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

Date

2018-02-01

Author

Ceylan, Tuba
Lefloch, Philippe G.
Okutmuştur, Baver

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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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-Lemaitre-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.

Subject Keywords

Physics and Astronomy (miscellaneous)

URI

https://hdl.handle.net/11511/46906

Collections

Department of Mathematics, Article