求解Oseen流的交替线松弛多重网格方法  

Solution of the Oseen Flow With the Multigrid Method Based on Alternating-Line Relaxation

作　　者：朱兴文[1,2] 张立翔[1] 

机构地区：[1]昆明理工大学工程力学系,昆明650500 [2]大理大学数学与计算机学院,云南大理671003

出　　处：《应用数学和力学》2016年第11期1145-1155,共11页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(51279071);教育部博士点基金(优先)资助项目(20135314130002)~~

摘　　要：利用Riemann解的通量差分分裂法——Godunov方法对Oseen流控制方程进行离散,得到了基于一阶上迎风格式的离散方程,并给出了使用多重网格方法求解该离散方程的V-循环算法和W-循环算法的收敛性分析.通过局部Fourier分析方法,对获得的离散方程的聚对称交替线GaussSeidel松弛的光滑性质进行了研究.结果表明:使用多重网格的两层网格及三层网格算法求解具有不同Reynolds数的Oseen流,即便是在高Reynolds数情况下,聚对称交替线Gauss-Seidel松弛具有很好的光滑性质,多重网格W-循环算法收敛性比V-循环算法好.The 1st-order upwind discretization form of the Oseen flow was obtained through the Godunovtype flux-difference splitting approach based on the Riemann solver. The convergence analysis of 2 kinds of cycling algorithms,i. e.,the V-cycle and the W-cycle in the multigrid method for the solution of the discretized equations,was performed. Furthermore,the smooth properties of the collective symmetrical alternating-line Gauss-Seidel relaxation was investigated by means of the local Fourier analysis. The numerical results show that the collective symmetrical alternating-line Gauss-Seidel relaxation has sound smooth properties,and the convergence of the W-cycle algorithm is better than that of the V-cycle one in the multigrid method for the solution of the Oseen flow with different Reynolds numbers.

关 键 词：通量差分分裂法 多重网格方法 Oseen流 局部Fourier分析 交替线松弛 

分 类 号：O241.8[理学—计算数学] O241.1[理学—数学]