An efficient implementation of flux formulae in multidimensional relativistic hydrodynamical codes

We derive and analyze a simplified formulation of the numerical viscosity terms appearing in the expression of the numerical fluxes associated to several High-Resolution Shock-Capturing schemes. After some algebraic preprocessing, we give explicit expressions for the numerical viscosity terms of two...

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Bibliographic Details
Published in:	Computer physics communications Vol. 120; no. 2; pp. 115 - 121
Main Authors:	Aloy, M.A., Pons, J.A., Ibáñez, J.M a.
Format:	Journal Article
Language:	English
Published:	Amsterdam Elsevier B.V 01-08-1999 Elsevier Science
Subjects:	47.11.+j 47.75.+f 95.30.Lz Astronomy Computational methods in fluid dynamics Earth, ocean, space Exact sciences and technology Fluid dynamics Fundamental areas of phenomenology (including applications) Fundamental aspects of astrophysics Fundamental astronomy and astrophysics. Instrumentation, techniques, and astronomical observations General relativistic hydrodynamics High resolution shock capturing methods Hydrodynamics Nonlinear systems of conservation laws Physics Relativistic fluid dynamics Special relativistic hydrodynamics Special relativistic hydrodynamics 47.75.+f Nonlinear systems of conservation laws High resolution shock capturing methods 95.30.Lz General relativistic hydrodynamics 47.11.+j Shock Conservation laws Special relativity General relativity Theoretical study Relativistic hydrodynamics Nonlinear systems Capture High-resolution methods
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Summary:	We derive and analyze a simplified formulation of the numerical viscosity terms appearing in the expression of the numerical fluxes associated to several High-Resolution Shock-Capturing schemes. After some algebraic preprocessing, we give explicit expressions for the numerical viscosity terms of two of the most widely used flux formulae, which implementation saves computational time in multidimensional simulations of relativistic flows. Additionally, such treatment explicitely cancels and factorizes a number of terms helping to damp the growing of round-off errors. We have checked the performance of our formulation running a 3D relativistic hydrodynamical code to solve a standard test-bed problem and found that the improvement in efficiency is of high practical interest in numerical simulations of relativistic flows in Astrophysics.
ISSN:	0010-4655 1879-2944
DOI:	10.1016/S0010-4655(99)00236-2