Weakly regular fluid flows with bounded variation on the domain of outer communication of a Schwarzschild blackhole spacetime. A numerical study

Philippe G Lefloch (1) , Shuyang Xiang (1)

1 LJLL - Laboratoire Jacques-Louis Lions

We study the dynamical behavior of compressible fluids evolving on the outer domain of communication of a Schwarzschild background. To this end, we design several numerical methods which take the Schwarzschild geometry into account and we treat, both, the relativistic Burgers equation and the relativistic Euler system under the assumption that the flow is spherically symmetric. All the schemes we construct are proven to be well-balanced and therefore to preserve the family of steady state solutions for both models. They enable us to study the nonlinear stability of fluid equilibria, and in particular to investigate the behavior of the fluid near the blackhole horizon. We state and numerically demonstrate several conjectures about the late-time behavior of perturbations of steady solutions.

Domaines: Equations aux dérivées partielles [math.AP]

Philippe G Lefloch, Shuyang Xiang. Weakly regular fluid flows with bounded variation on the domain of outer communication of a Schwarzschild blackhole spacetime. A numerical study. 2016. ⟨hal-01423454⟩