基于非结构网格的高效求解方法研究  

Efficient solution of Euler/N-S equations on unstructured grids

作　　者：蒋跃文[1] 叶正寅[1] 王刚[1] 

机构地区：[1]西北工业大学翼型叶栅空气动力学国防科技重点实验室,西安710072

出　　处：《计算力学学报》2012年第2期217-223,235,共8页Chinese Journal of Computational Mechanics

基　　金：博士论文创新基金;国家自然科学基金(11072199;10802067)资助项目

摘　　要：非结构网格的求解效率一直是计算流体力学工作者十分关注的问题。本文从一个新的角度分析了N-S(Euler/Navier-Stokes)方程求解效率的高低,表明计算效率不仅涉及时间离散的效率,空间离散和程序算法都与之息息相关。采用不同的计算状态,对目前非结构网格上广泛应用的LU-SGS、对称Gauss-Seidel和GMRES方法进行较详细地比较和分析,考查了空间离散的耗时对方程求解效率的影响。结果表明,LU-SGS方法的计算效率在所给的算例中均是最低的;在不考虑大量内存消耗时,GMRES算法求解Euler方程的效率较高,松耦合求解N-S方程时效率会有所降低;在大规模计算中,多次对称的Gauss-Seidel迭代方法应是较好的选择,特别是N-S方程的求解。The implicit time integration method has been investigated to be an efficient approach for solving Euler/Navier-Stokes（N-S） equations.The resulting linear equations are typically large,sparse,nonsymmetric,and ill-conditioned.In general,the linear equations are approximately solved through LU-SGS,symmetric Gauss-Seidel and GMRES algorithms,etc.Compared to the structured grid,the order of unstructured grid is irregular,which significantly affects the computational efficiency.In the traditional efficiency analysis,the effect of spatial efficiency has been hardly considered.The different calculations and comparisons were presented in the paper.If the memory requirement is accomplished,GMRES algorithm is efficient.But the calculation of SA turbulence model in N-S equations affects the rate of the convergence.If the spatial discretization is efficient,the symmetric Gauss-Seidel with inner iterations is performed well.It is a better choice for the large-scale calculations,especially for viscous flow.

关 键 词：EULER/N-S方程 隐式 效率 GAUSS-SEIDEL GMRES 

分 类 号：O35[理学—流体力学]