On first-order formulations of the least-squares finite element method for incompressible flows

被引：10

作者：

Ding, X ^{[1
]}

Tsang, TTH ^{[1
]}

机构：

[1] Univ Kentucky, Dept Chem & Mat Engn, Lexington, KY 40506 USA

来源：

INTERNATIONAL JOURNAL OF COMPUTATIONAL FLUID DYNAMICS | 2003年 / 17卷 / 03期

关键词：

least-squares finite element method; incompressible flows; vorticity; pressure formulations;

D O I：

10.1080/1061856031000123580

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

To reduce the element continuity requirement for the least-squares finite element method (LSFEM), it is customary to rewrite the Navier-Stokes equations as first-order partial differential equations. In this work, numerical experiments for three-dimensional incompressible flows are carried out by using the LSFEM based on three types of first-order formulations, namely the velocity-vorticity-pressure (VVP) formulation, the velocity-stress-pressure (VSP) formulation and the velocity-velocity gradient-pressure (VVGP) formulation. In addition, two modifications for each formulation are considered. Numerical results indicate that proper problem formulation can significantly reduce computing time and improve the accuracy of numerical solutions.

引用

页码：183 / 197

页数：15

共 22 条

[1] ESTIMATES NEAR BOUNDARY FOR SOLUTIONS OF ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS SATISFYING GENERAL BOUNDARY CONDITIONS .2. [J].

AGMON, S ;

DOUGLIS, A ;

NIRENBERG, L .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1964, 17 (01) :35-&

[2] Analysis of velocity-flux least-squares principles for the Navier-Stokes equations: Part II [J].

Bochev, P ;

Manteuffel, TA ;

McCormick, SF .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1999, 36 (04) :1125-1144

[3] LEAST-SQUARES METHODS FOR THE VELOCITY-PRESSURE-STRESS FORMULATION OF THE STOKES EQUATIONS [J].

BOCHEV, PB ;

GUNZBURGER, MD .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1995, 126 (3-4) :267-287

[4] Analysis of least-squares finite element methods for the Navier-Stokes equations [J].

Bochev, PB .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1997, 34 (05) :1817-1844

[5] Finite element methods of least-squares type [J].

Bochev, PB ;

Gunzburger, MD .

SIAM REVIEW, 1998, 40 (04) :789-837

[6] FINITE DIMENSIONAL APPROXIMATION OF NON-LINEAR PROBLEMS .1. BRANCHES OF NONSINGULAR SOLUTIONS [J].

BREZZI, F ;

RAPPAZ, J ;

RAVIART, PA .

NUMERISCHE MATHEMATIK, 1980, 36 (01) :1-25

[7] First-order system least squares for the Stokes equations, with application to linear elasticity [J].

Cai, Z ;

Manteuffel, TA ;

McCormick, SF .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1997, 34 (05) :1727-1741

[8] A least-squares finite element method for incompressible flow in stress-velocity-pressure version [J].

Chang, CL ;

Yang, SY ;

Hsu, CH .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1995, 128 (1-2) :1-9

[9] Issues related to least-squares finite element methods for the Stokes equations [J].

Deang, JM ;

Gunzburger, MD .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 1998, 20 (03) :878-906

[10] Large eddy simulation of turbulent flows by a least-squares finite element method [J].

Ding, X ;

Tsang, TTH .

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, 2001, 37 (03) :297-319

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