Prof. Florin Adrian Radu, Manuel Antonio Borregales Reverón and Erlend Storvik from the Department of Mathematics, University of Bergen (Norway) will give a short course, entitled: "Solvers for nonlinear and/or coupled problems in porous media".
Date: 5th to 8th February 2019
Time: 9 am - 1 pm
Place: Pfaffenwaldring 57, Room 2.136, Campus Vaihingen
The aim of this compact course is to give an overview over the most important techniques for solving nonlinear and/or coupled problems in porous media. Two model problems will be considered: the Richards equation and the (saturated and unsaturated) Biot equations. Linearization techniques, i.e. Newton method, L-scheme and Picard method will be presented. The convergence of the resulting schemes will be discussed. The techniques will be applied to Richards´ equation and implemented (FE or FV can be used). A study on the advantages and disadvantages of these methods w.r.t. efficiency and robustness will be performed (see ).
In the second part of the course iterative schemes, e.g. the fixed-stress method for the fully coupled Biot equations will be presented and implemented (see ). Nonlinear extensions (incl. unsaturated poromechanics) of the model and application of iterative schemes in combination with linearization will be then discussed (se [3, 4]).
Requirements: linear algebra, finite element or finite volume method, a laptop and a software package for solving PDEs (like DUNE, Fenics or even Matlab).
1. F. List, F.A. Radu, A study on iterative methods for Richards´ equation, Computational Geosciences 20, 2016, pp. 341-353.
2. J. W. Both, M. Borregales, J.M. Nordbotten, K. Kumar, F.A. Radu, Robust fixed stress splitting for Biot´s equation in heterogeneous media, Applied Math. Letters 68, 2017, pp. 101-108.
3. M. Borregales, F.A. Radu, K. Kumar, J.M. Nordbotten, Robust schemes for non-linear poromechanics, Computational Geosciences 22, 2018, pp. 1021-1038.
4. J. W. Both, K. Kumar, J.M. Nordbotten, F.A. Radu, Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media, Computers and Mathematics with Applications, 2018, DOI: 10.1016/j.camwa.2018.07.033.