Asymptotic and Stationary Preserving Schemes for Kinetic and Hyperbolic Partial Differential Equations
Farah Kanbar
Broschiertes Buch

Asymptotic and Stationary Preserving Schemes for Kinetic and Hyperbolic Partial Differential Equations

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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 develop...