Euler方程的自适应多重非结构网格计算

介绍一种基于四面体网格的多重网格技术,用于求解三维Euler方程定常解,具有十分明显的加速收敛效果。求解Euler方程的基本算法采用有限体积中心差分格点格式。多重网格技术采用一组几何上相互独立的粗细不同的网格。流动变量、余量和修正量在相邻粗细网格间的相互传递通过线性插值实现。采用自适应技术对网格进行加密,可以获得较优的网格,并作为一套细网格,进行多重网格计算。数值实验表明本文自适应多重网格法十分有效。

Three Dimensional Adaptive Multigrid for the Euler Equatoins

This paper describes a three-dimensional adaptive multigrid method on unstructured meshes for the Euler equations. The basic algorithm for the Euler solver consists of an explicit vertex-based finite volume method. The multigrid method uses three independently generated coarse and fine meshes to accelerate the convergence to steady state of the fine grid solution. Flow variables, residuals, and corrections are passed back and forth between the various meshes using linear interpolation. An adaptive strategy is used to generate optimum meshes. The Delaunay triangulation is used both to generate the meshes and to refine the meshes. Numerical examples are given to show the accuracy and efficiency of the present method.