Well-balanced algorithms for relativistic fluids on a Schwarzschild background

Abstract

A class of well-balanced finite volume methods with first and higher order of accuracy is designed for two spherical symmetric fluid models on a Schwarzschild curved background: the Burgers-Schwarzschild model and the Euler-Schwarzschild model. We take advantage of the explicit or implicit forms available for the stationary solutions of these models to design numerical methods that preserve them. These methods are then used to investigate the late time behaviour of the flows.