A Numerical Method for General Relativistic Magnetohydrodynamics

This paper describes the development and testing of a general relativistic magnetohydrodynamic (GRMHD) code to study ideal MHD in the fixed background of a Kerr black hole. The code is a direct extension of the hydrodynamic code of Hawley, Smarr, & Wilson and uses Evans & Hawley constrained transport (CT) to evolve the magnetic fields. Two categories of test cases were undertaken. A one-dimensional version of the code (Minkowski metric) was used to verify code performance in the special relativistic limit. The tests include Alfvén wave propagation, fast and slow magnetosonic shocks, rarefaction waves, and both relativistic and nonrelativistic shock tubes. A series of one- and two-dimensional tests were also carried out in the Kerr metric: magnetized Bondi inflow, a magnetized inflow test due to Gammie, and two-dimensional magnetized constant-l tori that are subject to the magnetorotational instability.

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

[2]  G. T'oth,et al.  HARM: A Numerical Scheme for General Relativistic Magnetohydrodynamics , 2003, astro-ph/0301509.

[3]  J. Hawley,et al.  Three-dimensional Hydrodynamic Simulations of Accretion Tori in Kerr Spacetimes , 2002, astro-ph/0204163.

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

[5]  J. Hawley.  Global Magnetohydrodynamical Simulations of Accretion Tori , 1999, astro-ph/9907385.

[6]  C. Gammie.  Efficiency of Magnetized Thin Accretion Disks in the Kerr Metric , 1999, astro-ph/9906223.

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

[8]  James M. Stone,et al.  MOCCT: A numerical technique for astrophysical MHD , 1995 .

[9]  D. Ryu,et al.  Numerical magnetohydrodynamics in astrophysics: Algorithm and tests for multidimensional flow , 1994, astro-ph/9505073.

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

[11]  Michael L. Norman,et al.  A test suite for magnetohydrodynamical simulations , 1992 .

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

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

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

[15]  John F. Hawley,et al.  A Numerical Study of Nonspherical Black Hole Accretion , 1984 .

[16]  E. Fenyves,et al.  SEVENTH TEXAS SYMPOSIUM ON RELATIVISTIC ASTROPHYSICS: December 16–20 , 1975 .

[17]  James R. Wilson.  SOME MAGNETIC EFFECTS IN STELLAR COLLAPSE AND ACCRETION fn1 , 1975 .

[18]  D. Lynden-Bell,et al.  The Evolution of viscous discs and the origin of the nebular variables. , 1974 .

[19]  L. Davis,et al.  The angular momentum of the solar wind. , 1967 .

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

[21]  David A. Clarke,et al.  A consistent method of characteristics for multidimensional magnetohydrodynamics , 1996 .

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

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

[24]  Michael L. Norman,et al.  Astrophysical radiation hydrodynamics , 1986 .

[25]  E. Fenyves,et al.  Seventh Texas Symposium on Relativistic Astrophysics , 1975 .

[26]  B. Dewitt,et al.  Black holes (Les astres occlus) , 1973 .

[27]  James R. Wilson.  Numerical Study of Fluid Flow in a Kerr Space , 1972 .