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 Toth, 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.

[1]  General relativistic simulations of early jet formation in a rapidly rotating black hole magnetosphere , 1999, astro-ph/9907435.

[2]  B. Punsly,et al.  Black hole gravitohydromagnetics , 2001 .

[3]  Dinshaw S. Balsara,et al.  Total Variation Diminishing Scheme for Relativistic Magnetohydrodynamics , 2001 .

[4]  D. Meier,et al.  Magnetohydrodynamic production of relativistic jets. , 2001, Science.

[5]  J. Hawley,et al.  Simulation of magnetohydrodynamic flows: A Constrained transport method , 1988 .

[6]  Saul A. Teukolsky,et al.  White Dwarfs and Neutron Stars: The Physics of Compact Objects , 1983 .

[7]  O. A. Kuznetsov,et al.  An approximate Riemann solver for relativistic magnetohydrodynamics , 2002 .

[8]  E. Toro.  Godunov Methods: Theory and Applications , 2001 .

[9]  D. Meier,et al.  Extraction of Black Hole Rotational Energy by a Magnetic Field and the Formation of Relativistic Jets , 2002, Science.

[10]  Larry Smarr,et al.  A numerical study of nonspherical black hole accretion. II: Finite differencing and code calibration , 1984 .

[11]  A. Gautschy,et al.  Computational methods for astrophysical fluid flow , 1998 .

[12]  Kazunari Shibata,et al.  Relativistic Jet Formation from Black Hole Magnetized Accretion Disks: Method, Tests, and Applications of a General RelativisticMagnetohydrodynamic Numerical Code , 1999 .

[13]  N. Bucciantini,et al.  An efficient shock-capturing central-type scheme for multidimensional relativistic flows , 2002 .

[14]  J. Hawley,et al.  A powerful local shear instability in weakly magnetized disks. I - Linear analysis. II - Nonlinear evolution , 1990 .

[15]  Garching,et al.  Numerical Hydrodynamics in Special Relativity , 1999, Living reviews in relativity.

[16]  José A. Font,et al.  Numerical Hydrodynamics in General Relativity , 2000, Living reviews in relativity.

[17]  Dongsu Ryu,et al.  Numerical magnetohydrodynamics in astrophysics: Algorithm and tests for multidimensional flow , 1995 .

[18]  P. Lax,et al.  Systems of conservation laws , 1960 .

[19]  Time‐dependent, force‐free, degenerate electrodynamics , 2002, astro-ph/0202447.

[20]  M. Norman,et al.  ZEUS-2D : a radiation magnetohydrodynamics code for astrophysical flows in two space dimensions. II : The magnetohydrodynamic algorithms and tests , 1992 .

[21]  V. Moncrief,et al.  Relativistic fluid disks in orbit around Kerr black holes , 1976 .

[22]  J. Hawley,et al.  Instability, turbulence, and enhanced transport in accretion disks , 1997 .

[23]  S. Komissarov,et al.  A Godunov-type scheme for relativistic magnetohydrodynamics , 1999 .

[24]  Relativistic MHD Simulations Using a Godunov-type Method , 2001 .

[25]  Angelo Marcello Anile,et al.  Relativistic fluids and magneto-fluids , 2005 .

[26]  G. Tóth.  The ∇·B=0 Constraint in Shock-Capturing Magnetohydrodynamics Codes , 2000 .

[27]  Y. Tatematsu,et al.  Magnetohydrodynamic flows in Kerr geometry : energy extraction from black holes , 1990 .

[28]  R. Blandford,et al.  Electromagnetic extraction of energy from Kerr black holes , 1977 .

[29]  Saul A. Teukolsky,et al.  Black Holes, White Dwarfs, and Neutron Stars , 1983 .

[30]  M. Putten.  A numerical implementation of MHD in divergence form , 1993 .

[31]  B. M. Marder,et al.  A method for incorporating Gauss' lasw into electromagnetic pic codes , 1987 .

[32]  S. Orszag,et al.  Small-scale structure of two-dimensional magnetohydrodynamic turbulence , 1979, Journal of Fluid Mechanics.

[33]  M. Norman,et al.  Why Ultrarelativistic Numerical Hydrodynamics is Difficult , 1986 .

[34]  P. Seymour.  Black Holes, White Dwarfs and Neutron Stars: The Physics of Compact Objects , 1984 .

[35]  A. M. Anile,et al.  Relativistic Fluid Dynamics , 1989 .

[36]  M. Brio,et al.  An upwind differencing scheme for the equations of ideal magnetohydrodynamics , 1988 .

[37]  J. Hawley,et al.  A Numerical Method for General Relativistic Magnetohydrodynamics , 2002, astro-ph/0210518.