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A numerical study
of the relativistic Burgers and Euler equations on a
Schwarzschild black hole exterior
Philippe G. LeFloch and Shuyang Xiang |
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Vol. 13 (2018), No. 2, 271–301
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Abstract |
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We study the dynamical behavior of compressible fluids evolving on the outer domain of communication of a Schwarzschild background. For both the relativistic Burgers equation and the relativistic Euler system, assuming spherical symmetry we introduce numerical methods that take the Schwarzschild geometry and, specifically, the steady state solutions into account. The schemes we propose preserve the family of steady state solutions and enable us to study the nonlinear stability of fluid equilibria and the behavior of solutions near the black hole horizon. We state and numerically demonstrate several properties about the late-time behavior of perturbed steady states. |
Keywords
relativistic fluid, Schwarzschild black hole, steady state
solution, generalized Riemann problem, random choice
method, finite volume scheme
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Mathematical Subject Classification 2010
Primary: 35L60, 35L65, 65M08, 76L05, 76M12
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Milestones
Received: 11 August 2017
Revised: 17 April 2018
Accepted: 25 June 2018
Published: 25 September 2018
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Authors |
| Philippe G. LeFloch | |
| Laboratoire Jacques-Louis
Lions Centre National de la Recherche Scientifique Sorbonne Université Paris France |
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| Shuyang Xiang | |
| Mathematics Division Center for Computational Engineering Science Rheinisch-Westfälische Technische Hochschule Aachen Aachen Germany |
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