Mathematical models and numerical methods for water management in soils

Duration: 02/2022 – 02/2024
Funding scheme: Funding for Mobility Cooperation with Germany
Funder: Academy of Finland
Budget: 18,000 €
My role: Finnish principal investigator
Sibling project: Discontinuous Galerkin methods and parameter estimation for microstructure models in porous media
German principal investigator: Nadja Ray

Public description

Nowadays, soils should meet more and more requirements. For example, they should be stable to build houses on them safely. In flood-prone areas, they should be able to absorb a lot of water, and in arid regions, they should hold water as well as possible. Soils also play an essential role in the greenhouse effect, as they (and not just the plants growing on their surface) can sequester enormous amounts of carbon and release it if not treated properly.

However, if we want to treat soils to meet all or at least some of these requirements, we need to understand the basic building blocks (i.e., microaggregates; see the picture) of soils and how their development affects soil properties. To this end, we develop two models and numerical methods to simulate them. First, we describe the formation of soil microaggregates, and second, we consider the flow of fluids through consolidated soil. Our goal is to apply the results to support water management.

The image is taken from Microaggregates in soils by Kai Uwe Totsche et al., licensed under CC BY 4.0.

Scientific abstract

This exchange program develops new mathematical tools for porous media applications. The main goal is to support water management by providing models for the consolidation of soils and the flow and transport through them as well as numerical methods to simulate them on the computer. We use these models and techniques to optimize soil parameters and ultimately serve the goal of treating the soil in such a way that, for example, plants find optimal growing conditions or icroorganisms in the ground can sequester as much CO2 as possible.

The first research focuses on parameter estimation for cellular automaton (CA) based models. Such models have been successfully developed and applied in soil science research by Andreas Rupp (Lappeenranta-Lahti University of Technology, abbreviated as LUT) and the group at the Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU). However, physically meaningful parameters that enter the CA model are not experimentally accessible. Consequently, the parameterization of the underlying models remains a challenge. Heikki Haario’s group (LUT) has published research articles on determining relevant parameters in partial differential equations. We use adapted versions of these methods to find appropriate parameters for the CA models.

In the second part of the exchange program, we address discontinuous Galerkin methods for models used to simulate soil applications with two porosities. Dual porosity models accurately describe flow through a porous medium whose solid matrix is composed of a porous medium. Here, we characterize the flow within the large pores by a Stokes equation while formulating the flow through the (micropores of the) porous matrix itself with Darcy’s law. Coupling strategies between the different flow models are constructed and analyzed using techniques developed in the context of petroleum applications or the interactions of lakes with their bottoms. Ultimately, our research may facilitate the design of more efficient batteries and accumulators. Thus, this research topic can be a starting point for collaborating with Prof. Bernardo Barbiellini (LUT) to optimize electric batteries further.

Keywords

cellular automaton model, coupled Stokes-Darcy flow, coupling condition, discontinuous Galerkin, dual-porosity flow, inverse problem, mathematical modeling, microaggregate, numerical methods, parameter estimation, soil science, water management