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

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2018-02-01
Ceylan, Tuba
Lefloch, Philippe G.
Okutmuştur, Baver
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.

Citation Formats
T. Ceylan, P. G. Lefloch, and B. Okutmuştur, “A Finite Volume Method for the Relativistic Burgers Equation on a FLRW Background Spacetime,” COMMUNICATIONS IN COMPUTATIONAL PHYSICS, vol. 23, pp. 500–519, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/46906.