HARM: A Numerical Scheme for General Relativistic Magnetohydrodynamics

TLDR

The paper presents a conservative, shock‑capturing scheme for evolving the equations of general relativistic magnetohydrodynamics. The scheme uses Harten–Lax–van Leer fluxes, a Tóth‑style constrained transport to keep the magnetic field divergence‑free, requires only the covariant metric in a coordinate basis, and is validated on a suite of special and general relativistic test problems. On smooth flows the method converges at second order, and the authors demonstrate its application to a magnetized torus orbiting a rotating black hole.

Abstract

We describe a conservative, shock-capturing scheme for evolving the equations of general relativistic magnetohydrodynamics. The fluxes are calculated using the Harten, Lax, & van Leer scheme. A variant of constrained transport, proposed earlier by Tóth, is used to maintain a divergence-free magnetic field. Only the covariant form of the metric in a coordinate basis is required to specify the geometry. We describe code performance on a full suite of test problems in both special and general relativity. On smooth flows we show that it converges at second order. We conclude by showing some results from the evolution of a magnetized torus near a rotating black hole.