基于非结构化同位网格的SIMPLE算法

通过基于非结构化网格的有限体积法对二维稳态Navier—Stokes方程进行了数值求解。其中对流项采用延迟修正的二阶格式进行离散；扩散项的离散采用二阶中心差分格式；对于压力-速度耦合利用SIMPLE算法进行处理；计算节点的布置采用同位网格技术，界面流速通过动量插值确定。本文对方腔驱动流、倾斜腔驱动流和圆柱外部绕流问题进行了计算，讨论了非结构化同位网格有限体积法在实现SIMPLE算法时，迭代次数与欠松弛系数的关系、不同网格情况的收敛性、同结构化网格的对比以及流场尾迹结构。通过和以往结果比较可知，本文的方法是准确和可信的。

Implement of SIMPLE algorithm based on unstructured colocated meshes

An unstructured colocated meshes based on the finite volume method has been applied for numerical simulation of two-dimensional, steady, incompressible Navier-Stokes equations. The convective flux is evaluated using the second-order scheme with deferred correction. The diffusive flux is solved using central difference scheme. SIMPLE algorithm is adopted to deal with the pressure-velocity coupling. A colocated arrangement of variables is introduced on numerical grids, and the cell face velocities are calculated by the momentum interpolation. As test cases, a lid-driven flow, a skewed lid-driven flow and a laminar flow around a circular cylinder in a channel have been carried out to examine the accuracy of the implement of SIMPLE algorithm based on unstructured colocated grids. Numerical results include the relationship between outer iteration numbers and under-relaxation parameters, the convergence of different computational grids, the comparison with the situation of structure meshes, and the flow status. Comparison with the benchmark results shows that the present method is accurate and trustable.