基于高阶紧致格式的二维不可压N-S方程求解

摘要

A high order compact difference scheme originally developed for computational aeroacoustic (CAA) is used in the solution of 2D unsteady incompressible Navier-Stokes equations in primitive variables. The present method is established on a non-staggered grid system. This method reduces the computational effort while offering easier boundary stencil specification when compared to conventional compact schemes. The Poisson equation is approximated using a fourth-order compact difference scheme constructed currently on the nine-point 2D stencil, and the successive over-relaxation ( SOR) method is used to solve it. Finally, a problem with analytical solution and driven cavity flow problem are solved to investigate the accuracy and efficiency of the scheme and a comparison of computational CPU time are given with the traditional central compact scheme.%介绍了一种基于原始变量的用于求解二维非定常不可压Navier-Stokes方程的高阶紧致格式.这种紧致格式最初是用于计算声学(CAA)的高精度格式,相对于传统的紧致格式,使用该格式的优点在于减少计算量的同时降低了边界模板的处理难度.这种方法建立在非交错网格上,空间离散具有六阶精度.压力Poisson方程基于九基点模板的四阶紧致格式进行离散,超松弛迭代进行求解.时间推进上采用四阶Runge-Kutta方法.为验证该方法的精度和有效性,利用该格式计算了一个具有解析解的问题,以及二维非定常情况下的方腔驱动流动问题,并且和传统的紧致格式进行了计算时间的对比.