求解不可压Navier-Stokes方程的一种高效两水平方法  

An Efficient Two-Level Method for Solving Incompressible Navier-Stokes Equations

作　　者：杜彬彬 黄建国 Du Binbin;Huang Jianguo(School of Mathematical Sciences,Shanghai Jiao Tong University,Shanghai 200240,China)

机构地区：[1]上海交通大学数学科学学院

出　　处：《南京师大学报（自然科学版）》2019年第3期157-162,共6页Journal of Nanjing Normal University(Natural Science Edition)

基　　金：国家自然科学基金面上项目(11571237)

摘　　要：提出了一种基于Arrow-Hurwicz(A-H)方法的两水平方法(以下简称m-A-H-1-Oseen方法)来求解不可压Navier-Stokes(N-S)方程.首先在粗网格上采用A-H方法求解不可压N-S方程,得到粗网格上的数值解.然后在细网格上利用粗网格上的数值解求解原方程线性化的Oseen格式,由此获得所需的两水平方法.对该方法的收敛性进行了系统理论分析.This paper proposes a two-level Arrow-Hurwicz(A-H)method(simply called the m-A-H-1-Oseen method)for solving incompressible Navier-Stokes(N-S)equations.The incompressible N-S equations are first solved by the A-H method to obtain a numerical solution on a coarse mesh.Next,the desired numerical solution is obtained by solving the Oseen scheme,which is derived on a fine mesh by linearizing the original equations using the coarse solution,leading to the required two-level method.The convergence analysis is developed systematically.

关 键 词：Arrow-Hurwicz方法 NAVIER-STOKES方程 两水平方法 Oseen格式 

分 类 号：O24[理学—计算数学]