layout, VK_SHADER_STAGE_VERTEX_BIT, 0, sizeof(glm::mat4), &mvp); + + VkBuffer vbuf = _vbuf; + VkDeviceSize offset = 0; + vkCmdBindVertexBuffers(cmd, 0, 1, &vbuf, &offset); + vkCmdDraw(cmd, _vertexCount, 1, 0, 0); +} + +} // namespace simv::vk diff --git a/src/vk/GridRenderer.h b/src/vk/GridRenderer.h new file mode 100644 index 0000000..c4759af --- /dev/null +++ b/src/vk/GridRenderer.h @@ -0,0 +1,43 @@ +#pragma once + +#include +#include +#include + +namespace simv::vk { + +class Context; + +// Draws the editor reference space: three grid planes (XY, XZ, YZ) through the +// origin plus the three coloured axes. Geometry is a static line list built once; +// the view-projection comes in as an MVP push constant. +class GridRenderer { +public: + explicit GridRenderer(Context& ctx); + ~GridRenderer(); + + GridRenderer(const GridRenderer&) = delete; + GridRenderer& operator=(const GridRenderer&) = delete; + + // (Re)build the pipeline when the color/depth attachment formats are known or change. + void EnsurePipeline(VkFormat colorFormat, VkFormat depthFormat); + + // Records the grid draw. Viewport/scissor must already be set by the caller. + void Draw(VkCommandBuffer cmd, const glm::mat4& mvp); + +private: + void BuildGeometry(); + void BuildPipeline(); + void DestroyPipeline(); + + Context* _ctx {nullptr}; + VkFormat _colorFormat {VK_FORMAT_UNDEFINED}; + VkFormat _depthFormat {VK_FORMAT_UNDEFINED}; + VkPipelineLayout _layout {VK_NULL_HANDLE}; + VkPipeline _pipeline {VK_NULL_HANDLE}; + VkBuffer _vbuf {VK_NULL_HANDLE}; + void* _vbufAlloc {nullptr}; // VmaAllocation, opaque + std::uint32_t _vertexCount {0}; +}; + +} // namespace simv::vk diff --git a/src/vk/Image.cpp b/src/vk/Image.cpp new file mode 100644 index 0000000..50ded8d --- /dev/null +++ b/src/vk/Image.cpp @@ -0,0 +1,99 @@ +#include "Image.h" +#include "Context.h" + +#include + +#include + +namespace simv::vk { + +Image::Image(Context& ctx, const Desc& desc) + : _ctx(&ctx), _extent(desc.extent), _format(desc.format) +{ + VkImageCreateInfo ici{ VK_STRUCTURE_TYPE_IMAGE_CREATE_INFO }; + ici.imageType = desc.type; + ici.format = desc.format; + ici.extent = desc.extent; + ici.mipLevels = 1; + ici.arrayLayers = 1; + ici.samples = VK_SAMPLE_COUNT_1_BIT; + ici.tiling = VK_IMAGE_TILING_OPTIMAL; + ici.usage = desc.usage; + ici.sharingMode = VK_SHARING_MODE_EXCLUSIVE; + ici.initialLayout = VK_IMAGE_LAYOUT_UNDEFINED; + + VmaAllocationCreateInfo aci{}; + aci.usage = VMA_MEMORY_USAGE_AUTO_PREFER_DEVICE; + + if (vmaCreateImage(_ctx->Allocator(), &ici, &aci, &_image, &_alloc, nullptr) != VK_SUCCESS) { + throw std::runtime_error("vmaCreateImage failed"); + } + + VkImageViewCreateInfo vci{ VK_STRUCTURE_TYPE_IMAGE_VIEW_CREATE_INFO }; + vci.image = _image; + vci.viewType = desc.viewType; + vci.format = desc.format; + vci.subresourceRange.aspectMask = VK_IMAGE_ASPECT_COLOR_BIT; + vci.subresourceRange.baseMipLevel = 0; + vci.subresourceRange.levelCount = 1; + vci.subresourceRange.baseArrayLayer = 0; + vci.subresourceRange.layerCount = 1; + if (vkCreateImageView(_ctx->Device(), &vci, nullptr, &_view) != VK_SUCCESS) { + vmaDestroyImage(_ctx->Allocator(), _image, _alloc); + throw std::runtime_error("vkCreateImageView failed"); + } +} + +Image::~Image() { Free(); } + +Image::Image(Image&& other) noexcept + : _ctx(other._ctx), _image(other._image), _view(other._view), + _alloc(other._alloc), _extent(other._extent), _format(other._format), + _layout(other._layout) +{ + other._ctx = nullptr; other._image = VK_NULL_HANDLE; + other._view = VK_NULL_HANDLE; other._alloc = nullptr; +} + +Image& Image::operator=(Image&& other) noexcept { + if (this != &other) { + Free(); + _ctx = other._ctx; _image = other._image; _view = other._view; + _alloc = other._alloc; _extent = other._extent; _format = other._format; + _layout = other._layout; + other._ctx = nullptr; other._image = VK_NULL_HANDLE; + other._view = VK_NULL_HANDLE; other._alloc = nullptr; + } + return *this; +} + +void Image::Free() { + if (!_ctx) return; + if (_view) vkDestroyImageView(_ctx->Device(), _view, nullptr); + if (_image) vmaDestroyImage(_ctx->Allocator(), _image, _alloc); + _view = VK_NULL_HANDLE; _image = VK_NULL_HANDLE; _alloc = nullptr; + _ctx = nullptr; +} + +void Image::TransitionTo(VkCommandBuffer cmd, VkImageLayout newLayout, + VkPipelineStageFlags2 srcStage, VkAccessFlags2 srcAccess, + VkPipelineStageFlags2 dstStage, VkAccessFlags2 dstAccess) +{ + if (newLayout == _layout) return; + VkImageMemoryBarrier2 b{ VK_STRUCTURE_TYPE_IMAGE_MEMORY_BARRIER_2 }; + b.srcStageMask = srcStage; + b.srcAccessMask = srcAccess; + b.dstStageMask = dstStage; + b.dstAccessMask = dstAccess; + b.oldLayout = _layout; + b.newLayout = newLayout; + b.image = _image; + b.subresourceRange = { VK_IMAGE_ASPECT_COLOR_BIT, 0, 1, 0, 1 }; + VkDependencyInfo dep{ VK_STRUCTURE_TYPE_DEPENDENCY_INFO }; + dep.imageMemoryBarrierCount = 1; + dep.pImageMemoryBarriers = &b; + vkCmdPipelineBarrier2(cmd, &dep); + _layout = newLayout; +} + +} // namespace simv::vk diff --git a/src/vk/Image.h b/src/vk/Image.h new file mode 100644 index 0000000..6d60a57 --- /dev/null +++ b/src/vk/Image.h @@ -0,0 +1,60 @@ +#pragma once + +#include +#include + +struct VmaAllocation_T; +using VmaAllocation = VmaAllocation_T*; + +namespace simv::vk { + +class Context; + +// Move-only RAII over a VMA-allocated VkImage + VkImageView. Targets compute +// storage usage (3D field textures) and sampled-image usage (slice rendering). +class Image { +public: + struct Desc { + VkImageType type {VK_IMAGE_TYPE_3D}; + VkFormat format {VK_FORMAT_R32G32B32A32_SFLOAT}; + VkExtent3D extent {1, 1, 1}; + VkImageUsageFlags usage {VK_IMAGE_USAGE_STORAGE_BIT + | VK_IMAGE_USAGE_SAMPLED_BIT}; + VkImageViewType viewType {VK_IMAGE_VIEW_TYPE_3D}; + }; + + Image() = default; + Image(Context& ctx, const Desc& desc); + ~Image(); + + Image(const Image&) = delete; + Image& operator=(const Image&) = delete; + Image(Image&&) noexcept; + Image& operator=(Image&&) noexcept; + + void Free(); + + [[nodiscard]] VkImage Handle() const noexcept { return _image; } + [[nodiscard]] VkImageView View() const noexcept { return _view; } + [[nodiscard]] VkExtent3D Extent() const noexcept { return _extent; } + [[nodiscard]] VkFormat Format() const noexcept { return _format; } + [[nodiscard]] VkImageLayout CurrentLayout() const noexcept { return _layout; } + [[nodiscard]] bool IsValid() const noexcept { return _image != VK_NULL_HANDLE; } + + // Issue a layout transition (synchronization2). The recorded layout cache + // tracks the *expected* layout post-barrier so the next call knows the source. + void TransitionTo(VkCommandBuffer cmd, VkImageLayout newLayout, + VkPipelineStageFlags2 srcStage, VkAccessFlags2 srcAccess, + VkPipelineStageFlags2 dstStage, VkAccessFlags2 dstAccess); + +private: + Context* _ctx {nullptr}; + VkImage _image {VK_NULL_HANDLE}; + VkImageView _view {VK_NULL_HANDLE}; + VmaAllocation _alloc {nullptr}; + VkExtent3D _extent {0, 0, 0}; + VkFormat _format {VK_FORMAT_UNDEFINED}; + VkImageLayout _layout {VK_IMAGE_LAYOUT_UNDEFINED}; +}; + +} // namespace simv::vk diff --git a/src/vk/MeshRenderer.cpp b/src/vk/MeshRenderer.cpp new file mode 100644 index 0000000..acf6ea5 --- /dev/null +++ b/src/vk/MeshRenderer.cpp @@ -0,0 +1,194 @@ +#include "MeshRenderer.h" + +#include "Context.h" +#include "GpuMesh.h" +#include "Shader.h" + +#include + +#include +#include + +namespace simv::vk { + +namespace { + +// Matches the push_constant block in shaders/editor/mesh.{vert,frag}. +// color.a is a "lit" flag: 1 = flat-shaded, 0 = constant colour (wireframe). +struct MeshPC { + glm::mat4 mvp; + glm::vec4 color; +}; + +} // namespace + +MeshRenderer::MeshRenderer(Context& ctx) : _ctx(&ctx) { + VkPushConstantRange pcr{}; + pcr.stageFlags = VK_SHADER_STAGE_VERTEX_BIT | VK_SHADER_STAGE_FRAGMENT_BIT; + pcr.offset = 0; + pcr.size = sizeof(MeshPC); + + VkPipelineLayoutCreateInfo pli{ VK_STRUCTURE_TYPE_PIPELINE_LAYOUT_CREATE_INFO }; + pli.pushConstantRangeCount = 1; + pli.pPushConstantRanges = &pcr; + if (vkCreatePipelineLayout(_ctx->Device(), &pli, nullptr, &_layout) != VK_SUCCESS) { + throw std::runtime_error("MeshRenderer: vkCreatePipelineLayout failed"); + } +} + +MeshRenderer::~MeshRenderer() { + DestroyPipelines(); + if (_layout) vkDestroyPipelineLayout(_ctx->Device(), _layout, nullptr); +} + +void MeshRenderer::DestroyPipelines() { + if (_fill) { vkDestroyPipeline(_ctx->Device(), _fill, nullptr); _fill = VK_NULL_HANDLE; } + if (_line) { vkDestroyPipeline(_ctx->Device(), _line, nullptr); _line = VK_NULL_HANDLE; } +} + +void MeshRenderer::EnsurePipelines(VkFormat colorFormat, VkFormat depthFormat) { + if (_fill && _colorFormat == colorFormat && _depthFormat == depthFormat) return; + DestroyPipelines(); + _colorFormat = colorFormat; + _depthFormat = depthFormat; + _fill = BuildPipeline(VK_POLYGON_MODE_FILL, /*depthBias*/false); + _line = BuildPipeline(VK_POLYGON_MODE_LINE, /*depthBias*/true); +} + +VkPipeline MeshRenderer::BuildPipeline(VkPolygonMode polyMode, bool depthBias) { + // RAII modules: freed on scope exit, including the throw paths below. + const ShaderModule vert(*_ctx, FindSpvPath("editor/mesh.vert.spv")); + const ShaderModule frag(*_ctx, FindSpvPath("editor/mesh.frag.spv")); + + VkPipelineShaderStageCreateInfo stages[2]{}; + stages[0].sType = VK_STRUCTURE_TYPE_PIPELINE_SHADER_STAGE_CREATE_INFO; + stages[0].stage = VK_SHADER_STAGE_VERTEX_BIT; + stages[0].module = vert.Handle(); stages[0].pName = "main"; + stages[1].sType = VK_STRUCTURE_TYPE_PIPELINE_SHADER_STAGE_CREATE_INFO; + stages[1].stage = VK_SHADER_STAGE_FRAGMENT_BIT; + stages[1].module = frag.Handle(); stages[1].pName = "main"; + + // Vertex input: tight float3 position stream (GpuMesh vertex buffer). + VkVertexInputBindingDescription bind{}; + bind.binding = 0; + bind.stride = sizeof(float) * 3; + bind.inputRate = VK_VERTEX_INPUT_RATE_VERTEX; + VkVertexInputAttributeDescription attr{}; + attr.location = 0; + attr.binding = 0; + attr.format = VK_FORMAT_R32G32B32_SFLOAT; + attr.offset = 0; + + VkPipelineVertexInputStateCreateInfo vi{ VK_STRUCTURE_TYPE_PIPELINE_VERTEX_INPUT_STATE_CREATE_INFO }; + vi.vertexBindingDescriptionCount = 1; + vi.pVertexBindingDescriptions = &bind; + vi.vertexAttributeDescriptionCount = 1; + vi.pVertexAttributeDescriptions = &attr; + + VkPipelineInputAssemblyStateCreateInfo ia{ VK_STRUCTURE_TYPE_PIPELINE_INPUT_ASSEMBLY_STATE_CREATE_INFO }; + ia.topology = VK_PRIMITIVE_TOPOLOGY_TRIANGLE_LIST; + + VkPipelineViewportStateCreateInfo vp{ VK_STRUCTURE_TYPE_PIPELINE_VIEWPORT_STATE_CREATE_INFO }; + vp.viewportCount = 1; vp.scissorCount = 1; + + VkPipelineRasterizationStateCreateInfo rs{ VK_STRUCTURE_TYPE_PIPELINE_RASTERIZATION_STATE_CREATE_INFO }; + rs.polygonMode = polyMode; + rs.cullMode = VK_CULL_MODE_NONE; // models may have mixed winding + rs.frontFace = VK_FRONT_FACE_COUNTER_CLOCKWISE; + rs.lineWidth = 1.0f; + if (depthBias) { + // Nudge the wireframe toward the camera so it sits on