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


Creative Commons License

Ceylan T., Lefloch P. G. , Okutmuştur B.

COMMUNICATIONS IN COMPUTATIONAL PHYSICS, vol.23, pp.500-519, 2018 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 23
  • Publication Date: 2018
  • Doi Number: 10.4208/cicp.020415.260717a
  • Title of Journal : COMMUNICATIONS IN COMPUTATIONAL PHYSICS
  • Page Numbers: 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-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

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.