A Finite Volume Method for the Relativistic Burgers Equation on a FLRW Background Spacetime (Communications in Computational Physics, 2018)
A relativistic generalization of the inviscid Burgers equation was introducedby LeFloch and co-authors and was recently investigated numerically on a Schwarzschildbackground. 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 interestand we study its basic properties, including the class of spatially homogeneous solutions.Then, we design a second-order accurate scheme based on the finite volumemethodology, which provides us with a tool for investigating the properties of solutions.Computational experiments demonstrate the efficiency of the proposed schemefor numerically capturing weak solutions.