top of the fill. + rs.depthBiasEnable = VK_TRUE; + rs.depthBiasConstantFactor = -1.0f; + rs.depthBiasSlopeFactor = -1.0f; + } + + VkPipelineMultisampleStateCreateInfo ms{ VK_STRUCTURE_TYPE_PIPELINE_MULTISAMPLE_STATE_CREATE_INFO }; + ms.rasterizationSamples = VK_SAMPLE_COUNT_1_BIT; + + VkPipelineDepthStencilStateCreateInfo dss{ VK_STRUCTURE_TYPE_PIPELINE_DEPTH_STENCIL_STATE_CREATE_INFO }; + dss.depthTestEnable = VK_TRUE; + dss.depthWriteEnable = VK_TRUE; + dss.depthCompareOp = VK_COMPARE_OP_LESS_OR_EQUAL; + dss.minDepthBounds = 0.0f; + dss.maxDepthBounds = 1.0f; + + VkPipelineColorBlendAttachmentState cb{}; + cb.colorWriteMask = VK_COLOR_COMPONENT_R_BIT | VK_COLOR_COMPONENT_G_BIT + | VK_COLOR_COMPONENT_B_BIT | VK_COLOR_COMPONENT_A_BIT; + VkPipelineColorBlendStateCreateInfo cbs{ VK_STRUCTURE_TYPE_PIPELINE_COLOR_BLEND_STATE_CREATE_INFO }; + cbs.attachmentCount = 1; + cbs.pAttachments = &cb; + + const std::array dyn{ VK_DYNAMIC_STATE_VIEWPORT, VK_DYNAMIC_STATE_SCISSOR }; + VkPipelineDynamicStateCreateInfo dynState{ VK_STRUCTURE_TYPE_PIPELINE_DYNAMIC_STATE_CREATE_INFO }; + dynState.dynamicStateCount = static_cast(dyn.size()); + dynState.pDynamicStates = dyn.data(); + + VkPipelineRenderingCreateInfo prc{ VK_STRUCTURE_TYPE_PIPELINE_RENDERING_CREATE_INFO }; + prc.colorAttachmentCount = 1; + prc.pColorAttachmentFormats = &_colorFormat; + prc.depthAttachmentFormat = _depthFormat; + + VkGraphicsPipelineCreateInfo gp{ VK_STRUCTURE_TYPE_GRAPHICS_PIPELINE_CREATE_INFO }; + gp.pNext = &prc; + gp.stageCount = 2; + gp.pStages = stages; + gp.pVertexInputState = &vi; + gp.pInputAssemblyState = &ia; + gp.pViewportState = &vp; + gp.pRasterizationState = &rs; + gp.pMultisampleState = &ms; + gp.pDepthStencilState = &dss; + gp.pColorBlendState = &cbs; + gp.pDynamicState = &dynState; + gp.layout = _layout; + + VkPipeline pipeline = VK_NULL_HANDLE; + const VkResult r = vkCreateGraphicsPipelines(_ctx->Device(), _ctx->PipelineCache(), + 1, &gp, nullptr, &pipeline); + if (r != VK_SUCCESS) { + throw std::runtime_error("MeshRenderer: vkCreateGraphicsPipelines failed"); + } + return pipeline; +} + +void MeshRenderer::Draw(VkCommandBuffer cmd, const GpuMesh& mesh, + const glm::mat4& mvp, RenderMode mode) +{ + if (!mesh.IsValid() || !_fill || !_line) return; + + VkBuffer vbuf = mesh.VertexBuffer(); + VkDeviceSize offset = 0; + vkCmdBindVertexBuffers(cmd, 0, 1, &vbuf, &offset); + vkCmdBindIndexBuffer(cmd, mesh.IndexBuffer(), 0, VK_INDEX_TYPE_UINT32); + + auto drawWith = [&](VkPipeline pipe, const glm::vec4& color) { + MeshPC pc{ mvp, color }; + vkCmdBindPipeline(cmd, VK_PIPELINE_BIND_POINT_GRAPHICS, pipe); + vkCmdPushConstants(cmd, _layout, + VK_SHADER_STAGE_VERTEX_BIT | VK_SHADER_STAGE_FRAGMENT_BIT, + 0, sizeof(MeshPC), &pc); + vkCmdDrawIndexed(cmd, mesh.IndexCount(), 1, 0, 0, 0); + }; + + // color.a: 1 = flat-shaded surface, 0 = constant colour (wireframe lines). + const glm::vec4 kSolid{ 0.72f, 0.74f, 0.78f, 1.0f }; + const glm::vec4 kWire { 0.78f, 0.82f, 0.88f, 0.0f }; + const glm::vec4 kOverlay{ 0.06f, 0.07f, 0.09f, 0.0f }; + + switch (mode) { + case RenderMode::Solid: + drawWith(_fill, kSolid); + break; + case RenderMode::Wireframe: + drawWith(_line, kWire); + break; + case RenderMode::SolidWire: + drawWith(_fill, kSolid); + drawWith(_line, kOverlay); + break; + } +} + +} // namespace simv::vk diff --git a/src/vk/MeshRenderer.h b/src/vk/MeshRenderer.h new file mode 100644 index 0000000..1965b71 --- /dev/null +++ b/src/vk/MeshRenderer.h @@ -0,0 +1,42 @@ +#pragma once + +#include "vk/RenderMode.h" + +#include +#include + +namespace simv::vk { + +class Context; +class GpuMesh; + +// Draws an indexed triangle mesh with flat shading and/or a wireframe overlay. +// Transform is passed per-draw as an MVP push constant — no descriptor sets. +// Two pipelines are built (fill + line); SolidWire draws both. +class MeshRenderer { +public: + explicit MeshRenderer(Context& ctx); + ~MeshRenderer(); + + MeshRenderer(const MeshRenderer&) = delete; + MeshRenderer& operator=(const MeshRenderer&) = delete; + + // (Re)build pipelines when the color/depth attachment formats are known or change. + void EnsurePipelines(VkFormat colorFormat, VkFormat depthFormat); + + // Records the mesh draw. Viewport/scissor must already be set by the caller. + void Draw(VkCommandBuffer cmd, const GpuMesh& mesh, const glm::mat4& mvp, RenderMode mode); + +private: + VkPipeline BuildPipeline(VkPolygonMode polyMode, bool depthBias); + void DestroyPipelines(); + + Context* _ctx {nullptr}; + VkFormat _colorFormat {VK_FORMAT_UNDEFINED}; + VkFormat _depthFormat {VK_FORMAT_UNDEFINED}; + VkPipelineLayout _layout {VK_NULL_HANDLE}; + VkPipeline _fill {VK_NULL_HANDLE}; + VkPipeline _line {VK_NULL_HANDLE}; +}; + +} // namespace simv::vk diff --git a/src/vk/RenderMode.h b/src/vk/RenderMode.h new file mode 100644 index 0000000..c0999ee --- /dev/null +++ b/src/vk/RenderMode.h @@ -0,0 +1,12 @@ +#pragma once + +namespace simv::vk { + +// How the loaded model is drawn in the viewport. +enum class RenderMode { + Solid, // filled triangles with flat shading + Wireframe, // triangle edges only + SolidWire, // filled triangles with a wireframe overlay +}; + +} // namespace simv::vk diff --git a/src/vk/Renderer.cpp b/src/vk/Renderer.cpp new file mode 100644 index 0000000..504f388 --- /dev/null +++ b/src/vk/Renderer.cpp @@ -0,0 +1,466 @@ +#include "Renderer.h" + +#include "Context.h" +#include "Swapchain.h" +#include "GpuMesh.h" +#include "GridRenderer.h" +#include "MeshRenderer.h" + +#include "core/Window.h" +#include "mesh/Mesh.h" + +#include +#include + +#include +#include +#include + +#include + +#include + +#include +#include +#include + +namespace simv::vk { + +namespace { + +constexpr std::uint32_t kFramesInFlight = 2; + +void CheckVk(VkResult r, const char* where) { + if (r != VK_SUCCESS) { + spdlog::error("[VK] {} failed: {}", where, static_cast(r)); + throw std::runtime_error(where); + } +} + +} // namespace + +// ---------------------------------------------------------------------------- + +struct Renderer::Impl { + explicit Impl(simv::core::Window& wnd); + ~Impl(); + + void InitFrames(); + void InitImGui(); + void ShutdownImGui(); + void CreateDepth(VkExtent2D extent); + void DestroyDepth(); + void RecreateSwapDependent(); + void DrawFrame(); + + simv::core::Window* window {nullptr}; + std::unique_ptr ctx; + std::unique_ptr swap; + + struct FrameState { + VkCommandPool cmdPool {VK_NULL_HANDLE}; + VkCommandBuffer cmd {VK_NULL_HANDLE}; + VkSemaphore imageAvailable {VK_NULL_HANDLE}; + VkFence inFlight {VK_NULL_HANDLE}; + }; + std::array frames{}; + std::vector renderFinishedPerImage; + VkDescriptorPool imguiPool {VK_NULL_HANDLE}; + std::uint32_t cursor {0}; + + VkImage depthImage {VK_NULL_HANDLE}; + VkImageView depthView {VK_NULL_HANDLE}; + VmaAllocation depthAlloc {nullptr}; + VkFormat depthFormat {VK_FORMAT_D32_SFLOAT}; + + std::unique_ptr meshRenderer; + std::unique_ptr gridRenderer; + GpuMesh gpuMesh; + + Renderer::UiCallback uiCallback; + glm::mat4 viewProj {1.0f}; + glm::mat4 model {1.0f}; + RenderMode renderMode {RenderMode::Solid}; + bool gridVisible {true}; + bool hasMesh {false}; +}; + +Renderer::Impl::Impl(simv::core::Window& wnd) : window(&wnd) { + ContextOptions opts{}; + opts.requireAsyncCompute = false; // no compute work in the editor + ctx = std::make_unique(wnd, opts); + swap = std::make_unique(*ctx, wnd, /*vsync*/true); + + InitFrames(); + CreateDepth(swap->Extent()); + InitImGui(); + + meshRenderer = std::make_unique(*ctx); + gridRenderer = std::make_unique(*ctx); + meshRenderer->EnsurePipelines(swap->ColorFormat(), depthFormat); + gridRenderer->EnsurePipeline(swap->ColorFormat(), depthFormat); +} + +Renderer::Impl::~Impl() { + if (!ctx) return; + ctx->WaitIdle(); + + ShutdownImGui(); + + gpuMesh.Free(); + meshRenderer.reset(); + gridRenderer.reset(); + + DestroyDepth(); + + for (auto& f : frames) { + if (f.inFlight) vkDestroyFence(ctx->Device(), f.inFlight, nullptr); + if (f.imageAvailable) vkDestroySemaphore(ctx->Device(), f.imageAvailable, nullptr); + if (f.cmdPool) vkDestroyCommandPool(ctx->Device(), f.cmdPool, nullptr); + } + for (auto sem : renderFinishedPerImage) { + if (sem) vkDestroySemaphore(ctx->Device(), sem, nullptr); + } + if (imguiPool) vkDestroyDescriptorPool(ctx->Device(), imguiPool, nullptr); +} + +void Renderer::Impl::InitFrames() { + for (auto& f : frames) { + VkCommandPoolCreateInfo cpi{ VK_STRUCTURE_TYPE_COMMAND_POOL_CREATE_INFO }; + cpi.flags = VK_COMMAND_POOL_CREATE_RESET_COMMAND_BUFFER_BIT; + cpi.queueFamilyIndex = ctx->GraphicsFamily(); + CheckVk(vkCreateCommandPool(ctx->Device(), &cpi, nullptr, &f.cmdPool), "vkCreateCommandPool"); + + VkCommandBufferAllocateInfo cai{ VK_STRUCTURE_TYPE_COMMAND_BUFFER_ALLOCATE_INFO }; + cai.commandPool = f.cmdPool; + cai.level = VK_COMMAND_BUFFER_LEVEL_PRIMARY; + cai.commandBufferCount = 1; + CheckVk(vkAllocateCommandBuffers(ctx->Device(), &cai, &f.cmd), "vkAllocateCommandBuffers"); + + VkSemaphoreCreateInfo si{ VK_STRUCTURE_TYPE_SEMAPHORE_CREATE_INFO }; + CheckVk(vkCreateSemaphore(ctx->Device(), &si, nullptr, &f.imageAvailable), "vkCreateSemaphore"); + + VkFenceCreateInfo fi{ VK_STRUCTURE_TYPE_FENCE_CREATE_INFO }; + fi.flags = VK_FENCE_CREATE_SIGNALED_BIT; + CheckVk(vkCreateFence(ctx->Device(), &fi, nullptr, &f.inFlight), "vkCreateFence"); + } + + // One renderFinished semaphore per swapchain image (signalled at present). + renderFinishedPerImage.resize(swap->Frames().size()); + for (auto& sem : renderFinishedPerImage) { + VkSemaphoreCreateInfo si{ VK_STRUCTURE_TYPE_SEMAPHORE_CREATE_INFO }; + CheckVk(vkCreateSemaphore(ctx->Device(), &si, nullptr, &sem), "vkCreateSemaphore"); + } +} + +void Renderer::Impl::CreateDepth(VkExtent2D extent) { + DestroyDepth(); + + VkImageCreateInfo ici{ VK_STRUCTURE_TYPE_IMAGE_CREATE_INFO }; + ici.imageType = VK_IMAGE_TYPE_2D; + ici.format = depthFormat; + ici.extent = { extent.width, extent.height, 1 }; + ici.mipLevels = 1; + ici.arrayLayers = 1; + ici.samples = VK_SAMPLE_COUNT_1_BIT; + ici.tiling = VK_IMAGE_TILING_OPTIMAL; + ici.usage = VK_IMAGE_USAGE_DEPTH_STENCIL_ATTACHMENT_BIT; + ici.initialLayout = VK_IMAGE_LAYOUT_UNDEFINED; + + VmaAllocationCreateInfo ai{}; + ai.usage = VMA_MEMORY_USAGE_AUTO_PREFER_DEVICE; + CheckVk(vmaCreateImage(ctx->Allocator(), &ici, &ai, &depthImage, &depthAlloc, nullptr), + "vmaCreateImage(depth)"); + + VkImageViewCreateInfo vci{ VK_STRUCTURE_TYPE_IMAGE_VIEW_CREATE_INFO }; + vci.image = depthImage; + vci.viewType = VK_IMAGE_VIEW_TYPE_2D; + vci.format = depthFormat; + vci.subresourceRange = { VK_IMAGE_ASPECT_DEPTH_BIT, 0, 1, 0, 1 }; + CheckVk(vkCreateImageView(ctx->Device(), &vci, nullptr, &depthView), "vkCreateImageView(depth)"); +} + +void Renderer::Impl::DestroyDepth() { + if (depthView) { vkDestroyImageView(ctx->Device(), depthView, nullptr); depthView = VK_NULL_HANDLE; } + if (depthImage) { vmaDestroyImage(ctx->Allocator(), depthImage, depthAlloc); depthImage = VK_NULL_HANDLE; depthAlloc = nullptr; } +} + +void Renderer::Impl::InitImGui() { + constexpr std::uint32_t kMax = 1000; + std::array sizes{{ + { VK_DESCRIPTOR_TYPE_SAMPLER, kMax }, + { VK_DESCRIPTOR_TYPE_COMBINED_IMAGE_SAMPLER, kMax }, + { VK_DESCRIPTOR_TYPE_SAMPLED_IMAGE, kMax }, + { VK_DESCRIPTOR_TYPE_STORAGE_IMAGE, kMax }, + { VK_DESCRIPTOR_TYPE_UNIFORM_TEXEL_BUFFER, kMax }, + { VK_DESCRIPTOR_TYPE_STORAGE_TEXEL_BUFFER, kMax }, + { VK_DESCRIPTOR_TYPE_UNIFORM_BUFFER, kMax }, + { VK_DESCRIPTOR_TYPE_STORAGE_BUFFER, kMax }, + { VK_DESCRIPTOR_TYPE_UNIFORM_BUFFER_DYNAMIC, kMax }, + { VK_DESCRIPTOR_TYPE_STORAGE_BUFFER_DYNAMIC, kMax }, + { VK_DESCRIPTOR_TYPE_INPUT_ATTACHMENT, kMax }, + }}; + + VkDescriptorPoolCreateInfo dpi{ VK_STRUCTURE_TYPE_DESCRIPTOR_POOL_CREATE_INFO }; + dpi.flags = VK_DESCRIPTOR_POOL_CREATE_FREE_DESCRIPTOR_SET_BIT; + dpi.maxSets = kMax * static_cast(sizes.size()); + dpi.poolSizeCount = static_cast(sizes.size()); + dpi.pPoolSizes = sizes.data(); + CheckVk(vkCreateDescriptorPool(ctx->Device(), &dpi, nullptr, &imguiPool), + "vkCreateDescriptorPool(imgui)"); + + IMGUI_CHECKVERSION(); + ImGui::CreateContext(); + ImGui::StyleColorsDark(); + + ImGui_ImplGlfw_InitForVulkan(window->Raw(), true); + + ImGui_ImplVulkan_InitInfo info{}; + info.Instance = ctx->Instance(); + info.PhysicalDevice = ctx->PhysicalDevice(); + info.Device = ctx->Device(); + info.QueueFamily = ctx->GraphicsFamily(); + info.Queue = ctx->GraphicsQueue(); + info.DescriptorPool = imguiPool; + info.MinImageCount = 2; + info.ImageCount = static_cast(swap->Frames().size()); + info.MSAASamples = VK_SAMPLE_COUNT_1_BIT; + info.UseDynamicRendering = true; + + // ImGui stores the pColorAttachmentFormats pointer, so the pointee must + // outlive the Init call — keep it static. + static VkFormat s_colorFormat; + s_colorFormat = swap->ColorFormat(); + + info.PipelineRenderingCreateInfo.sType = VK_STRUCTURE_TYPE_PIPELINE_RENDERING_CREATE_INFO; + info.PipelineRenderingCreateInfo.colorAttachmentCount = 1; + info.PipelineRenderingCreateInfo.pColorAttachmentFormats = &s_colorFormat; + // Must match the depth attachment present in the render pass instance. + info.PipelineRenderingCreateInfo.depthAttachmentFormat = depthFormat; + + ImGui_ImplVulkan_Init(&info); +} + +void Renderer::Impl::ShutdownImGui() { + ImGui_ImplVulkan_Shutdown(); + ImGui_ImplGlfw_Shutdown(); + ImGui::DestroyContext(); +} + +void Renderer::Impl::RecreateSwapDependent() { + ctx->WaitIdle(); + swap->Recreate(*window, /*vsync*/true); + CreateDepth(swap->Extent()); + + // A failed vkAcquireNextImageKHR can leave a per-frame imageAvailable + // semaphore signalled; recreate them so the next acquire starts clean. + for (auto& f : frames) { + vkDestroySemaphore(ctx->Device(), f.imageAvailable, nullptr); + VkSemaphoreCreateInfo si{ VK_STRUCTURE_TYPE_SEMAPHORE_CREATE_INFO }; + CheckVk(vkCreateSemaphore(ctx->Device(), &si, nullptr, &f.imageAvailable), "vkCreateSemaphore"); + } + + // Swapchain image count may change → rebuild the per-image semaphores. + for (auto sem : renderFinishedPerImage) { + if (sem) vkDestroySemaphore(ctx->Device(), sem, nullptr); + } + renderFinishedPerImage.assign(swap->Frames().size(), VK_NULL_HANDLE); + for (auto& sem : renderFinishedPerImage) { + VkSemaphoreCreateInfo si{ VK_STRUCTURE_TYPE_SEMAPHORE_CREATE_INFO }; + CheckVk(vkCreateSemaphore(ctx->Device(), &si, nullptr, &sem), "vkCreateSemaphore"); + } + + meshRenderer->EnsurePipelines(swap->ColorFormat(), depthFormat); + gridRenderer->EnsurePipeline(swap->ColorFormat(), depthFormat); +} + +void Renderer::Impl::DrawFrame() { + int fbw = 0, fbh = 0; + window->GetFramebufferSize(fbw, fbh); + if (fbw == 0 || fbh == 0) return; // minimised — nothing to draw + + auto& frame = frames[cursor % kFramesInFlight]; + + vkWaitForFences(ctx->Device(), 1, &frame.inFlight, VK_TRUE, UINT64_MAX); + + std::uint32_t imageIdx = 0; + VkResult acq = vkAcquireNextImageKHR(ctx->Device(), swap->Handle(), UINT64_MAX, + frame.imageAvailable, VK_NULL_HANDLE, &imageIdx); + if (acq == VK_ERROR_OUT_OF_DATE_KHR) { + RecreateSwapDependent(); + return; + } + + // ----- ImGui frame (panels populate via the UI callback) ----- + ImGui_ImplVulkan_NewFrame(); + ImGui_ImplGlfw_NewFrame(); + ImGui::NewFrame(); + if (uiCallback) uiCallback(); + ImGui::Render(); + + vkResetFences(ctx->Device(), 1, &frame.inFlight); + vkResetCommandBuffer(frame.cmd, 0); + + VkCommandBufferBeginInfo bi{ VK_STRUCTURE_TYPE_COMMAND_BUFFER_BEGIN_INFO }; + bi.flags = VK_COMMAND_BUFFER_USAGE_ONE_TIME_SUBMIT_BIT; + vkBeginCommandBuffer(frame.cmd, &bi); + + VkImage swapImg = swap->Frames()[imageIdx].image; + VkImageView swapView = swap->Frames()[imageIdx].view; + const VkExtent2D extent = swap->Extent(); + + // Transition colour: UNDEFINED → COLOR_ATTACHMENT_OPTIMAL. + { + VkImageMemoryBarrier2 b{ VK_STRUCTURE_TYPE_IMAGE_MEMORY_BARRIER_2 }; + b.srcStageMask = VK_PIPELINE_STAGE_2_TOP_OF_PIPE_BIT; + b.dstStageMask = VK_PIPELINE_STAGE_2_COLOR_ATTACHMENT_OUTPUT_BIT; + b.dstAccessMask = VK_ACCESS_2_COLOR_ATTACHMENT_WRITE_BIT; + b.oldLayout = VK_IMAGE_LAYOUT_UNDEFINED; + b.newLayout = VK_IMAGE_LAYOUT_COLOR_ATTACHMENT_OPTIMAL; + b.image = swapImg; + b.subresourceRange = { VK_IMAGE_ASPECT_COLOR_BIT, 0, 1, 0, 1 }; + + VkImageMemoryBarrier2 d{ VK_STRUCTURE_TYPE_IMAGE_MEMORY_BARRIER_2 }; + d.srcStageMask = VK_PIPELINE_STAGE_2_TOP_OF_PIPE_BIT; + d.dstStageMask = VK_PIPELINE_STAGE_2_EARLY_FRAGMENT_TESTS_BIT + | VK_PIPELINE_STAGE_2_LATE_FRAGMENT_TESTS_BIT; + d.dstAccessMask = VK_ACCESS_2_DEPTH_STENCIL_ATTACHMENT_WRITE_BIT; + d.oldLayout = VK_IMAGE_LAYOUT_UNDEFINED; + d.newLayout = VK_IMAGE_LAYOUT_DEPTH_ATTACHMENT_OPTIMAL; + d.image = depthImage; + d.subresourceRange = { VK_IMAGE_ASPECT_DEPTH_BIT, 0, 1, 0, 1 }; + + VkImageMemoryBarrier2 barriers[2] = { b, d }; + VkDependencyInfo dep{ VK_STRUCTURE_TYPE_DEPENDENCY_INFO }; + dep.imageMemoryBarrierCount = 2; + dep.pImageMemoryBarriers = barriers; + vkCmdPipelineBarrier2(frame.cmd, &dep); + } + + VkRenderingAttachmentInfo color{ VK_STRUCTURE_TYPE_RENDERING_ATTACHMENT_INFO }; + color.imageView = swapView; + color.imageLayout = VK_IMAGE_LAYOUT_COLOR_ATTACHMENT_OPTIMAL; + color.loadOp = VK_ATTACHMENT_LOAD_OP_CLEAR; + color.storeOp = VK_ATTACHMENT_STORE_OP_STORE; + color.clearValue.color = { { 0.05f, 0.06f, 0.08f, 1.0f } }; + + VkRenderingAttachmentInfo depth{ VK_STRUCTURE_TYPE_RENDERING_ATTACHMENT_INFO }; + depth.imageView = depthView; + depth.imageLayout = VK_IMAGE_LAYOUT_DEPTH_ATTACHMENT_OPTIMAL; + depth.loadOp = VK_ATTACHMENT_LOAD_OP_CLEAR; + depth.storeOp = VK_ATTACHMENT_STORE_OP_DONT_CARE; + depth.clearValue.depthStencil = { 1.0f, 0 }; + + VkRenderingInfo ri{ VK_STRUCTURE_TYPE_RENDERING_INFO }; + ri.renderArea = { {0, 0}, extent }; + ri.layerCount = 1; + ri.colorAttachmentCount = 1; + ri.pColorAttachments = &color; + ri.pDepthAttachment = &depth; + + vkCmdBeginRendering(frame.cmd, &ri); + + // Viewport/scissor shared by both scene renderers. + VkViewport vp{ 0.0f, 0.0f, static_cast(extent.width), + static_cast(extent.height), 0.0f, 1.0f }; + VkRect2D sc{ {0, 0}, extent }; + vkCmdSetViewport(frame.cmd, 0, 1, &vp); + vkCmdSetScissor(frame.cmd, 0, 1, &sc); + + if (gridVisible) gridRenderer->Draw(frame.cmd, viewProj); + if (hasMesh) meshRenderer->Draw(frame.cmd, gpuMesh, viewProj * model, renderMode); + + ImGui_ImplVulkan_RenderDrawData(ImGui::GetDrawData(), frame.cmd); + vkCmdEndRendering(frame.cmd); + + // Transition colour: COLOR_ATTACHMENT_OPTIMAL → PRESENT_SRC. + { + VkImageMemoryBarrier2 b{ VK_STRUCTURE_TYPE_IMAGE_MEMORY_BARRIER_2 }; + b.srcStageMask = VK_PIPELINE_STAGE_2_COLOR_ATTACHMENT_OUTPUT_BIT; + b.srcAccessMask = VK_ACCESS_2_COLOR_ATTACHMENT_WRITE_BIT; + b.dstStageMask = VK_PIPELINE_STAGE_2_BOTTOM_OF_PIPE_BIT; + b.oldLayout = VK_IMAGE_LAYOUT_COLOR_ATTACHMENT_OPTIMAL; + b.newLayout = VK_IMAGE_LAYOUT_PRESENT_SRC_KHR; + b.image = swapImg; + b.subresourceRange = { VK_IMAGE_ASPECT_COLOR_BIT, 0, 1, 0, 1 }; + VkDependencyInfo dep{ VK_STRUCTURE_TYPE_DEPENDENCY_INFO }; + dep.imageMemoryBarrierCount = 1; + dep.pImageMemoryBarriers = &b; + vkCmdPipelineBarrier2(frame.cmd, &dep); + } + + vkEndCommandBuffer(frame.cmd); + + VkSemaphoreSubmitInfo waitSi{ VK_STRUCTURE_TYPE_SEMAPHORE_SUBMIT_INFO }; + waitSi.semaphore = frame.imageAvailable; + waitSi.stageMask = VK_PIPELINE_STAGE_2_COLOR_ATTACHMENT_OUTPUT_BIT; + + VkSemaphore renderFinished = renderFinishedPerImage[imageIdx]; + VkSemaphoreSubmitInfo sigSi{ VK_STRUCTURE_TYPE_SEMAPHORE_SUBMIT_INFO }; + sigSi.semaphore = renderFinished; + sigSi.stageMask = VK_PIPELINE_STAGE_2_ALL_GRAPHICS_BIT; + + VkCommandBufferSubmitInfo cmdSi{ VK_STRUCTURE_TYPE_COMMAND_BUFFER_SUBMIT_INFO }; + cmdSi.commandBuffer = frame.cmd; + + VkSubmitInfo2 si{ VK_STRUCTURE_TYPE_SUBMIT_INFO_2 }; + si.waitSemaphoreInfoCount = 1; + si.pWaitSemaphoreInfos = &waitSi; + si.commandBufferInfoCount = 1; + si.pCommandBufferInfos = &cmdSi; + si.signalSemaphoreInfoCount = 1; + si.pSignalSemaphoreInfos = &sigSi; + vkQueueSubmit2(ctx->GraphicsQueue(), 1, &si, frame.inFlight); + + VkSwapchainKHR swapHandle = swap->Handle(); + VkPresentInfoKHR pi{ VK_STRUCTURE_TYPE_PRESENT_INFO_KHR }; + pi.waitSemaphoreCount = 1; + pi.pWaitSemaphores = &renderFinished; + pi.swapchainCount = 1; + pi.pSwapchains = &swapHandle; + pi.pImageIndices = &imageIdx; + VkResult pres = vkQueuePresentKHR(ctx->GraphicsQueue(), &pi); + if (pres == VK_ERROR_OUT_OF_DATE_KHR || pres == VK_SUBOPTIMAL_KHR) { + RecreateSwapDependent(); + } + + cursor++; +} + +// ---------------------------------------------------------------------------- + +Renderer::Renderer(simv::core::Window& window) + : _impl(std::make_unique(window)) {} + +Renderer::~Renderer() = default; + +void Renderer::SetUiCallback(UiCallback cb) { _impl->uiCallback = std::move(cb); } +void Renderer::SetViewProj(const glm::mat4& vp) { _impl->viewProj = vp; } +void Renderer::SetRenderMode(RenderMode mode) { _impl->renderMode = mode; } +void Renderer::SetGridVisible(bool visible) { _impl->gridVisible = visible; } +void Renderer::DrawFrame() { _impl->DrawFrame(); } +void Renderer::WaitIdle() { _impl->ctx->WaitIdle(); } + +float Renderer::AspectRatio() const { + const VkExtent2D e = _impl->swap->Extent(); + if (e.height == 0) return 1.0f; + return static_cast(e.width) / static_cast(e.height); +} + +void Renderer::SetMeshCpu(const simv::mesh::Mesh& mesh) { + if (mesh.Empty()) return; + _impl->ctx->WaitIdle(); // mesh load is rare — safe to stall briefly + _impl->gpuMesh.Upload(*_impl->ctx, mesh); + const glm::vec3 center = 0.5f * (mesh.bboxMin + mesh.bboxMax); + _impl->model = glm::translate(glm::mat4(1.0f), -center); + _impl->hasMesh = true; +} + +void Renderer::ClearMesh() { + _impl->ctx->WaitIdle(); + _impl->gpuMesh.Free(); + _impl->model = glm::mat4(1.0f); + _impl->hasMesh = false; +} + +} // namespace simv::vk diff --git a/src/vk/Renderer.h b/src/vk/Renderer.h new file mode 100644 index 0000000..ca6a7cf --- /dev/null +++ b/src/vk/Renderer.h @@ -0,0 +1,55 @@ +#pragma once + +#include "vk/RenderMode.h" + +#include + +#include +#include + +namespace simv::core { class Window; } +namespace simv::mesh { struct Mesh; } + +namespace simv::vk { + +// Owns the entire Vulkan presentation stack — context, swapchain, depth buffer, +// per-frame command buffers/sync, the ImGui-Vulkan backend, and the scene +// renderers (grid + mesh). Its public surface is deliberately Vulkan-free so the +// rest of the application never touches the Vulkan API directly. +class Renderer { +public: + explicit Renderer(simv::core::Window& window); + ~Renderer(); + + Renderer(const Renderer&) = delete; + Renderer& operator=(const Renderer&) = delete; + + // ImGui panels are drawn from this callback (between NewFrame and Render). + using UiCallback = std::function; + void SetUiCallback(UiCallback cb); + + // Camera view-projection used for the next scene draw. + void SetViewProj(const glm::mat4& viewProj); + + // Upload a CPU mesh for display; the model is recentred on the origin. + void SetMeshCpu(const simv::mesh::Mesh& mesh); + void ClearMesh(); + + void SetRenderMode(RenderMode mode); + void SetGridVisible(bool visible); + + // Current framebuffer aspect ratio (width / height), for the projection. + [[nodiscard]] float AspectRatio() const; + + // Render one frame: ImGui + grid + mesh, then present. + void DrawFrame(); + + // Block until the GPU is idle (call before tearing things down). + void WaitIdle(); + +private: + struct Impl; + std::unique_ptr _impl; +}; + +} // namespace simv::vk diff --git a/src/vk/Shader.cpp b/src/vk/Shader.cpp new file mode 100644 index 0000000..332e700 --- /dev/null +++ b/src/vk/Shader.cpp @@ -0,0 +1,74 @@ +#include "Shader.h" +#include "Context.h" + +#include +#include + +namespace simv::vk { + +std::vector ReadSpirvFile(const std::filesystem::path& path) { + std::ifstream f(path, std::ios::binary | std::ios::ate); + if (!f) { + throw std::runtime_error("ReadSpirvFile: cannot open " + path.string()); + } + const auto bytes = static_cast(f.tellg()); + if (bytes % sizeof(std::uint32_t) != 0) { + throw std::runtime_error("ReadSpirvFile: file size not multiple of 4: " + path.string()); + } + std::vector words(bytes / sizeof(std::uint32_t)); + f.seekg(0); + f.read(reinterpret_cast(words.data()), static_cast(bytes)); + return words; +} + +std::filesystem::path FindSpvPath(const std::filesystem::path& rel) { + const std::filesystem::path candidates[] = { + std::filesystem::path("spirv") / rel, + std::filesystem::current_path() / "spirv" / rel, + }; + for (const auto& p : candidates) { + if (std::filesystem::exists(p)) return p; + } + throw std::runtime_error("SPIR-V not found: " + rel.string()); +} + +ShaderModule::ShaderModule(Context& ctx, const std::filesystem::path& spvPath) + : ShaderModule(ctx, ReadSpirvFile(spvPath)) {} + +ShaderModule::ShaderModule(Context& ctx, const std::vector& spirv) + : _ctx(&ctx) +{ + VkShaderModuleCreateInfo ci{}; + ci.sType = VK_STRUCTURE_TYPE_SHADER_MODULE_CREATE_INFO; + ci.codeSize = spirv.size() * sizeof(std::uint32_t); + ci.pCode = spirv.data(); + if (vkCreateShaderModule(_ctx->Device(), &ci, nullptr, &_handle) != VK_SUCCESS) { + throw std::runtime_error("vkCreateShaderModule failed"); + } +} + +ShaderModule::~ShaderModule() { Free(); } + +ShaderModule::ShaderModule(ShaderModule&& other) noexcept + : _ctx(other._ctx), _handle(other._handle) +{ + other._ctx = nullptr; other._handle = VK_NULL_HANDLE; +} + +ShaderModule& ShaderModule::operator=(ShaderModule&& other) noexcept { + if (this != &other) { + Free(); + _ctx = other._ctx; _handle = other._handle; + other._ctx = nullptr; other._handle = VK_NULL_HANDLE; + } + return *this; +} + +void ShaderModule::Free() { + if (_handle && _ctx) { + vkDestroyShaderModule(_ctx->Device(), _handle, nullptr); + } + _ctx = nullptr; _handle = VK_NULL_HANDLE; +} + +} // namespace simv::vk diff --git a/src/vk/Shader.h b/src/vk/Shader.h new file mode 100644 index 0000000..1ba3272 --- /dev/null +++ b/src/vk/Shader.h @@ -0,0 +1,42 @@ +#pragma once + +#include +#include +#include + +namespace simv::vk { + +class Context; + +// Loads a SPIR-V binary from disk into a VkShaderModule. Move-only RAII. +class ShaderModule { +public: + ShaderModule() = default; + ShaderModule(Context& ctx, const std::filesystem::path& spvPath); + ShaderModule(Context& ctx, const std::vector& spirv); + ~ShaderModule(); + + ShaderModule(const ShaderModule&) = delete; + ShaderModule& operator=(const ShaderModule&) = delete; + ShaderModule(ShaderModule&& other) noexcept; + ShaderModule& operator=(ShaderModule&& other) noexcept; + + void Free(); + + [[nodiscard]] VkShaderModule Handle() const noexcept { return _handle; } + [[nodiscard]] bool IsValid() const noexcept { return _handle != VK_NULL_HANDLE; } + +private: + Context* _ctx {nullptr}; + VkShaderModule _handle {VK_NULL_HANDLE}; +}; + +// Read the full file into a uint32 vector (SPIR-V words). Throws on failure. +std::vector ReadSpirvFile(const std::filesystem::path& path); + +// Resolve a SPIR-V file given a path relative to the spirv/ tree (e.g. +// "editor/mesh.vert.spv"). Probes spirv/ and current_path()/spirv/, +// matching the layout copied next to the executable. Throws if not found. +std::filesystem::path FindSpvPath(const std::filesystem::path& rel); + +} // namespace simv::vk diff --git a/src/vk/Swapchain.cpp b/src/vk/Swapchain.cpp new file mode 100644 index 0000000..aaf42b3 --- /dev/null +++ b/src/vk/Swapchain.cpp @@ -0,0 +1,57 @@ +#include "Swapchain.h" +#include "Context.h" +#include "core/Window.h" + +#include +#include + +namespace simv::vk { + +Swapchain::Swapchain(Context& ctx, simv::core::Window& window, bool vsync) + : _ctx(&ctx) { Recreate(window, vsync); } + +Swapchain::~Swapchain() { Destroy(); } + +void Swapchain::Destroy() { + if (!