Title: Asymptotic and Stationary Preserving Schemes for Kinetic and Hyperbolic Partial Differential Equations
Publisher: Wurzburg University Press
Publication Date: 2023
Language: English
ISBN 10: 3958262104
ISBN 13: 9783958262102
Binding: Soft cover
Condition: New

About this title

Synopsis

In this thesis, we are interested in numerically preserving stationary solutions of balance laws. We start by developing finite volume well-balanced schemes for the system of Euler equations and the system of Magnetohydrodynamics (MHD) equations with gravitational source term. Since fluid models and kinetic models are related, this leads us to investigate Asymptotic Preserving (AP) schemes for kinetic equations and their ability to preserve stationary solutions. In an attempt to mimic our result for kinetic equations in the context of fluid models, for the isentropic Euler equations we developed an AP scheme in the limit of the Mach number going to zero. The properties of the schemes we developed and its criteria are validated numerically by various test cases from the literature.

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