February 5, 2019

IRTG-IMPM Short Course: Florin Adrian Radu, Manuel Borregales & Erlend Storvik

From 5th until 8th February 2019

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

Abstract
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 [1]).

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 [2]). 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).


References

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.

Contact

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