Numerical methods for porous media flow models: iterative schemes and domain decomposition approaches
Time: 12:45 – 13:30, April 11
Mathematical models for porous media flows appear are relevant for numerous real-life applications. Examples in this sense are enhanced oil recovery, geological CO2 storage, geothermal energy or the design of fuel cells. Mathematical modelling and numerical simulation are essential tools for understanding and controlling such processes. Commonly, the resulting mathematical models are (systems of) nonlinear partial differential equations of evolution type, with nonlinearities that vanish or become unbounded depending on the solution of the equation. The occurrence of such degenerate situations makes developing numerical schemes for such problems particularly challenging. We start by presenting some concepts related to the mathematical modelling of unsaturated or two-phase flow in porous media. Then we focus on the numerical discretisation, which is implicit or semi-implicit in time and therefore leads at each time step to a nonlinear time discrete or fully discrete problem. We present some approaches for solving these nonlinear problems. In particular, we present a scheme combining linear iterations with domain decomposition, and analyse its convergence.
Presenter: Prof. Sorin PopIuliu Sorin Pop is professor of Computational Mathematics at the Universities of Hasselt (Belgium) and Bergen (Norway). His research interest is the mathematical analysis, numerical simulation and upscaling of mathematical models for flow and reactive transport in complex media. He is Program Director of the Activity Group on Geosciences of the Society for Industrial and Applied Mathematics (SIAM). In 2015 he received the InterPore Procter & Gamble Award for Porous Media Research.