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

Philippe G. Lefloch (1) , Carlos Parés , Ernesto Pimentel-García

1 LJLL - Laboratoire Jacques-Louis Lions

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.

Mots clés: Compressible fluid; Relativistic flow; Schwarzschild black hole; Well-balanced algorithm; Asymptotic behavior

Domaines: Physique mathématique [math-ph]; Informatique [cs]; Relativité Générale et Cosmologie Quantique [gr-qc]

Philippe G. Lefloch, Carlos Parés, Ernesto Pimentel-García. A class of well-balanced algorithms for relativistic fluids on a Schwarzschild background. J.Sci.Comput., 2021, 89 (1), pp.1-43. ⟨10.1007/s10915-021-01611-y⟩. ⟨hal-03047545⟩