Numerical analysis of relativistic burgers model on FLRW spacetime

A relativistic generalization of Burgers equations was proposed by LeFloch, Makhlof, and Okutmustur and then investigated on Schwarzschild, de Sitter, Schwarzschild--de Sitter and Schwarzschild--Anti--de Sitter spacetimes. In this work, we extend these analysis to a Friedmann--Lemaitre--Robertson--Walker (FLRW) background. This problem is more challenging due to the existence of nontrivial spatially homogeneous solutions. We derive the relativistic Burgers model under consideration and determine its spatially homogeneous solutions. We design a numerical scheme based on a finite volume technique, which is well-preserving in the sense that spatially homogeneous solutions are preserved at the discrete level of approximation. Numerical experiments demonstrate the efficiency of the proposed method for solutions that may contain shock waves