_ctx) return; + for (auto& f : _frames) { + if (f.view) vkDestroyImageView(_ctx->Device(), f.view, nullptr); + } + _frames.clear(); + if (_swapchain) { + vkDestroySwapchainKHR(_ctx->Device(), _swapchain, nullptr); + _swapchain = VK_NULL_HANDLE; + } +} + +void Swapchain::Recreate(simv::core::Window& window, bool vsync) { + _ctx->WaitIdle(); + Destroy(); + + int w = 0, h = 0; + window.GetFramebufferSize(w, h); + + vkb::SwapchainBuilder sb(_ctx->PhysicalDevice(), _ctx->Device(), _ctx->Surface()); + sb.set_desired_format(VkSurfaceFormatKHR{ VK_FORMAT_B8G8R8A8_UNORM, VK_COLOR_SPACE_SRGB_NONLINEAR_KHR }) + .set_desired_present_mode(vsync ? VK_PRESENT_MODE_FIFO_KHR : VK_PRESENT_MODE_MAILBOX_KHR) + .set_desired_extent(static_cast(w), static_cast(h)) + .add_image_usage_flags(VK_IMAGE_USAGE_COLOR_ATTACHMENT_BIT | VK_IMAGE_USAGE_TRANSFER_DST_BIT); + + auto res = sb.build(); + if (!res) { + throw std::runtime_error("Swapchain build failed: " + res.error().message()); + } + auto sc = res.value(); + _swapchain = sc.swapchain; + _colorFormat = sc.image_format; + _extent = sc.extent; + + auto imgs = sc.get_images().value(); + auto vws = sc.get_image_views().value(); + _frames.reserve(imgs.size()); + for (std::size_t i = 0; i < imgs.size(); ++i) { + _frames.push_back({ imgs[i], vws[i] }); + } +} + +} // namespace simv::vk diff --git a/src/vk/Swapchain.h b/src/vk/Swapchain.h new file mode 100644 index 0000000..324856e --- /dev/null +++ b/src/vk/Swapchain.h @@ -0,0 +1,45 @@ +#pragma once + +#include +#include +#include + +namespace simv::core { class Window; } + +namespace simv::vk { + +class Context; + +struct FrameImage { + VkImage image {VK_NULL_HANDLE}; + VkImageView view {VK_NULL_HANDLE}; +}; + +// Minimal swapchain via vk-bootstrap. Recreated on resize. +// Targets dynamic-rendering pipelines — we do NOT create a render pass or framebuffer. +class Swapchain { +public: + Swapchain(Context& ctx, simv::core::Window& window, bool vsync = true); + ~Swapchain(); + + Swapchain(const Swapchain&) = delete; + Swapchain& operator=(const Swapchain&) = delete; + + void Recreate(simv::core::Window& window, bool vsync = true); + + [[nodiscard]] VkSwapchainKHR Handle() const noexcept { return _swapchain; } + [[nodiscard]] VkFormat ColorFormat() const noexcept { return _colorFormat; } + [[nodiscard]] VkExtent2D Extent() const noexcept { return _extent; } + [[nodiscard]] const std::vector& Frames() const noexcept { return _frames; } + +private: + void Destroy(); + + Context* _ctx {nullptr}; + VkSwapchainKHR _swapchain {VK_NULL_HANDLE}; + VkFormat _colorFormat {VK_FORMAT_B8G8R8A8_UNORM}; + VkExtent2D _extent {0, 0}; + std::vector _frames; +}; + +} // namespace simv::vk diff --git a/tests/CMakeLists.txt b/tests/CMakeLists.txt new file mode 100644 index 0000000..67987d9 --- /dev/null +++ b/tests/CMakeLists.txt @@ -0,0 +1,11 @@ +add_executable(simv_tests + unit/test_mesh.cpp +) +target_link_libraries(simv_tests PRIVATE + Catch2::Catch2WithMain + simv_mesh + glm::glm +) +target_include_directories(simv_tests PRIVATE ${CMAKE_CURRENT_SOURCE_DIR}) +simv_set_warnings(simv_tests) +catch_discover_tests(simv_tests) diff --git a/tests/unit/test_mesh.cpp b/tests/unit/test_mesh.cpp new file mode 100644 index 0000000..7d49656 --- /dev/null +++ b/tests/unit/test_mesh.cpp @@ -0,0 +1,65 @@ +#include "mesh/Mesh.h" +#include "mesh/MeshDecimator.h" + +#include +#include + +using simv::mesh::Mesh; +using Catch::Matchers::WithinAbs; + +TEST_CASE("Mesh::RecalculateBounds finds AABB", "[mesh]") { + Mesh m; + m.positions = { + {-1.0f, -2.0f, -3.0f}, + { 4.0f, 5.0f, 6.0f}, + { 0.5f, 0.0f, 1.0f}, + }; + m.RecalculateBounds(); + REQUIRE_THAT(m.bboxMin.x, WithinAbs(-1.0f, 1e-6f)); + REQUIRE_THAT(m.bboxMin.y, WithinAbs(-2.0f, 1e-6f)); + REQUIRE_THAT(m.bboxMin.z, WithinAbs(-3.0f, 1e-6f)); + REQUIRE_THAT(m.bboxMax.x, WithinAbs( 4.0f, 1e-6f)); + REQUIRE_THAT(m.bboxMax.y, WithinAbs( 5.0f, 1e-6f)); + REQUIRE_THAT(m.bboxMax.z, WithinAbs( 6.0f, 1e-6f)); +} + +TEST_CASE("WeldVertices collapses near-duplicate vertices", "[mesh][decimator]") { + Mesh m; + // Two triangles sharing an edge with verts placed within tolerance. + m.positions = { + {0.0f, 0.0f, 0.0f}, + {1.0f, 0.0f, 0.0f}, + {0.0f, 1.0f, 0.0f}, + {0.0001f, 0.0f, 0.0f}, // ≈ #0 + {1.0001f, 0.0f, 0.0f}, // ≈ #1 + {1.0f, 1.0f, 0.0f}, + }; + m.indices = { 0, 1, 2, 3, 4, 5 }; + + simv::mesh::WeldVertices(m, /*tolerance=*/0.01f); + + REQUIRE(m.positions.size() == 4); + REQUIRE(m.indices.size() == 6); // both triangles still valid + // Bounds should match the "real" hull regardless of welding order. + REQUIRE_THAT(m.bboxMax.x, WithinAbs(1.0001f, 1e-3f)); +} + +TEST_CASE("WeldVertices drops degenerate triangles", "[mesh][decimator]") { + Mesh m; + // One real triangle + a degenerate one (all three verts within tolerance). + m.positions = { + {0.0f, 0.0f, 0.0f}, + {1.0f, 0.0f, 0.0f}, + {0.0f, 1.0f, 0.0f}, + {2.0f, 2.0f, 0.0f}, + {2.00005f, 2.0f, 0.0f}, + {2.0f, 2.00005f, 0.0f}, + }; + m.indices = { 0, 1, 2, 3, 4, 5 }; + + simv::mesh::WeldVertices(m, /*tolerance=*/0.001f); + + // The degenerate triangle's three verts collapsed to one — that triangle + // should be removed entirely. + REQUIRE(m.indices.size() == 3); +}