Peter Knabner from the Univerity of Erlangen-Nürnberg will give Short Courses every Monday and Tuesday (19. November – 21. December 2018) about: "The mathematics of multicomponent reactive transport and flow models".
In his lecture series Peter Knabner 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 he 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 he 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.
Date: 19. November – 21. December 2018, Mondays and Tuesdays
Time: 2 - 3:30 pm
Location: Pfaffenwaldring 57, 2.136
Audience: Graduate and Ph.D. students from Mathematics, Computer Science, Natural Sciences and Engineering