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

Abstract

We design well-balanced numerical algorithms with first-, second-, and third-order of accuracy for the spherically symmetry evolution of a compressible fluid on a Schwarzschild black hole. We treat both the relativistic Burgers-Schwarzschild model and the relativistic Euler-Schwarzschild model. Our schemes follow the finite volume methodology and preserve the stationary solutions and allow us to investigate the global asymptotic behavior of such flows and reach definite conclusions about the behavior of the mass density and velocity field.

Well-balanced methods for computational astrophysics

“…Magneto-hydrostatic steadystate preserving well-balanced schemes were devised by Fuchs et al (2010aFuchs et al ( , 2010bFuchs et al ( , 2011. Well-balanced schemes for relativistic hydrodynamics on curved spacetime were considered by Kastaun (2006), LeFloch and Makhlof (2014), Gosse (2015), LeFloch et al (2020), Gaburro et al (2021).…”