一种求解不可压N-S方程的非结构化网格方法

Method on Unstructured Grid for Incompressible Flows

将Date压力修正算法推广到非结构化网格中来处理压力与速度的耦合,用具有二阶精度的迎风最小二乘格式离散对流项,用梯度投影法离散扩散项,得到了一种在非结构化网格上求解N-S方程的同位网格法.它充分利用了单元梯度,避免了利用顶点信息计算交叉扩散通量的麻烦,所有界面速度都采用线性插值,克服了Rhie＆Chow动量插值法的缺点.算例表明,该算法精度较高且健壮稳定,收敛特性也比较好.

A method for solving steady incompressible Navier-Stokes equations on hybrid unstructured grids was presented. The pressure correction method, originally developed by Date for flow on structured grids, was employed to enforce mass conservation on hybrid unstructured grids. All the variables were defined at the center of each cell while the face velocities were calculated by interpolation at the mid-points of the corresponding cell faces. The convection flux was calculated with upwind least-square method and the diffusion flux was calculated with the gradient projection method. Both the momentum and Poisson equations were integrated with the finite volume method which is independent of cell shapes. The algebraic equations were solved with Gauss-Seidel method. The present numerical method was applied to two different benchmark problems and is confirmed to be accurate and efficient.