A Comparison of SPH Artificial Viscosities and Their Impact on the Keplerian Disk

Hydrodynamical simulations of rotating disks play important roles in the field of astrophysical and planetary science. Smoothed particle hydrodynamics (SPH) has been widely used for such simulations. However, it has been known that when using SPH, a cold and thin Kepler disk breaks up due to the unwanted angular momentum transfer. Two possible reasons have been suggested for this breaking up of the disk; the artificial viscosity (AV) and the numerical error in the evaluation of pressure gradient in SPH. Which one is dominant is still unclear. In this paper, we investigate the reason for this rapid breaking up of the disk. We implemented most of the popular formulations of AV and switches, and measured the angular momentum transfer due to both AV and the error of SPH’s estimate of the pressure gradient. We found that the angular momentum transfer due to AV at the inner edge triggers the breaking up of the disk. We also found that the classical von Neumann–Richtmyer–Landshoff type AV with a high-order estimate for can maintain the disk for ∼100 orbits even when used with the standard formulation of SPH.