解不可压缩Navier-Stokes方程的非精确块因子分解预处理子  

An inexact block factorization preconditioner for solving incompressible Navier-Stokes equations

作　　者：宋胜重 黄正达 SONG Sheng-zhong;HUANG Zheng-da(School of Mathematical Sciences,Zhejiang University,Hangzhou 310058,China;Fundation Science Education Center,Hangzhou City University,Hangzhou 310015,China)

机构地区：[1]浙江大学数学科学学院,浙江杭州310058 [2]浙大城市学院理学基础教育中心,浙江杭州310015

出　　处：《高校应用数学学报（A辑）》2023年第3期317-328,共12页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11871430)。

摘　　要：针对相关于不可压缩Navier-Stokes方程数值求解的一类3×3块结构的线性方程组,基于线性方程组的等价形式,构造了一个非精确的块因子分解预处理子,在新的特征值等价矩阵形式的基础上,得到了预处理矩阵特征值实部和虚部的上下界估计.数值实验表明,与已有的预处理子相比,所构造的预处理子可以使得GMRES迭代方法对网格尺寸,网格形式以及粘度系数的依赖性都比较弱,且在迭代步数和CPU时间上都占优.For solving the system of linear equations with a 3×3 block structure related to the incompressible Navier-Stokes equations,an inexact block factorization preconditioner is constructed based on an equivalent form of the system,the upper and lower bounds of the real and imaginary parts of eigenvalues of the preconditioned matrix are estimated by transforming the preconditioned matrix to a similar one.Numerical experiments show that compared to existed preconditioners,the constructed preconditioner can make the GMRES depend weakly on the mesh size,grid form and kinematic viscosity,and is superior in the number of iteration steps and CPU time.

关 键 词：不可压缩NAVIER-STOKES方程 预处理子 特征值 GMRES 

分 类 号：O241.6[理学—计算数学]