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Seminario di Analisi Numerica: “Micro and Macro Modeling in Porous Media Apllications”

Mercoledì 31 Maggio 2017, ore 11:30 - Aula 2BC30 - Peter Knabner

ARGOMENTI: Seminari

Mercoledì 31 Maggio 2017 alle ore 11:30 in Aula 2BC30, Peter Knabner (Universität Erlangen-Nürnberg - Department Mathematik - Chair of Applied Mathematics 1) terrà un seminario dal titolo “Micro and Macro Modeling in Porous Media Apllications”.

Abstract
Continuum mechanics based process modeling and simulation in porous media (being composed of a porous matrix and a pore space) has considerably developed in the last thirty years.
In this talk, we focus on the models’ upscaling to mathematically transfer the process description from the small scale to that of the mesoscale (laboratory scale).
In our models, various small-scale processes may be taken into account: molecular diffusion, convection, drift emerging from electric forces, and homogeneous reactions of chemical species in a solvent. Additionally, our model may consider heterogeneous reactions at the porous matrix, thus altering both the porosity and the matrix. Moreover, our model may additionally address biophysical processes, such as the growth of biofilms and how this affects the shape of the pore space. Both of the latter processes result in an intrinsically variable soil structure in space and time.
Upscaling such models under the assumption of a locally periodic setting must be performed meticulously to preserve information regarding the complex coupling of processes in the evolving heterogeneous medium. Generally, a micro-macro model emerges that is then comprised of several levels of couplings: Macroscopic equations that describe the transport and fluid flow at the scale of the porous medium (mesoscale) include averaged time- and space-dependent coefficient functions. These functions may be explicitly computed by means of auxiliary cell problems (microscale). Finally, the pore space in which the cell problems are defined is time- and space dependent and its geometry inherits information from the transport equation's solutions.
Numerical computations using mixed Finite Elements Methods (FEM)/Discontinuous Galerkin (DG) methods and Cellular Automaton Methods (CAM) on potentially random initial data, e.g. that of porosity, complement our theoretical results.