An Implementation of the Relativistic Hydrodynamic Equations in Conservative Form Using DoGPack
Let gμν 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 + ∇· F ( q) = S , which is a system of hyperbolic partial differential equations. These hyperbolic equati...
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| Format: | Dissertation |
| Language: | English |
| Published: |
ProQuest Dissertations & Theses
01-01-2016
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| Online Access: | Get full text |
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| Summary: | Let gμν 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 + ∇· F ( q) = 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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| ISBN: | 1339846470 9781339846477 |