Emergence in porous media

Emergence in natural porous media
Participants: Nadja Ray, Alexander Prechtel, Andreas RuppSerge Kräutle

The grand goal of this group is the development, analytical, and numerical investigation of a mechanistic model describing processes of formation, stability, and turnover of soil micro-aggregates, i.e., particles in the range up to 250 micrometers. In contrast to existing conceptual aggregation models and compartment models for carbon turnover and aggregation, we focus on specific, experimentally identified transformation processes of soil microaggregates.
Since we are interested in giving an improved mechanistic, qualitative and even quantitative description of aggregation, we transfer the gained insights of 1. to a mechanistic model in terms of ordinary differential equations (ODEs), partial differential equations (PDEs), and perhaps algebraic equations (AEs). To that end, we aim to take into account information/identified processes on different spatial scales as well as spatial heterogeneity and variability. All our modeling is done in a rigorous, deterministic way and our modeling concepts are based on continuum mechanics, i.e. a description via concentrations and not a description considering single particles. We start our investigations at the pore scale and apply multiscale techniques to obtain a comprehensive mathematical model at the macroscale (bottom up). In particular, the interplay of geochemistry and microbiology is considered, and also their link to soil functions.

The coupled ODE/PDE systems and complex micro-macro problems can not be treated numerically with standard software packages. The number of species, nonlinearity of the processes and heterogeneity of the medium results in a high computational effort that requires accurate and efficient discretization methods and solution algorithms. Moreover sophisticated numerical multiscale methods have to be applied.
In our simulations, we do not aim to recreate reality in every detail. Instead, we aim to illustrate, compare, and reveal influencing factors and mechanisms by abstracting relevant processes.

Friedrich-Alexander-Universität Erlangen-Nürnberg