Variational multiscale Finite Element Method for flows in highly porous media

  • We present a two-scale finite element method 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 byWang 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.

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Metadaten
Author:O. Iliev, R. Lazarov, J. Willems
URN (permanent link):urn:nbn:de:hbz:386-kluedo-16527
Serie (Series number):Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) (187)
Document Type:Report
Language of publication:English
Year of Completion:2010
Year of Publication:2010
Publishing Institute:Fraunhofer-Institut für Techno- und Wirtschaftsmathematik
Tag:Brinkman equations ; Darcy’s law ; flow in heterogeneous porous media ; numerical upscaling ; subgrid approximation
Faculties / Organisational entities:Fraunhofer (ITWM)
DDC-Cassification:510 Mathematik

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