Doctoral Thesis Defence by Elissa Eggenweiler

October 14, 2022 /

Dissertation: "Interface Conditions for Arbitrary Flows in Stokes–Darcy Systems: Derivation, Analysis and Validation" | 14 October 2022 | 10 am CET

Elissa Eggenweiler, doctoral researcher at the Institute of Applied Analysis and Numerical Simulation (IANS), and member within the framework of SFB 1313 and the Integrated Research Training Group IRTG-IMPM, will defend her dissertation: 

Title: "Interface Conditions for Arbitrary Flows in Stokes–Darcy Systems: Derivation, Analysis and Validation"
Date:
14 October 2022
Time: 10 am CET
Venue: Aula 8.122, Pfaffenwaldring 57, 70569 Stuttgart- Vaihingen

Abstract

Coupled free-flow and porous-medium flow systems occur in nature as well as in a wide range of technical applications, for example, groundwater filtration or water management in fuel cells. The free flow is typically described by the Stokes equations and the flow through the porous medium by Darcy’s law. One of the major challenges in modeling such flow systems is the accurate coupling of both mathematical models across the fluid–porous interface. Traditional coupling concepts are developed for unidirectional flows, parallel or perpendicular to the porous layer, however, they are not applicable if arbitrary flow directions occur, such as in industrial filtration. This fact significantly restricts the amount of applications that can be accurately modeled. Therefore, new interface conditions accounting for arbitrary flows in Stokes–Darcy systems are needed.

In this dissertation, we develop generalized coupling conditions that are valid for arbitrary flow directions to the fluid–porous interface. These conditions are rigorously derived using homogenization with two-scale asymptotic expansions and boundary layer theory. All coefficients appearing in the generalized interface conditions are computed based on the pore geometry in the vicinity of the interface. This is a great advantage over the traditionally applied coupling conditions, which are limited to unidirectional flows and contain unknown model parameters that must be fitted before the conditions can be used in numerical simulations. We derive the variational formulation of the Stokes–Darcy problem with the newly derived coupling conditions and prove existence and uniqueness of a weak solution. We develop a finite volume discretization scheme to solve the coupled problem numerically and employ finite element methods to compute all effective model parameters and to solve the pore-scale problem. To validate the generalized coupling conditions we compare microscale and macroscale numerical simulation results. We demonstrate that the derived interface conditions are more accurate than the classical conditions in case of unidirectional flows, and that they are valid in case of arbitrary flow directions to the interface, whereas the classical conditions fail.

This image shows Elissa Eggenweiler

Elissa Eggenweiler

 

Doctoral Researcher, Research Project A03

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