Numerical upscaling for flows in heterogeneous porous media

June 26, 2008

Time: June 26, 2008
Lecturer: Dr. Iryna Rybak
Institut für Angewandte Analysis und Numerische Simulation, Uni Stuttgart
Venue: Pfaffenwaldring 61, Raum U1.003 (MML), Universität Stuttgart
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Porous media are often highly heterogeneous. Solving porous media problems at the fine scale, whichresolves all the heterogeneities, is computationally expensive due to the required memory and computational time. Upscaling techniques, such as homogenization, averaging, etc., have to be used to make solving multiscale problems possible.

Essential success was achieved during the last decades in the studies of problems with clearlyseparated fine and coarse scales (periodic microstructure, statistically homogeneous porous media). When the fine and the coarse scales can be decoupled, solving a multiscale problem reducesto one way two-stage procedure: i) solve fine scale "cell-problem" and use its solution to upscale the effective properties of the multiscale media; ii) solve coarse scale equations with the calculated effective coefficients. The separation of scales, however, is not always possible, and developing numerical upscaling techniques for such problems is the subject of this presentation.

We consider pressure equation, obtained by combining the continuity equation and Darcy's law, for steady state incompressible single-phase flow. Finite volume discretization (Multi-Point Flux Approximation) for this problem is developed in the case of jump discontinuities for the permeability. The effective properties of the media are calculated, two-grid method is discussed and the results from numerical experiments are presented.

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