HARM: A Numerical Scheme for General Relativistic Magnetohydrodynamics 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.

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  1. Balsara, Dinshaw S.; Amano, Takanobu; Garain, Sudip; Kim, Jinho: A high-order relativistic two-fluid electrodynamic scheme with consistent reconstruction of electromagnetic fields and a multidimensional Riemann solver for electromagnetism (2016)
  2. Balsara, Dinshaw S.; Kim, Jinho: A subluminal relativistic magnetohydrodynamics scheme with ADER-WENO predictor and multidimensional Riemann solver-based corrector (2016)
  3. Meliani, Z.; Grandclément, P.; Casse, F.; Vincent, F.H.; Straub, O.; Dauvergne, F.: GR-AMRVAC code applications: accretion onto compact objects, boson stars versus black holes (2016)
  4. Mösta, Philipp; Mundim, Bruno C.; Faber, Joshua A.; Haas, Roland; Noble, Scott C.; Bode, Tanja; Löffler, Frank; Ott, Christian D.; Reisswig, Christian; Schnetter, Erik: GRHydro: a new open-source general-relativistic magnetohydrodynamics code for the Einstein toolkit (2014)
  5. Keppens, R.; Meliani, Z.; Van Marle, A.J.; Delmont, P.; Vlasis, A.; van der Holst, B.: Parallel, grid-adaptive approaches for relativistic hydro and magnetohydrodynamics (2012)
  6. Bernstein, J.P.; Hughes, P.A.: Refining a relativistic, hydrodynamic solver: admitting ultra-relativistic flows (2009)
  7. Cécere, Mariana; Lehner, Luis; Reula, Oscar: Constraint preserving boundary conditions for the ideal Newtonian MHD equations (2008)
  8. Cerdá-Durán, P.; Font, J.A.; Antón, L.; Müller, E.: A new general relativistic magnetohydrodynamics code for dynamical spacetimes (2008)
  9. Font, J.A.: General relativistic hydrodynamics and magnetohydrodynamics: hyperbolic systems in relativistic astrophysics (2008)
  10. Bonazzola, S.; Villain, L.; Bejger, M.: Magnetohydrodynamics of rotating compact stars with spectral methods: Description of the algorithm and tests (2007)
  11. Hawley, John F.; Beckwith, Kris; Krolik, Julian H.: General relativistic MHD simulations of black hole accretion disks and jets (2007)
  12. Neilsen, David; Hirschmann, Eric W.; Millward, R.Steven: Relativistic MHD and excision: formulation and initial tests (2006)
  13. Hujeirat, A.: A problem-orientable numerical algorithm for modeling multi-dimensional radiative MHD flows in astrophysics-the hierarchical solution scenario (2005)