Finite Volume Method for the Relativistic Burgers Model on a (1+1)-Dimensional de Sitter Spacetime

TL;DR

This paper develops a finite volume numerical scheme for a relativistic Burgers model on (1+1)-dimensional de Sitter spacetime, demonstrating its effectiveness in capturing shock and rarefaction waves.

Contribution

It introduces a novel relativistic Burgers model on de Sitter spacetime and constructs a second order Godunov scheme for numerical analysis.

Findings

The scheme accurately captures shock waves.

The method effectively models rarefaction waves.

Numerical experiments analyze the impact of the cosmological constant.

Abstract

Several generalizations of the relativistic models of Burgers equations have recently been established and developed on different spacetime geometries. In this work, we take into account the de Sitter spacetime geometry, introduce our relativistic model by a technique based on the vanishing pressure Euler equations of relativistic compressible fluids on a (1+1)-dimensional background and construct a second order Godunov type finite volume scheme to examine numerical experiments within an analysis of the cosmological constant. Numerical results demonstrate the efficiency of the method for solutions containing shock and rarefaction waves.