An implementation of the relativistic hydrodynamic equations in conservative form using Dogpack

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2016-01-01
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Taylor, Milo
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James Rossmanith
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Mathematics
Abstract

Let $g_{\mu\nu}$ be the metric associated with a stationary spacetime. In the $3+1$ splitting

of spacetime, this allows us to cast the relativistic hydrodynamic equations as a balance law of

the form $q_{,t} + \nabla\cdot\vect{F}(q) = \vect{S}$, which is

a system of hyperbolic partial differential equations. These hyperbolic equations admit shocks

and rarefactions in their weak solutions. Because of this, we employ a Runge-Kutta Discontinuous

Galerkin method in both Minkowski and Schwarzschild spacetimes through the use of the

Discontinuous Galerkin Package. In this thesis, we give a quick

background on topics in general relativity necessary to implement the method, as well as details

on the DG method itself. We present tests of the method in the form of shock tube tests and

smooth flow into a black hole to show its versatility.

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Fri Jan 01 00:00:00 UTC 2016