Defect correction method for time-dependent viscoelastic fluid flow

被引：14

作者：

Zhang, Yunzhang ^{[1
]}

Hou, Yanren ^{[1
]}

Mu, Baoying ^{[1
]}

机构：

[1] Xi An Jiao Tong Univ, Sch Sci, Xian 710049, Peoples R China

来源：

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2011年 / 88卷 / 07期

基金：

中国国家自然科学基金;

关键词：

viscoelastic fluid flow; finite element; time dependent; defect correction method; discontinuous Galerkin; error estimate; Weissenberg number; NAVIER-STOKES EQUATIONS; SCHEME; FEM;

D O I：

10.1080/00207160.2010.521549

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A defect correction method for solving the time-dependent viscoelastic fluid flow, aiming at high Weissenberg numbers, is presented. In the defect step, the constitutive equation is computed with the artificially reduced Weissenberg parameter for stability, and the residual is considered in the correction step. We show the convergence of the method and derive an error estimate. Numerical experiments support the theoretical results and demonstrate the effectiveness of the method.

引用

页码：1546 / 1563

页数：18

共 20 条

[1]

[Anonymous], 2003, SOBOLEV SPACES

[2] DEFECT CORRECTION METHODS FOR CONVECTION DOMINATED CONVECTION-DIFFUSION PROBLEMS [J].

AXELSSON, O ;

LAYTON, W .

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 1990, 24 (04) :423-455

[3] FINITE-ELEMENT APPROXIMATION OF VISCOELASTIC FLUID-FLOW - EXISTENCE OF APPROXIMATE SOLUTIONS AND ERROR-BOUNDS .1. DISCONTINUOUS CONSTRAINTS [J].

BARANGER, J ;

SANDRI, D .

NUMERISCHE MATHEMATIK, 1992, 63 (01) :13-27

[4] NUMERICAL-ANALYSIS OF A FEM FOR A TRANSIENT VISCOELASTIC FLOW [J].

BARANGER, J ;

WARDI, S .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1995, 125 (1-4) :171-185

[5]

Brenner S. C., 2007, MATH THEORY FINITE E

[6] A fractional step θ-method approximation of time-dependent viscoelastic fluid flow [J].

Chrispell, J. C. ;

Ervin, V. J. ;

Jenkins, E. W. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 232 (02) :159-175

[7] A two-parameter defect-correction method for computation of steady-state viscoelastic fluid flow [J].

Ervin, Vincent J. ;

Howell, Jason S. ;

Lee, Hyesuk .

APPLIED MATHEMATICS AND COMPUTATION, 2008, 196 (02) :818-834

[8] Defect correction method for viscoelastic fluid flows at high Weissenberg number [J].

Ervin, VJ ;

Lee, H .

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2006, 22 (01) :145-164

[9] Adaptive defect-correction methods for viscous incompressible flow problems [J].

Ervin, VJ ;

Layton, WJ ;

Maubach, JM .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2000, 37 (04) :1165-1185

[10]

GULLOPE C, 1990, NONLINEAR ANAL, V15, P849

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