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Advanced Numerical Methods in the Mathematical Sciences

Beatrice Riviere, Rice University
High Order Methods for Flows in Heterogeneous Porous Media


We formulate high order discontinuous Galerkin methods in space for coupled flow and transport problems in heterogeneous porous media. Heterogeneities include large variations in the permeability and porosity fields. We apply the method to two problems: a miscible displacement and a three-phase flow. Convergence of the method is obtained theoretically with minimum regularity assumption on the input data. Robustness and scalability of the method is obtained for three-dimensional problems.