Variational Multiscale Finite Element Method for Flows in Highly Porous Media

We present a two-scale finite element method (FEM) for solving Brinkman's and Darcy's equations. These systems of equations model fluid flows in highly porous and porous media, respectively. The method uses a recently proposed discontinuous Galerkin FEM for Stokes' equations by Wang a...

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Bibliographic Details
Published inMultiscale modeling & simulation Vol. 9; no. 4; pp. 1350 - 1372
Main Authors Iliev, O., Lazarov, R., Willems, J.
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.10.2011
Subjects
Applied mathematics
Approximation
Finite element analysis
Informatics
Methods
Permeability
Porous materials
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Summary:We present a two-scale finite element method (FEM) for solving Brinkman's and Darcy's equations. These systems of equations model fluid flows in highly porous and porous media, respectively. The method uses a recently proposed discontinuous Galerkin FEM for Stokes' equations by Wang and Ye and the concept of subgrid approximation developed by Arbogast for Darcy's equations. In order to reduce the "resonance error" and to ensure convergence to the global fine solution, the algorithm is put in the framework of alternating Schwarz iterations using subdomains around the coarse-grid boundaries. The discussed algorithms are implemented using the Deal.II finite element library and are tested on a number of model problems. [PUBLICATION ABSTRACT]
ISSN:1540-3459
1540-3467
DOI:10.1137/10079940X