基于全隐式无分裂算法求解三维N-S方程

Solver of three-dimensional Navier-Stokes equations based on the fully implicit unfactored algorithm

基于多块结构网格,本文研究和发展了三维N-S方程的全隐式无分裂算法。对流项的离散运用Roe格式,粘性项的离散利用中心型格式。在每一次隐式时间迭代中,运用GMRES方法直接求解隐式离散引起的大型稀疏线性方组。为了降低内存需求以及矩阵与向量之间的运算操作数,Jacobian矩阵的一种逼近方法被应用在本文的算法之中。计算结果与实验结果基本吻合,表明本文的全隐式无分裂方法是有效和可行的。

A fully implicit unfactored algorithm of three-dimensional N-S equations is developed and test- ed on multi-block curvilinear meshes. The convective terms are discretized using Roe scheme; the viscous terms are discretized using a center scheme. The large-scale sparse linear system arising from each implicit time step is solved by GMRES method combined with the block incomplete lower-upper preconditioner. In order to reduce memory requirements and matrix-vector operation counts, an approximate method for the derivation of Jacobian matrix is applied in the present work, which counts to a half of the values using the exact Jacobian matrix. Comparison of numerical results is made with experimental data and good agreement between them is achieved, demonstrating that the implicit algorithm presented in the paper is effective and efficient.