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Institut für Wasserbau - IWS

Selected Topics and International Network Lectures

16:00 Uhr
Dr. Iuliu Sorin Pop, Dept. of Mathematics and Computer Science, TU Eindhoven, Niederlande

Numerical Approaches for Porous Media Flows

In this talk we discuss some numerical methods that are appropriate for models describing porous media flows. Such problems are typically parabolic nonlinear, but - depending on the values of the unknown - may degenerate into elliptic or hyperbolic ones. As a consequence, the solution may lack regularity and develop singularities.

Appropriate numerical algorithms are requested for dealing with such kind of problems. We focus here on the particular case of a scalar model that can be formulated in a fixed domain. To overcome the difficulties that are due to the degeneracy, we first perturb the original model and end up with a regular parabolic one. For the resulting we employ standard discretization methods (implicit in time and an upwinded box scheme in space) and show that these lead to stable and convergent algorithms. A few words will be said on how to solve the time discrete nonlinear problems.