November 10, 2009
||Dipl. Math. Frederike Kissling
Institut für angewandte Analysis und numerische Simulation, Universität Stuttgart
||Pfaffenwaldring 61, Raum U1.003 (MML), Universität Stuttgart
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The quantitative prediction of multiphase dynamics is of practical interest inmany subsurface processes like in petroleum engineering, simulation of contaminantintrusions or geological CO2-sequestration. To get a general idea of thestructure of the solution and to develop a numerical scheme we confine ourselvesto one-dimensional two-phase flow through porous media.We consider weak solutions of the Buckley-Leverett equation as singular limitsof solutions for an extension of the Buckley-Leverett equation. This extensionincludes a third order mixed derivatives term and takes into accountrate-dependent capillarity effects. We are interested in situations with saturationovershoot that means undercompressive (Non-Laxian) shock waves occurin the limit. In this setting one can view the Buckley-Leverett equation as amacroscale formulation while the extension can be understood as the microscalemodel. With this point of view we use a heterogeneous multiscale approach tosolve the macroscale model. We introduce a new mass-conserving numericalmethod based on this concept and test it.