The second year training of doctoral researchers consists of specialised short courses given by the researchers of the SFB and the international partners. At least 3 credits must be achieved by full and associate members of IRTG-IMPM. For more information on the content of the courses and to register please scroll further down.
|Name of module||Credits||Instructors||Time and place|
|The mathematics of multicomponent reactive transport and flow models||3||P. Knabner||
19.11-21.12.2018, Mondays and Tuesdays, 2 - 3:30 pm,
|Solvers for nonlinear and/or coupled problems in porous media||3||F. A. Radu||5.2.-8.2.2019,
9 am - 1 pm Pfaffenwaldring 57, 2.136
|Courses offered by the International Research Training Group (IRTG) DROPIT||3||see DROPIT website||see DROPIT website|
|Courses offered by the Graduate School of SimTech||3||see SimTech website||see SimTech website|
In this lecture series we will address various mathematical aspects of modeling and simulating general reactive multicomponent transport problems (in porous media). The important aspect of porous media is to have not only homogeneous reactions (i.e. in one phase) as in classical chemical engineering, but heterogeneous reactions due to the involvement of several phases (i.e. liquid-solid). In a microscopic formulation theses are surface processes, in a macroscopic one they give size to species obeying different transport mechanism. “General” not only means general reaction networks, but also quasi-stationary equilibrium description besides kinetic ones and their combinations.
In the Modeling Part we will discuss various examples on the way to a macroscopic general formulation. This will show that additionally to the classification above also a distinction between (surface) reactions like adsorption or ion exchange and “classical” dissolution/precipitation reactions is necessary. The Linear Algebra of reaction networks gives rise to a reduced formulation, which is also numerically beneficial. Further questions are the global in time existence of solutions and the derivations of such macroscopic upscaled models by periodic homogenization. Typically a surface reaction changes the topology of the porous medium. If this cannot be ignored, problems with evolving microstructure emerge, for which classical and recent (micro-macro) models will be introduced.
In the Simulation Part we will concentrate on the efficient resolution of (large) sets of nonlinear equations or complementarity systems, as they arise by any discretization in time and space of the aforementioned models. There in a particular structure due to the spatial coupling for each species and the local reactive coupling between the species. There has been a long lasting discussion whether splitting type or all-in-one type methods are to be preferred. We will use the notion of inexact and approximative Newton’s methods to provide a unifying framework, in which also the (approximative) use of iterative methods to solve the set of linear equations for the (Newton) update and/or the use of approximations for the Jacobian (up to Jacobi-free methods) can be analyzed.
Audience: Graduate and Ph.D. students from Mathematics, Computer Science, Natural Sciences and Engineering
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.
The courses and seminars on droplet dynamics by IRTG DROPIT are also open for interested members of the IRTG-IMPM. For further information please visit the DROPIT website.
Registration for short course "Solvers for nonlinear and/or coupled problems in porous media" coming soon!
Registration for short course "The mathematics of multicomponent reactive transport and flow models"
(open until 14.11.18!)
This is the registration form for the short course "The mathematics of multicomponent reactive transport and flow models" by P. Knabner. It will take place 19.11-21.12.18, every Monday and Tuesday 14:00-15:30 in Pfaffenwaldring 57, 2.136.
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Accommodation for course participants from outside Stuttgart
Hotel am Feuersee
Alex 30 Hostel
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|SFB 1313 - What are the challenges?||3||R. Helmig||7 May, 11 June, 18 June, 2 July, 16 July 2018, always 9:30-13:00, Pfaffenwaldring 61, U1.003|
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