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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:273

Article

Mu, Lin¹  Wang, Junping²  Ye, Xiu³ 

[1] Michigan State Univ, Dept Math, E Lansing, MI 48824 USA

[2] Natl Sci Fdn, Div Math Sci, Arlington, VA 22230 USA

[3] Univ Arkansas, Dept Math, Little Rock, AR 72204 USA

关键词: Weak Galerkin;    Finite element methods;    The Brinkman equations;    Polyhedral meshes;   

DOI  :  10.1016/j.jcp.2014.04.017

来源: Elsevier

【 摘 要 】

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. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

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