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

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

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.

Original language	English
Pages (from-to)	21-39
Number of pages	19
Journal	International Journal of Computational Fluid Dynamics
Volume	4
Issue number	1-2
DOIs	https://doi.org/10.1080/10618569508904516
State	Published - Jan 1 1995

Bibliographical note

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

Funding

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

Funders	Funder number
National Science Foundation (NSF)

Keywords

Iterative Methods
Jacobi Conjugate Gradient Method
Least-squares Finite Element Method
incompressible Flows

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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10.1080/10618569508904516

Cite this

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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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author = "Tang, {L. Q.} and Tsang, {T. T.H.}",

note = "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",

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PY - 1995/1/1

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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.

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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

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

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