嵌套式迭代法数值求解粘性可压NS方程

A NESTED ITERATIVE METHOD FOR SOLVING THE COMPRESSIBLE NAVIER-STOKES EQUATIONS

1.引言计算技术的飞速发展为气动问题的数值模拟提供了良好的工具,虽然近年来数值方法的研究取得了很大进展,但如何提高计算效率仍是一个重要课题。显式方法计算简单,但时间步长受到很大限制,Beam和Warming提出的隐式方法提高了计算效率。一般说来,隐式法对二维问题需对五对角块矩阵进行求逆,而对三维问题需对七对角块矩阵求逆,目前还没有一个好的方法直接求解这类问题,近似因式分解法使求解过程大为简化,

For numerical simulation of aerodynamic problems, complex algebraic equations have to be solved. The technique with approximate factorization is a quite simple method for solving the aerodynamic equations but new truncation error is introduced. In the present paper, a nested iterative method is proposed using the special Jacobian matrix splitting. With this method instead of block-tridiagonal matrices only tridiagonal matrices need to be inverted. Computational work is much reduced with the nested terative method. The suggested method has been used to solve practical problems.