交错网格上二维Stokes流的多重网格分布松弛的光滑分析  

Smoothing analysis of distributive relaxation for solving 2D Stokes flow on staggered grid by multigrid method

作　　者：朱兴文 张立翔[2] ZHU Xingwen 1 , ZHANG Lixiang 2(1. School of Mathematics and Computer, Dali University, Dali, Yunnan 671003, China;2. School of Architectural Engineering, Kunming University of Science and Technology, Kunming 650500, Chin)

机构地区：[1]大理大学数学与计算机学院,云南大理671003 [2]昆明理工大学建筑工程学院,昆明650500

出　　处：《中国科技论文》2018年第5期584-587,共4页China Sciencepaper

基　　金：高等学校博士学科点专项科研基金资助项目(20135314130002);国家自然科学基金资助项目(51279071);大理大学博士科研启动费资助项目(KYBS201731)

摘　　要：为了给出多重网格方法中光滑松弛的最佳光滑因子及最优松弛参数,主要利用局部Fourier分析方法对多重网格方法求解二维Stokes流的分布松弛进行了讨论。对交错网格上的离散Stokes算子,通过对其椭圆率进行的计算,表明交错的离散格式是稳定的,从而给出适合于此离散格式的分布松弛方法,得出多重网格松弛的光滑因子只由离散系统的泊松算子决定,对该分布松弛的迭代算子进行了多重网格光滑性分析,在红黑雅克比逐点松弛格式下,利用局部Fourier分析方法给出了最优一阶段松弛参数及最优光滑因子。结果表明:从理论上证明目前已有的控制参数的合理性,为改进多重网格计算效率以及参数的选用提供理论参考,对提升流动数值模拟的精度具有重要意义。To discover the optimal relaxation parameter and related smoothing factor in multigrid method,smoothing properties of distributive relaxation for Stokes flow are investigated by local Fourier analysis（LFA）in multigrid method.As discretizing Stokes operator on the staggered grid,the measure of hellipticity is computed to prove the discrete system is stable.Then the distributive relaxation for discrete Stokes system is developed.It is shown that the smoothing factor of the discrete system is determined by Poisson operator.Finally,with red-black Jacobi point relaxation,the optimal one-stage relaxation parameter and related smoothing factor are presented by LFA.The result proves theoretically the rationality of the existing control parameters,which provides a theoretical reference for improving the efficiency of multigrid computation and parameter selection,and is significant for improving the accuracy of flow numerical simulation.

关 键 词：光滑因子 局部Fourier分析 分布松弛 多重网格方法 

分 类 号：O241.8[理学—计算数学] O241.1[理学—数学]