Simulating Structure Formation in Soils across Scales using Discontinuous Galerkin Methods

Abschlussarbeit
(Dissertation)


Details zur Publikation

Autorinnen und Autoren: Rupp A
Verlag: Shaker Verlag GmbH
Verlagsort: Düren
Jahr der Veröffentlichung: 2019
ISBN: 978-3-8440-6801-6


Abstract

This thesis deals with mathematical modeling, analysis, and numerical
realization of microaggregates in soils. These microaggregates have the
size of a few hundred micrometers and can be understood as the
fundamental building units of soil. Thus, understanding their
dynamically evolving, three-dimensional structure is crucial for
modeling and interpreting many soil parameters such as diffusivities and
flow paths that come into play in CO2-sequestration or oil recovery
scenarios.



Moreover, effects and knowledge deduced from the model are transfered to
scales which are more relevant for applications. The quality of these
averaged models is of general interest, since simulations for the
field-scale that resolve the pore-scale are not applicable for
economical reasons. Thus, this book compares parameterizations of
diffusivities with mathematically rigorous results and gives suggestions
to improve the formulas that can be found in the literature.



Last but not least, it is imperative to apply a proper numerical method
to implement the model in silico. The local discontinuous Galerkin (LDG)
method seems to be suitable for this task, since it is locally
mass-conservative and is stable for discontinuous data - that might, for
example, originate from the discrete movement of the geometry or from
the sharp boundaries between the different phases. Additionally, this
method has no problems with complicated transfer conditions. These
aspects are demonstrated in a mathematically rigorous way, and the
method is improved upon by reducing the linear system of equations
resulting from the discretization. This is a real enhancement, since it
does not diminish the order of convergence but decreases the
computational costs.


FAU-Autorinnen und Autoren / FAU-Herausgeberinnen und Herausgeber

Rupp, Andreas
Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)


Zitierweisen

APA:
Rupp, A. (2019). Simulating Structure Formation in Soils across Scales using Discontinuous Galerkin Methods (Dissertation).

MLA:
Rupp, Andreas. Simulating Structure Formation in Soils across Scales using Discontinuous Galerkin Methods. Dissertation, Düren: Shaker Verlag GmbH, 2019.

BibTeX: 

Zuletzt aktualisiert 2019-09-07 um 22:23