Title
An implementation of the relativistic hydrodynamic equations in conservative form using Dogpack
Degree Type
Thesis
Date of Award
2016
Degree Name
Master of Science
Department
Mathematics
Major
Applied Mathematics
First Advisor
James Rossmanith
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.
DOI
https://doi.org/10.31274/etd-180810-4801
Copyright Owner
Milo Thomas Taylor
Copyright Date
2016
Language
en
File Format
application/pdf
File Size
50 pages
Recommended Citation
Taylor, Milo Thomas, "An implementation of the relativistic hydrodynamic equations in conservative form using Dogpack" (2016). Graduate Theses and Dissertations. 15199.
https://lib.dr.iastate.edu/etd/15199
