A stable numerical algorithm for the Brinkman equations by weak Galerkin finite element methods

This paper presents a stable numerical algorithm for the Brinkman equations by using weak Galerkin (WG) finite element methods. The Brinkman equations can be viewed mathematically as a combination of the Stokes and Darcy equations which model fluid flow in a multi-physics environment, such as flow i...

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Vydané v:Journal of computational physics Ročník 273; s. 327 - 342
Hlavní autori: Mu, Lin, Wang, Junping, Ye, Xiu
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier Inc 15.09.2014
Predmet:
Computational fluid dynamics
Computer simulation
Finite element method
Finite element methods
Fluid flow
Mathematical analysis
Mathematical models
Numerical analysis
Polyhedral meshes
Stokes law (fluid mechanics)
The Brinkman equations
Weak Galerkin
Weak Galerkin
Finite element methods
The Brinkman equations
Polyhedral meshes
ISSN:0021-9991, 1090-2716
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Shrnutí:This paper presents a stable numerical algorithm for the Brinkman equations by using weak Galerkin (WG) finite element methods. The Brinkman equations can be viewed mathematically as a combination of the Stokes and Darcy equations which model fluid flow in a multi-physics environment, such as flow in complex porous media with a permeability coefficient highly varying in the simulation domain. In such applications, the flow is dominated by Darcy in some regions and by Stokes in others. It is well known that the usual Stokes stable elements do not work well for Darcy flow and vice versa. The challenge of this study is on the design of numerical schemes which are stable for both the Stokes and the Darcy equations. This paper shows that the WG finite element method is capable of meeting this challenge by providing a numerical scheme that is stable and accurate for both Darcy and the Stokes dominated flows. Error estimates of optimal order are established for the corresponding WG finite element solutions. The paper also presents some numerical experiments that demonstrate the robustness, reliability, flexibility and accuracy of the WG method for the Brinkman equations.
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ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2014.04.017