Resolving high Reynolds numbers in SPH simulations of subsonic turbulence

TL;DR

This paper demonstrates that the effective Reynolds number in SPH simulations of subsonic turbulence depends on the Mach number and can be increased by adjusting artificial viscosity, enabling accurate turbulence modeling.

Contribution

It reveals the Mach number dependence of SPH Reynolds number and shows how to recover Kolmogorov turbulence spectra by reducing artificial viscosity.

Findings

SPH Reynolds number scales linearly with Mach number in subsonic flows.

Adjusting artificial viscosity allows SPH to resolve turbulent cascades.

SPH can reproduce Kolmogorov turbulence spectra with proper viscosity control.

Abstract

Accounting for the Reynolds number is critical in numerical simulations of turbulence, particularly for subsonic flow. For Smoothed Particle Hydrodynamics (SPH) with constant artificial viscosity coefficient alpha, it is shown that the effective Reynolds number in the absence of explicit physical viscosity terms scales linearly with the Mach number - compared to mesh schemes, where the effective Reynolds number is largely independent of the flow velocity. As a result, SPH simulations with alpha=1 will have low Reynolds numbers in the subsonic regime compared to mesh codes, which may be insufficient to resolve turbulent flow. This explains the failure of Bauer and Springel (2011, arXiv:1109.4413v1) to find agreement between the moving-mesh code AREPO and the GADGET SPH code on simulations of driven, subsonic (v ~ 0.3 c_s) turbulence appropriate to the intergalactic/intracluster medium, where it was alleged that SPH is somehow fundamentally incapable of producing a Kolmogorov-like turbulent cascade. We show that turbulent flow with a Kolmogorov spectrum can be easily recovered by employing standard methods for reducing alpha away from shocks.