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A locally conservative variational multiscale method for the simulation of porous media flow with multiscale source term

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dc.contributor.author Juanes, Ruben
dc.contributor.author Dub, Francois-Xavier
dc.contributor.other Massachusetts Institute of Technology. Earth Resources Laboratory en_US
dc.date.accessioned 2012-01-11T22:15:01Z
dc.date.available 2012-01-11T22:15:01Z
dc.date.issued 2008
dc.identifier.uri http://hdl.handle.net/1721.1/68202
dc.description.abstract We present a variational multiscale mixed finite element method for the solution of Darcy flow in porous media, in which both the permeability field and the source term display a multiscale character. The formulation is based on a multiscale split of the solution into coarse and subgrid scales. This decomposition is invoked in a variational setting that leads to a rigorous definition of a (global) coarse problem and a set of (local) subgrid problems. One of the key issues for the success of the method is the proper definition of the boundary conditions for the localization of the subgrid problems. We identify a weak compatibility condition that allows for subgrid communication across element interfaces, a feature that turns out to be essential for obtaining high-quality solutions. We also remove the singularities due to concentrated sources from the coarse-scale problem by introducing additional multiscale basis functions, based on a decomposition of fine-scale source terms into coarse and deviatoric components. The method is locally conservative and employs a low-order approximation of pressure and velocity at both scales. We illustrate the performance of the method on several synthetic cases and conclude that the method is able to capture the global and local flow patterns accurately. en_US
dc.publisher Massachusetts Institute of Technology. Earth Resources Laboratory en_US
dc.relation.ispartofseries Earth Resources Laboratory Industry Consortia Annual Report;2008-05
dc.title A locally conservative variational multiscale method for the simulation of porous media flow with multiscale source term en_US
dc.type Technical Report en_US
dc.contributor.mitauthor Juanes, Ruben
dc.contributor.mitauthor Dub, Francois-Xavier
dspace.orderedauthors Juanes, Ruben; Dub, Francois-Xavier en_US


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