Volume 23, Issue 2
A Finite Volume Method for the Relativistic Burgers Equation on a FLRW Background Spacetime

Tuba Ceylan ,  Philippe G. LeFloch and Baver Okutmustur

10.4208/cicp.020415.260717a

Commun. Comput. Phys., 23 (2018), pp. 500-519.

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  • 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-Lemaˆıtre-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.

  • History

Published online: 2018-02

  • AMS Subject Headings

35L65, 76N10, 83A05

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