Pressure stabilization of finite element approximations of time-dependent incompressible flow problems

被引：11
作者：
Barrenechea, Gabriel R.
Blasco, Jordi
机构：
[1] Univ Concepcion, Dept Ingn Matemat, Concepcion, Chile
[2] Univ Politecn Cataluna, Dept Matemat Aplicada 1, E-08028 Barcelona, Spain
来源：
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING | 2007年 / 197卷 / 1-4期
关键词：
incompressible flow; time-dependent Stokes problem; pressure stabilization; stability analysis; finite elements;
D O I：
10.1016/j.cma.2007.07.027
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
In this paper we develop and analyze pressure stabilized, finite element methods for the solution of the transient Stokes problem, which is a linear model problem of transient incompressible flow. A model for the bubble enrichment is proposed to stabilize the numerical solution and an implicit backward Euler method is considered for the time approximation. Different methods are obtained depending on whether bubbles are allowed to evolve with time or they are considered quasi-static. Stability estimates are provided for the two methods considered, both for the velocity and the pressure solutions. Numerical results obtained on test cases are also given, which confirm the theoretical stability results. (c) 2007 Elsevier B.V. All rights reserved.
引用
收藏
页码：219 / 231
页数：13
相关论文
共 36 条
[11]   On inf-sup stabilized finite element methods for transient problems [J].
Bochev, PB ;
Gunzburger, MD ;
Shadid, JN .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2004, 193 (15-16) :1471-1489
[12]   A RELATIONSHIP BETWEEN STABILIZED FINITE-ELEMENT METHODS AND THE GALERKIN METHOD WITH BUBBLE FUNCTIONS [J].
BREZZI, F ;
BRISTEAU, MO ;
FRANCA, LP ;
MALLET, M ;
ROGE, G .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1992, 96 (01) :117-129
[13]  
Brezzi F., 1984, Efficient Solutions of Elliptic Systems, V10, P11
[14]  
Brezzi F., 1991, SPRINGER SERIES COMP, V15
[15]   STREAMLINE UPWIND PETROV-GALERKIN FORMULATIONS FOR CONVECTION DOMINATED FLOWS WITH PARTICULAR EMPHASIS ON THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS [J].
BROOKS, AN ;
HUGHES, TJR .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1982, 32 (1-3) :199-259
[16]   Analysis of a pressure-stabilized finite element approximation of the stationary Navier-Stokes equations [J].
Codina, R ;
Blasco, J .
NUMERISCHE MATHEMATIK, 2000, 87 (01) :59-81
[17]   Stabilized finite element method for the transient Navier-Stokes equations based on a pressure gradient projection [J].
Codina, R ;
Blasco, J .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2000, 182 (3-4) :277-300
[18]  
Codina R, 1998, INT J NUMER METH FL, V27, P13, DOI 10.1002/(SICI)1097-0363(199801)27:1/4<13::AID-FLD647>3.0.CO
[19]  
2-8
[20]   A finite element formulation for the Stokes problem allowing equal velocity-pressure interpolation [J].
Codina, R ;
Blasco, J .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1997, 143 (3-4) :373-391
1234