ISBN 9783843948746

978-3-8439-4874-6, Reihe Mathematik

David Seus
LDD Schemes for Two-Phase Flow Systems

227 Seiten, Dissertation Universität Stuttgart (2021), Hardcover, A5

Zusammenfassung / Abstract

Flow processes through porous media, and notably two-phase flow processes occur in a vast range of applications.

Soil remediation for contaminated soil, geological groundwater flow, enhanced oil recovery, CO₂ storage, subsurface energy storage or the design of filters and efficient fuel cells are among the most relevant examples.

Since experimentation on large scales can be very expensive or otherwise infeasible, mathematical modelling and simulation become primary tools to investigate questions at hand, specifically when large scale domains are of interest.

Questions arising, range from being of purely scientific nature to questions of technical and economic nature, i.e. questions of feasibility, risk and cost of an envisioned technology like storing CO₂ in the subsurface for example.

The heterogeneous nature of the subsurface poses significant challenges for numerical methods with respect to robustness and limited computational resource.

This thesis contributes to alleviating these issues by proposing a domain decomposition (DD) solver, the so-called LDD solver, for two-phase flow systems founded on a fixed point iteration approach.

Robustness is achieved through a linearisation step (L-linearisation) that not only linearises appearing doubly nonlinear equations, but moreover, simultaneously decouples the substructured problem.

In this way, the resulting solver becomes inherently accessible to parallel computing.

To further increase efficiency, a unified formulation of the method for two-phase flow systems is achieved allowing not only for its application to either the Richards equation or the full two-phase flow system, but notably so, to a flexible combination of both models.

In situations where this combination of both models is justified, this approach lowers computational cost.

Convergence proofs of the method are provided in all cases and numerical validation and testing is performed.