Advanced methods for finite element simulation of rheology models for geophysical flows

  • Fortgeschrittene Methoden der Finite Elemente Simulation rheologischer Modelle für geophysikalische Strömungen
  • Métodos avançados para simulação por elementos finitos de modelos reológicos para escoamentos geofísicos

Gesenhues, Linda Gabriele; Behr, Marek (Thesis advisor); Coutinho, Alvaro (Thesis advisor)

Aachen (2020)
Dissertation / PhD Thesis

Dissertation, Rheinisch-Westfälische Technische Hochschule Aachen, 2020. - Dissertation, Federal University of Rio de Janeiro, 2020

Abstract

Geophysical flows, like debris flows, mud flows, or turbidity currents, can have a great impact on the vegetation, river and ocean currents, can destroy constructions and infrastructure and even can be life-threatening to humans. They have also an essential influence on vital resources like oil and water. Therefore, understanding and modeling geophysical flows is of highest importance. Numerical simulation, and particularly finite element methods offer a chance to understand the characteristics of such complex flows. As the particle concentration rises, the dense granular flow can be represented by non-Newtonian viscoplastic rheology models. The objective of this thesis is to develop methods for a more precise simulation of geophysical flows and their rheology. To accomplish that, rheology models for geophysical flows are implemented in an already existing numerical framework for fluid flows, and incorporating models of free surface flow. Continuum rheology models with viscoplastic behavior, e.g., the Bingham model, or those based on Coulomb's friction law, like the $\mu$($I$)-rheology, are the main focus of the thesis. Problems like discontinuities and non-linearities are tackled with regularization strategies and methods to accurately resolve flow problems in complex domains. Various regularization strategies are applied, and a design of experiments to analyze the influence of artificial regularization parameters on the results is set up. Several geometries are simulated including a 3D column and a column collapse down a slope over a rigid obstacle. Two different fluid flow solvers are used to perform the numerical experiments. Firstly, a semi-discrete solver that is built upon a residual-based variational multiscale framework. This software also provides adaptive spatial mesh refinement for different error estimator variables. The second solver uses a space-time method with the possibility of adaptivity in time.

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