A Numerical Method for General Relativistic Magnetohydrodynamics

By Jean-Pierre De Villiers, J. Hawley. 2002

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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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/4fcca7dabff8a9235db34a128b52c275a65aded8

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Citations in the corpus

Black Hole Spin Evolution (2003, background): “A similar suppression of accreted angular momentum has been observed in fully relativistic MHD simulations of accretion onto black holes by de Villiers & Hawley (2003b) and de Villiers et al. (2003).”
A Measurement of the Electromagnetic Luminosity of a Kerr Black Hole (2004, methodology): “The right panel in figure 2 defines some useful terminology inspired by the left panel, following De Villiers & Hawley (2003) and Hirose et al. (2003).”
Magnetically Driven Accretion Flows in the Kerr Metric. II. Structure of the Magnetic Field (2003, methodology): “With the construction of a fully general-relativistic three dimensional MHD code (De Villiers & Hawley 2003, hereafter DH03), it is now possible to achieve a physical description of black hole accretion that is much more complete.”
Electron Thermodynamics in GRMHD Simulations of Low-Luminosity Black Hole Accretion (2015, methodology): “Our basic model is thus to take a single-fluid GRMHD solution (e.g.,Komissarov 1999; Gammie, McKinney & Tóth 2003; De Villiers & Hawley 2003) as an accurate description of the total fluid (composed of both the electron and proton gas) dynamicsand thus the accretion flow density, magnetic field…”
THE SUBMILLIMETER BUMP IN Sgr A* FROM RELATIVISTIC MHD SIMULATIONS (2010, background): “Simulations from Fragile et al. (2007, 2009) evolve internal energy and use the initial torus configuration from De Villiers & Hawley (2003), whereas those from McKinney & Blandford (2009) conserve total energy and use an initial torus placed much closer to the black hole (Gammie et al. 2003).”
Spin, Accretion, and the Cosmological Growth of Supermassive Black Holes (2004, background): “…and references) and (2) a relativistic, MHD accretion disk that accounts for the presence of a frozen-in magnetic field in a perfectly conducting plasma (De Villiers & Hawley 2003; De Villiers, Hawley & Krolick 2003; Gammie, Shapiro & McKinney 2003; McKinney & Gammie 2004; and references therein).”
The X-Ray-to-Optical Properties of Optically Selected Active Galaxies over Wide Luminosity and Redshift Ranges (2006, unknown): “…the environments around accreting SMBHs from first principles using relativistic magneto-hydrodynamic simulations (e.g., Hawley et al. 1995; De Villiers & Hawley 2003; Krolik et al. 2005) will be able to explain the observed αOX - l2500Å relation, but to our knowledge these simulations have…”
HARM: A Numerical Scheme for General Relativistic Magnetohydrodynamics (2003, methodology): “This code and the code described in a companion paper (De Villiers & Hawley 2003) are the first that stably evolve a relativistic plasma in a Kerr spacetime for many light crossing times.”
Hot Accretion Flows Around Black Holes (2014, methodology): “A number of codes have been used, notably, ZEUS (Stone & Norman 1992a, 1992b), HARM (Gammie et al. 2003), the GRMHD code of De Villiers & Hawley (2003a), COSMOS++ (Anninos et al. 2005), and ATHENA (Stone et al. 2008).”
A public code for general relativistic, polarised radiative transfer around spinning black holes (2016, methodology): “With the development of general relativistic MHD simulations of black hole accretion (De Villiers & Hawley 2003; Gammie, McKinney & Tóth 2003), ray tracing has become popular as a post-processing step to study their variability properties (Schnittman, Krolik & Hawley 2006; Noble & Krolik 2009;…”
Efficient Generation of Jets from Magnetically Arrested Accretion on a Rapidly Spinning Black Hole (2011, background): “99fc starts with a rapidly spinning BH (a = 0.99) at the centre of an equilibrium hydrodynamic torus (Chakrabarti 1985; De Villiers & Hawley 2003).”
Athena: A New Code for Astrophysical MHD (2008, methodology): “The key advantage of the method is its simplicity, making it easy to extend with more complex physics (for example, Stone et al. 1992b; Turner & Stone 2001; De Villiers & Hawley 2003; Hayes & Norman 2003).”
ECHO: a Eulerian conservative high-order scheme for general relativistic magnetohydrodynamics and magnetodynamics (2007, methodology): “For our numerical test, we use the settings proposed by Gammie et al. (2003) and De Villiers & Hawley (2003); that is, we study the accretion onto a Kerr black hole with a = 0.5, which gives an event horizon at rh = 1 + (1 − a2)1/2 1.866 (the spherical surface where γrr diverges) and a marginally…”
DIRECT CALCULATION OF THE RADIATIVE EFFICIENCY OF AN ACCRETION DISK AROUND A BLACK HOLE (2008, methodology): “Initially these simulations assumed Newtonian dynamics in a pseudo-Newtonian potential; in the middle of this effort, new codes were developed that permit simulations in general relativity (De Villiers & Hawley 2003; Gammie et al. 2003).”
Three-Dimensional Simulations of Magnetized Thin Accretion Disks around Black Holes: Stress in the Plunging Region (2008, methodology): “We began the simulation with an equilibrium torus (Chakrabarti 1985; De Villiers & Hawley 2003) with inner edge atr = 20M and pressure maximum atr = 35M and adjusted the model parameters so the torus hadh/r = 0.1 at 35M.”
Magnetically Driven Accretion Flows in the Kerr Metric. IV. Dynamical Properties of the Inner Disk (2004, methodology): “The specific form of the equations we solve, and the numerical algorithm incorporated into the GRMHD code are described in detail in De Villiers & Hawley (2003).”