定常Navier-Stokes方程压力投影子格稳定化Defect-Correction方法  

A SUBGRID STABILIZED DEFECT-CORRECTION METHODS FOR THE STATIONARY NAVIER-STOKES PROBLEM BASED ON POLYNOMIAL PRESSURE PROJECTIONS

作　　者：尹蕾[1] 冯民富[1] 覃燕梅[1] 

机构地区：[1]四川大学数学学院,成都610064

出　　处：《高等学校计算数学学报》2011年第3期235-249,共15页Numerical Mathematics A Journal of Chinese Universities

基　　金：四川省科技攻关课题(编号:05GG006-006-2)资助项目

摘　　要：粘性不可压缩Navier—Stokes方程的有限元法研究一直是人们研究的热点问题．通常混合有限元法研究需要处理两个基本问题：一是要求速度一压力有限元空间组合必须满足inf-sup条件，这一条件根本限制了工程上计算方便的等阶插值有限元空间组合的应用．二是粘性系数很小出现对流占优时，解呈现出不稳定性．This article combines the pressure projection stabilization with the subgrid stabilization to develop a new Defect-Correction method for the stationary Navier-Stokes problem.This method not only solves the convection-dominated problem when the Reynolds number is too high,but also avoids the limit of satisfying the so called inf-sup condition.Towards the equal-order interpolation of velocity- pressure pair ,the theoretical analysis is presented.

关 键 词：NAVIER-STOKES方程 不稳定性 压力 混合有限元法 INF-SUP条件 子格 投影 定常 

分 类 号：O241.8[理学—计算数学]