An efficient least-squares finite element method for incompressible flows and transport processes

L. Q. Tang; T. T.H. Tsang

doi:10.1080/10618569508904516

An efficient least-squares finite element method for incompressible flows and transport processes

L. Q. Tang
, T. T.H. Tsang

Chemical and Materials Engineering

Producción científica: Article › revisión exhaustiva

13 Citas (Scopus)

Resumen

A numerical procedure based on a least-squares finite clement method (LSFEM) and Jacobi conjugate gradient method (JCG) is presented for the numerical solution of fluid flow and transport problems. Unlike many finite element methods, the LSFEM does not involve any upwinding factor. Furthermore, the LSFEM leads to a symmetric and positive definite linear system of equations which can be solved satisfactorily by a preconditioned conjugate gradient method. Four examples, lid-driven cavity flow, thermally-driven cavity flow, Rayleigh-Bcnard convection and doubly-diffusive flow, are presented to validate the preconditioned conjugate gradient method. A comparison of the least-squares finite element method and the Galerkin finite element method (G FEM) is also given. Finally, we demonstrate that the least-squares finite element method with the Jacobi conjugate gradient iterative technique is a promising approach to solve three-dimensional fluid flow and transport problems.

Idioma original	English
Páginas (desde-hasta)	21-39
Número de páginas	19
Publicación	International Journal of Computational Fluid Dynamics
Volumen	4
N.º	1-2
DOI	https://doi.org/10.1080/10618569508904516
Estado	Published - ene 1 1995

Nota bibliográfica

Funding Information:
The work was partially supported by the National Science Foundation (Grant No. ASC-8811171; NSF/KY EPSCoR program). We would like to thank Dr. B. N. Jiang or the NASA Lewis Research Center and Dr. X. C Cai or the Department or Mathematics at the University or Kentucky for useful discussions on preconditioned conjugate gradient iterative methods. We also thank Prof. T. W. Cheng for his participation

Financiación

The work was partially supported by the National Science Foundation (Grant No. ASC-8811171; NSF/KY EPSCoR program). We would like to thank Dr. B. N. Jiang or the NASA Lewis Research Center and Dr. X. C Cai or the Department or Mathematics at the University or Kentucky for useful discussions on preconditioned conjugate gradient iterative methods. We also thank Prof. T. W. Cheng for his participation

Financiadores
National Science Foundation (NSF)

ASJC Scopus subject areas

Computational Mechanics
Aerospace Engineering
Condensed Matter Physics
Energy Engineering and Power Technology
Mechanics of Materials
Mechanical Engineering

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title = "An efficient least-squares finite element method for incompressible flows and transport processes",

abstract = "A numerical procedure based on a least-squares finite clement method (LSFEM) and Jacobi conjugate gradient method (JCG) is presented for the numerical solution of fluid flow and transport problems. Unlike many finite element methods, the LSFEM does not involve any upwinding factor. Furthermore, the LSFEM leads to a symmetric and positive definite linear system of equations which can be solved satisfactorily by a preconditioned conjugate gradient method. Four examples, lid-driven cavity flow, thermally-driven cavity flow, Rayleigh-Bcnard convection and doubly-diffusive flow, are presented to validate the preconditioned conjugate gradient method. A comparison of the least-squares finite element method and the Galerkin finite element method (G FEM) is also given. Finally, we demonstrate that the least-squares finite element method with the Jacobi conjugate gradient iterative technique is a promising approach to solve three-dimensional fluid flow and transport problems.",

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AU - Tsang, T. T.H.

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PY - 1995/1/1

Y1 - 1995/1/1

N2 - A numerical procedure based on a least-squares finite clement method (LSFEM) and Jacobi conjugate gradient method (JCG) is presented for the numerical solution of fluid flow and transport problems. Unlike many finite element methods, the LSFEM does not involve any upwinding factor. Furthermore, the LSFEM leads to a symmetric and positive definite linear system of equations which can be solved satisfactorily by a preconditioned conjugate gradient method. Four examples, lid-driven cavity flow, thermally-driven cavity flow, Rayleigh-Bcnard convection and doubly-diffusive flow, are presented to validate the preconditioned conjugate gradient method. A comparison of the least-squares finite element method and the Galerkin finite element method (G FEM) is also given. Finally, we demonstrate that the least-squares finite element method with the Jacobi conjugate gradient iterative technique is a promising approach to solve three-dimensional fluid flow and transport problems.

AB - A numerical procedure based on a least-squares finite clement method (LSFEM) and Jacobi conjugate gradient method (JCG) is presented for the numerical solution of fluid flow and transport problems. Unlike many finite element methods, the LSFEM does not involve any upwinding factor. Furthermore, the LSFEM leads to a symmetric and positive definite linear system of equations which can be solved satisfactorily by a preconditioned conjugate gradient method. Four examples, lid-driven cavity flow, thermally-driven cavity flow, Rayleigh-Bcnard convection and doubly-diffusive flow, are presented to validate the preconditioned conjugate gradient method. A comparison of the least-squares finite element method and the Galerkin finite element method (G FEM) is also given. Finally, we demonstrate that the least-squares finite element method with the Jacobi conjugate gradient iterative technique is a promising approach to solve three-dimensional fluid flow and transport problems.

KW - Iterative Methods

KW - Jacobi Conjugate Gradient Method

KW - Least-squares Finite Element Method

KW - incompressible Flows

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An efficient least-squares finite element method for incompressible flows and transport processes

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