November 15, 2011
||Prof. Dr. Christian Engwer
Institut für Numerische und Angewandte Mathematik,Fachbereich Mathematik und Informatik der Universität Münster
||Pfaffenwaldring 61, Raum U1.003 (MML), Universität Stuttgart
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For simulations of processes in porous media usually a homogenizedmacroscopic scale is considered. On the macro scale empirical laws areused, which require effective parameters. The models, as well a theparameters are directly linked to pore scale physics and the geometryof the pore space. Pore scale simulations can help where experimentsare not possible, or hard to conduct. They give an opportunity fordifferent application, e.g. parameter estimation or modelverification.We present the Unfitted Discontinuous Galerkin method, a numericalscheme for solving PDEs on domains with a complicated geometricshape. This method is well suited for simulations on the porescale. The method uses finite element meshes which are significantlycoarser then those required by standard conforming finite elementapproaches and is flexible enough to be used for elliptic, hyperbolicand parabolic problems.We apply this method to numerical upscaling using direct simulation onthe pore scale, as well as model verification. The method is robustwith respect to computations on coarse meshes.