A Finite Volume Method for the Relativistic Burgers Equation on a FLRW Background Spacetime

A Finite Volume Method for the Relativistic Burgers Equation on a FLRW Background Spacetime

Year:    2018

Communications in Computational Physics, Vol. 23 (2018), Iss. 2 : pp. 500–519

Abstract

A relativistic generalization of the inviscid Burgers equation was introduced by LeFloch and co-authors and was recently investigated numerically on a Schwarzschild background. We extend this analysis to a Friedmann-Lemaître-Robertson-Walker (FLRW) background, which is more challenging due to the existence of time-dependent, spatially homogeneous solutions. We present a derivation of the model of interest and we study its basic properties, including the class of spatially homogeneous solutions. Then, we design a second-order accurate scheme based on the finite volume methodology, which provides us with a tool for investigating the properties of solutions. Computational experiments demonstrate the efficiency of the proposed scheme for numerically capturing weak solutions.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.020415.260717a

Communications in Computational Physics, Vol. 23 (2018), Iss. 2 : pp. 500–519

Published online:    2018-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    20

Keywords:    Relativistic Burgers equation FLRW metric hyperbolic balance law finite volume scheme.

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