Discontinuous Galerkin approximation of two-phase flows in heterogeneous porous media with discontinuous capillary pressures |
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| Authors: | A. Ern I. Mozolevski L. Schuh |
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| Affiliation: | 1. Department of Mathematics, University of Bergen, Allégaten 41, Bergen 5007, Norway;2. Department of Mathematics, KTH Royal Institute of Technology, Lindstedtsvägen 25, Stockholm 11428, Sweden;3. Department of Hydromechanics and Modelling of Hydrosystems, University of Stuttgart, Pfaffenwaldring 61, Stuttgart 70569, Germany;4. Laboratory for Modeling and Scientific Computing MOX, Politecnico di Milano, p.za Leonardo da Vinci 32, Milano 20133, Italy;5. Department of Applied Geology, Geosciences Center, University of Göttingen, Goldschmidtstrasse 3, Göttingen 3707, Germany;6. Department of Earth Sciences, Uppsala University, Villavägen 16, Uppsala S-75236, Sweden;7. University of Côte d’Azur, CNRS, INRIA, LJAD, Nice, France;8. Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, Pfaffenwaldring 57, Stuttgart 70569, Germany;9. FEC-Universidade Estadual de Campinas, R. Josiah Willard Gibbs 85 - Cidade Universitäria, Campinas SP, Brazil, CEP 13083-839;10. Institute of Earth Sciences, University of Lausanne, Building Geopolis, UNIL-Mouline, Lausanne 1015, Switzerland;11. Section de Mathämatiques, University de Genäve, 2–4 rue du Liävre, CP 64, Genäve 1211, Switzerland;12. Graduate Institute of Applied Geology, National Central University, Taiwan;13. Center for Environmental Studies, National Central University, Taiwan;14. Los Alamos National Laboratory, New Mexico, USA;15. Department of Environmental Engineering, Technical University of Denmark, Bygningstorvet, Building 115, Lyngby 2800 Kgs., Denmark;p. Numerical Simulation in Science, Medicine and Engineering Group, Institute of Computational Science, University della Svizzera italiana Via G. Buffi 13, Lugano Ticino 6900, Switzerland;q. Marchuk Institute of Numerical Mathematics of Russian Academy of Sciences, Moscow, Russia;r. ETH Zürich, Geothermal Energy and Geofluids Group, Institute of Geophysics, Zürich 8092, Switzerland |
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| Abstract: | We design and investigate a sequential discontinuous Galerkin method to approximate two-phase immiscible incompressible flows in heterogeneous porous media with discontinuous capillary pressures. The nonlinear interface conditions are enforced weakly through an adequate design of the penalties on interelement jumps of the pressure and the saturation. An accurate reconstruction of the total velocity is considered in the Raviart–Thomas(–Nédélec) finite element spaces, together with diffusivity-dependent weighted averages to cope with degeneracies in the saturation equation and with media heterogeneities. The proposed method is assessed on one-dimensional test cases exhibiting rough solutions, degeneracies, and capillary barriers. Stable and accurate solutions are obtained without limiters. |
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