HARM: A Numerical Scheme for General Relativistic Magnetohydrodynamics

2003/01/25 by Charles F. Gammie, Jonathan C. McKinney, Gábor Tóth · 19 citations
Engineering · Mathematics · Physics and Astronomy · #Astrophysical Phenomena and Observations #Classical mechanics #Computational Fluid Dynamics and Aerodynamics #Covariant transformation #Divergence (linguistics) #General relativity #Geometry #Magnetic field #Magnetohydrodynamics #Mathematical physics #Mathematics #Metric (unit) #Numerical relativity #Physics #Pulsars and Gravitational Waves Research #Quantum mechanics #Torus #astro-ph

paper · pdf · doi:10.1086/374594

published as Astrophys.J. 589 (2003) 444-457 · 38 pages, 18 figures, submitted to ApJ

arxiv created 2003/01/25 · openalex publication_date 2003/05/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Numerical Hydrodynamics in General Relativity
• Black Holes, White Dwarfs, and Neutron Stars: The Physics of Compact Objects
• On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws
• A powerful local shear instability in weakly magnetized disks. I - Linear analysis. II - Nonlinear evolution
• Efficiency of Magnetized Thin Accretion Disks in the Kerr Metric

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