A comparison of SPH artificial viscosities and their impact on the Keplerian disk

TL;DR

This study compares different artificial viscosities in SPH simulations to determine their impact on the stability of Keplerian disks, finding that certain AV formulations can significantly prolong disk integrity.

Contribution

It identifies the dominant role of artificial viscosity in disk breakup and demonstrates that high-order AV formulations can sustain disks for about 100 orbits.

Findings

AV at the inner edge triggers disk breakup

High-order AV maintains disk stability for ~100 orbits

Classical AV with high-order divergence estimate is effective

Abstract

Hydrodynamical simulations of rotating disk play important roles in the field of astrophysical and planetary science. Smoothed Particle Hydrodynamics (SPH) has been widely used for such simulations. It, however, has been known that with 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 has been still unclear. In this paper, we investigate the reason for this rapid breaking up of the disk. We implemented most of popular formulations of AV and switches and measured the angular momentum transfer due to both AV and the error of SPH estimate of 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 $\nabla \cdot \vec{v}$ can maintain the disk for $\sim 100$ orbits even when used with the standard formulation of SPH.