定常不可压Navier-Stokes方程的两水平grad-div稳定化有限元方法  

Two-level Grad-div Stabilized Finite Element Methods for Steady Incompressible Navier-Stokes Equations

作　　者：王雅莉 郑波 尚月强 WANG Yali;ZHENG Bo;SHANG Yueqiang(School of Mathematics and Statistics,Southwest University,Chongqing 400715,China)

机构地区：[1]西南大学数学与统计学院,重庆400715

出　　处：《计算物理》2024年第4期418-425,共8页Chinese Journal of Computational Physics

基　　金：重庆市自然科学基金(cstc2021jcyj-msxmX1044)资助项目。

摘　　要：使用标准的混合有限元方法数值求解定常不可压Navier-Stokes方程所得速度解的精度常常受压力的影响。为了克服或减弱压力对速度精度的影响,本文将grad-div稳定化方法和两水平有限元方法相结合,提出数值求解定常不可压Navier-Stokes方程的两水平grad-div稳定化有限元方法。首先在粗网格上求解grad-div稳定化的非线性Navier-Stokes问题,然后在细网格上分别求解grad-div稳定化的Stokes型、Newton型和Oseen型的线性问题。最后给出数值算例验证两水平grad-div稳定化有限元方法的高效性。Accuracy of the approximate velocity of the steady incompressible Navier-Stokes equations computed by the standard mixed finite element methods is often affected by the pressure.In order to circumvent or weaken the influence of pressure on the accuracy of the computed velocity,by combining grad-div stabilized method with two-level finite element method,this paper presents a kind of twolevel grad-div stabilized finite element methods for solving the steady incompressible Navier-Stokes equations numerically.The basic idea of the methods is to first solve a grad-div stabilized nonlinear Navier-Stokes problems on a coarse grid,and then solve,respectively,Stokes-linearized,Newton-linearized and Oseen-linearized Navier-Stokes problem with grad-div stabilization on a fine grid.Numerical examples are given to verify the high efficiency of the two-level grad-div stabilized finite element methods.

关 键 词：NAVIER-STOKES方程 grad-div稳定化 两水平方法 有限元方法 

分 类 号：O241.82[理学—计算数学]