Testing Convergence for Global Accretion Disks

TL;DR

This paper establishes resolution criteria for global accretion disk simulations using the Athena code, emphasizing the importance of numerical methods and sufficient grid resolution to accurately capture MRI-driven turbulence.

Contribution

It introduces specific resolution metrics and thresholds necessary for reliable global disk simulations, aligning them with established shearing box results.

Findings

Adequate resolution requires Qz > 15 and Qphi > 20.

Use of advanced flux solvers improves effective resolution.

High grid resolution is essential for accurate MRI turbulence modeling.

Abstract

Global disk simulations provide a powerful tool for investigating accretion and the underlying magnetohydrodynamic turbulence driven by the magneto-rotational instability (MRI). Using them to predict accurately quantities such as stress, accretion rate, and surface brightness profile requires that purely numerical effects, arising from both resolution and algorithm, be understood and controlled. 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: Qz and Qphi, the ratio of the grid zone size to the characteristic MRI wavelength, alpha_mag, the ratio of the Maxwell stress to the magnetic pressure, and the ratio of radial to toroidal magnetic field energy. For the initial conditions considered here, adequate resolution is characterized by Qz > 15, Qphi > 20, alpha_mag = 0.45, and a field energy ratio of 0.2. These values are associated with > 35 zones per scaleheight, a result consistent with shearing box simulations. Numerical algorithm is also important. Use of the HLLE flux solver or second-order interpolation can significantly degrade the effective resolution compared to the HLLD flux solver and third-order interpolation. Resolution at this standard can be achieved only with large numbers of grid zones, arranged in a fashion that matches the symmetries of the problem and the scientific goals of the simulation.