三维不可压N-S方程的多重网格求解

应用全近似存储(Full Approximation Storage,FAS)多重网格法和人工压缩性方法求解了三维不可压Navi-er-Stokes方程.在解粗网格差分方程时,对Neumann边界条件采用增量形式进行更新,离散方程用对角化形式的近似隐式因子分解格式求解,其中空间无粘项分别用MUSCL格式和对称TVD格式进行离散.对90°弯曲的方截面管道流动和4:1椭球体层流绕流的数值模拟表明,多重网格的计算时间比单重网格节省一半以上,且无限制函数的MUSCL格式比TVD格式对流动结构有更好的分辨能力.

MULTIGRID SOLUTIONS FOR THE THREE-DIMENSIONAL INCOMPRESSIBLE NAVIER-STOKES EQUATIONS IN ARTIFICIAL COMPRESSIBILITY FORMULATION

The full approximation storage (FAS) multigrid algorithm is applied in conjunction with the artificial compressibility method to accelerate steady solutions of the 3D incompressible Navier Stokes equations. Neumann boundary conditions in terms of the solution correction are implemented on the coarse grid when solving the coarse grid equations. The basic scheme used is the diagonalized approximate factorization scheme, and the spatial difference for inviscid fluxes adopts both MUSCL scheme and symmetric TVD scheme respectively for comparing. The performance of the present method is studied for the entry flow through a 90° bent square duct and the flow past an inclined prolate spheroid with an axes ratio of 4:1. It is found that the proposed multigrid method can save the computing time by at least half, and that MUSCL scheme is slightly better than TVD scheme in resolving the flow structures.