A class of well-balanced algorithms for relativistic fluids on a Schwarzschild background

TL;DR

This paper introduces well-balanced finite volume algorithms for simulating relativistic fluids on Schwarzschild backgrounds, effectively preserving stationary solutions and enabling analysis of their long-term behavior.

Contribution

The authors develop first- and second-order well-balanced schemes for relativistic fluid models on Schwarzschild backgrounds, leveraging explicit or implicit stationary solutions.

Findings

Algorithms preserve stationary solutions accurately.

Methods enable investigation of asymptotic behavior of flows.

Applicable to relativistic Burgers and Euler models.

Abstract

For the evolution of a compressible fluid in spherical symmetry on a Schwarzschild curved background, we design a class of well-balanced numerical algorithms with first-order or second-order of accuracy. We treat both the relativistic Burgers-Schwarzschild model and the relativistic Euler-Schwarzschild model and take advantage of the explicit or implicit forms available for the stationary solutions of these models. Our schemes follow the finite volume methodology and preserve the stationary solutions. Importantly, they allow us to investigate the global asymptotic behavior of such flows and determine the asymptotic behavior of the mass density and velocity field of the fluid.