Numerical methods for porous media flows
by Sorin Pop (Hasselt University, Belgium)
Porous media flows are encountered in numerous applications of utmost societal and technological relevance. Examples in this sense are in water resource management, geological CO2 sequestration, oil recovery, or geothermal energy. Mathematical modelling and numerical simulation are key approaches for understanding such processes in their entire complexity, and further for providing reliable predictive information.
In this presentation we start by addressing different aspects related to the modelling of porous media flows, including equilibrium and non-equilibrium cases. Next, after summarizing some existence and uniqueness results, we focus on the numerical methods. The discussion includes rigorous convergence of the discretization schemes, as well as linear iterative methods for approximating the solutions of the nonlinear, time discrete or fully discrete problems.
Finally, we consider heterogeneous media, and discuss some numerical results and relate these with experimental ones.