TESTING CONVERGENCE FOR GLOBAL ACCRETION DISKS

• Published in: The Astrophysical journal Vol. 772; no. 2; pp. 1 - 17
• Main Authors: Hawley, John F, Richers, Sherwood A, Guan, Xiaoyue, Krolik, Julian H
• Format: Journal Article
• Language: English
• Published: United States 01.08.2013
• Subjects: ACCRETION DISKS; ALGORITHMS; ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; BLACK HOLES; Brackets; BRIGHTNESS; CONVERGENCE; Flux; Initial conditions; Instability; INTERPOLATION; MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS; SIMULATION; Solvers; SYMMETRY; TURBULENCE; WAVELENGTHS
• DOI: 10.1088/0004-637X/772/2/102
• ISSN: 0004-637X

Global disk simulations provide a powerful tool for investigating accretion and the underlying magnetohydrodynamic turbulence driven by magneto-rotational instability (MRI). We use the flux-conservative Athena code to conduct a series of experiments on disks having a variety of magnetic topologies to determine what constitutes adequate resolution. We develop and apply several resolution metrics: [left angle bracket]Q sub(z)[right angle bracket] and [left angle bracket]Q sub([phi])[right angle bracket], the ratio of the grid zone size to the characteristic MRI wavelength, alpha sub(mag), the ratio of the Maxwell stress to the magnetic pressure, and [left angle bracket]B super(2)R[right angle bracket]/[left angle bracket]B super(2)[phi][right angle bracket], the ratio of radial to toroidal magnetic field energy. For the initial conditions considered here, adequate resolution is characterized by [left angle bracket]Q sub(z)[right angle bracket] [> or =, slanted] 15, [left angle bracket]Q sub([phi])[right angle bracket] [> or =, slanted] 20, alpha sub(mag) approximately 0.45, and [left angle bracket]B super(2)R[right angle bracket]/[left angle bracket]B super(2)[phi][right angle bracket] approximately 0.2. Use of the Harten-Lax-van Leer-Einfeldt flux solver or second-order interpolation can significantly degrade the effective resolution compared to the Harten-Lax-van Leer discontinuities flux solver and third-order interpolation.