freshlu11 / SIMPLE-taichi

A SIMPLE incompressible fluid solver written in Taichi.

SIMPLE-taichi

SIMPLE-taichi is an incompressible fluid solver implementing the SIMPLE method written in Taichi. The target flow field is rectangular with typical boundary conditions (inflow/outflow/wall).

Features

• Finite Volume Method (FVM)
• Built-in Conjugate-Gradient (CG) and BiCGSTAB solver

Requirement

• Taichi 1.0.0
• Matplotlib

Demo

As a concrete validation, the computation results of a lid-driven cavity case are compared with the well-know literature values.

压力修正法

$$ 不可压缩流连续方程离散格式：[(\rho u)_w - (\rho u)_e] \cdot \Delta y + [(\rho v)_s - (\rho v)_n] \cdot \Delta x = b\

a_W = \rho_e d_e \Delta y = \rho_e {A_e \over a_n} \Delta y = \rho \Delta y \Delta y / a_w $$

求解代数方程

BICG算法

双共轭梯度求解压力修正的离散方程

BICGSTAB算法

稳定双共轭梯度求解动量守恒的离散方程

初始化：

迭代：

部分公式： $$ rho = \bold r^T_k \bold r_k \ alpha_lower = \bold p^T_k \bold A \bold p_k \ alpha = rho / alpha_lower \

\bold s = \bold r_k - \alpha_k * \bold A \bold p_k \

\bold p_{k+1} := \bold r_{k+1} + \beta_k ·(\bold p_k - \omega *\bold A \bold p) \ $$