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NotBigGhostandClaude Opus 5 5d762ad9d6 Решатель KBC-2D на Rust: ядро по статьям, два бэкенда, гифка в реальном времени 
Переписанный с нуля двумерный решатель LBM D2Q9 с энтропийным столкновением KBC
в варианте «модель D» (табл. I 2D-статьи Bösch/Chikatamarla/Karlin, arXiv:1507.02509;
в трёхмерных работах — KBC-N1). Код разложен по ролям на пять файлов: математика
решателя, бэкенд под процессор, бэкенд под видеокарту, оркестратор, блок гифок.

Ядро сверено с первоисточниками тестами (22 шт.):
* проектор на сдвиг, выписанный аналитически из представления популяций через
  натуральные моменты (ур. 10), совпадает с матричным до 1e-13, идемпотентен;
* γ из замкнутой оценки (ур. 17) — корень условия максимума энтропии (ур. 15);
* сдвиговые моменты релаксируют ровно с 2β при любой γ, вязкость по ур. (5)
  воспроизводится затуханием сдвиговой волны с точностью лучше 1%;
* сквозной бенчмарк статьи (дважды периодический сдвиговый слой, Re=3e4) сходится
  с fp64-эталоном питоновского решателя 0.6035.

Порог вырожденности γ относительный (доля от ⟨Δ|Δ⟩): абсолютный подменял бы γ на 2
на большинстве узлов, молча превращая KBC в LBGK. Доля таких узлов печатается в отчёте.

Бэкенды взаимозаменяемы и согласованы: CPU (rayon, f64) и GPU (wgpu/WGSL, f32) на одной
постановке совпадают до 4–5 значащих цифр шаг в шаг; на Intel Iris Xe GPU даёт ~105 MLUPS
против ~18 у процессора. Топология задачи строится один раз в cpu.rs и загружается в
буферы, дублируется только физика — в WGSL.

Анимация привязана к физическому времени потока, а не к скорости счёта: задержка кадра
берётся из δt = u_lat·δx/u_phys. Дробная задержка раскладывается по целым сотым долям
секунды накопителем (3,3,4,3,3,4,…), поэтому накопленное время кадров не уходит от
физического; режим --gif-every auto подбирает шаг под реальное время при заданной частоте.

Параметризовано: скорость и направление потока, число Рейнольдса, размер домена и размер
ячейки в метрах, коэффициент и границы вложенного патча измельчения, семь форм тела
(цилиндр, квадрат, ромб, эллипс, профиль NACA, треугольник, пластина) с углом атаки,
время и разгон, оператор столкновения, режим выхода и губка, бэкенд, вся анимация и
три уровня подробности отчёта.

Известное расхождение с питоновским решателем на канальном случае (Cd выше на 9%,
St ниже на 12% при совпадающих ⟨ρ⟩, ⟨Cm⟩ и rms Cl) описано в README вместе с тем,
что уже исключено как причина.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
2026-08-14 18:23:03 +03:00

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