Resolving high Reynolds numbers in SPH simulations of subsonic turbulence

Daniel J. Price (Monash Centre for Astrophysics)

[ Full text pdf (833Kb) ] accepted (4th Nov 2011) for publication in MNRAS Letters (arXiv:1111.1255)

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 α, 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 α=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 α away from shocks.

Movies	Movies and images (c) 2011 Daniel Price, released under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License. [directory listing of all movies here]
	Rendering of abs(v) in 256³ particle SPH calculation (800 x 600, 5Mb H.264 Quicktime .mov)
	Cross section slice showing abs(v) in 256³ particle SPH calculation (512 x 512, 5Mb H.264 Quicktime .mov) The Reynolds number is ~ 6000 at this resolution with standard viscosity switches employed. This is sufficiently high for turbulence to develop.
	Time evolution of the power spectra in calculations employing 64³, 128³ and 256³ SPH particle calculations (5.9Mb H.264 Quicktime .mov) These are shown compensated by k^5/3, such that a Kolmogorov slope would appear horizontal in this plot. Note the strong intermittency in the power spectra that is characteristic of turbulence.
	Resolution study showing abs(v) and density in a cross section slice using 64³, 128³ and 256³ SPH particles (Full res: 1950 x 1200, 26Mb H.264 Quicktime .mov)