Abstract
Visco-plastic materials have been attracting a great amount of
attention among researchers in the study of fluid flow due to their
widespread presence in various fields of science. While numerical
techniques for simulating their flow have seen significant
improvements in the last few decades, the efficient solution of the
nonlinear partial differential equations modelling them still poses
many challenges. From a mathematical point of view, the major
difficulty associated with the numerical solution of these
equations is the presence of singularities in (a priori unknown)
parts of the domain. This "irregularity" of the equations generally
reflects in slow convergence of numerical solvers. In this thesis
we introduce an augmented formulation of the Bingham visco-plastic
flow which is aimed at circumventing the singularity of the
equations. We develop a nonlinear solver based on this new
formulation and compare its performance to other common techniques
for solving the Bingham flow, indicating superior convergence
properties of the solver based on the new formulation. Upon
linearization and discretization of the augmented formulation, a
sequence of linear systems is obtained which are in general very
large and sparse. We introduce a nonlinear geometric multilevel
technique for the efficient solution of these linear systems. The
convergence of this multilevel technique is accelerated by a
flexible Krylov subspace method. We test the resulting numerical
scheme on both academic test cases and problems arising from
real-life applications with a particular emphasis on problems in
hemodynamics.
Table of Contents
- Introduction
- Mathematical Formulation
- Well-Posedness of the Continuous Problem
- Linearization and Discretization
- Performance of the Augmented Nonlinear Solver
- Preconditioning
- Numerical Results
- Conclusion and Future Work
About this Dissertation
Rights statement
- Permission granted by the author to include this thesis or dissertation in this repository. All rights reserved by the author. Please contact the author for information regarding the reproduction and use of this thesis or dissertation.
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