TESTING CONVERGENCE FOR GLOBAL ACCRETION DISKS - Hawley, John F; Richers, Sherwood A; Guan, Xiaoyue; Krolik, Julian H (The Astrophysical journal, 2013)
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.