Revisiting spherically symmetric relativistic hydrodynamics

TL;DR

This paper revisits classical relativistic hydrodynamics problems, illustrating numerical methods for shock handling and coupling fluid evolution with spacetime in spherical symmetry.

Contribution

It provides detailed implementation of numerical methods for relativistic shocks and coupling fluid dynamics with spacetime evolution in spherical symmetry.

Findings

Demonstrates numerical methods for relativistic shocks

Shows coupling of fluid and spacetime evolution

Illustrates implementation on classical problems

Abstract

In this paper we revise two classical examples of Relativistic Hydrodynamics in order to illustrate in detail the numerical methods commonly used in fluid dynamics, specifically those designed to deal with shocks, which are based on a finite volume approximation. The two cases we consider are the relativistic blast wave problem and the evolution of a Tolman-Oppenheimer-Volkoff star model, in spherical symmetry. In the first case we illustrate the implementation of relativistic Euler's equations on a fixed background space-time, whereas in the second case we also show how to couple the evolution of the fluid to the evolution of the space-time.