NS方程的非结构化网格方法及其差分格式

Unstructured Grid Method and Its Differential Schemes for NSEquations

采用同位非结构化网格上的有限体积法，对ＮａｖｉｅｒＳｔｏｋｅｓ 方程的ＳＩＭＰＬＥ 算法及差分格式进行了研究．提出了适用于非结构化网格的不用求解单元顶点变量值的二阶混合差分格式．该格式的优点在于：１） 减少了计算工作量；２） 避免了普通混合差分格式因使用简单的一阶迎风差分格式所引起的网格界面方向相关性的问题．最后，采用三角形网格，利用提出的方法及差分格式，对方腔内的驱动层流及绕翼型湍流进行了数值计算。

The SIMPLEalgorithm and differential schemes are used for solving Navier Stokes equa tions through finite volume method with collocated unstructured grid . Atwo order hybrid scheme withoutthe necessity of computing the variables at elements verticesis presented .Compared with the ordinary hybrid scheme,the advantages are :1)computation is reduced ;2)grid dependency problem , which is resultedfrom one order upwindinterpolationin ordinary hybrid scheme on unstructured grid , can be avoided .Finally ,the proposed method and schemes are used to calculatelaminarflow in alid driven cavity and turbulentflow around an airfoil. The numericalresults fit benchmark solutions and experiments better than those calculated through ordinary hybrid scheme .