Subsonic turbulence in smoothed particle hydrodynamics and moving-mesh simulations

Highly supersonic, compressible turbulence is thought to be of tantamount importance for star formation processes in the interstellar medium. Likewise, cosmic structure formation is expected to give rise to subsonic turbulence in the intergalactic medium, which may substantially modify the thermodynamic structure of gas in virialized dark matter haloes and affect small-scale mixing processes in the gas. Numerical simulations have played a key role in characterizing the properties of astrophysical turbulence, but thus far systematic code comparisons have been restricted to the supersonic regime, leaving it unclear whether subsonic turbulence is faithfully represented by the numerical techniques commonly employed in astrophysics. Here we focus on comparing the accuracy of smoothed particle hydrodynamics (SPH) and our new moving-mesh technique AREPO in simulations of driven subsonic turbulence. To make contact with previous results, we also analyse simulations of transsonic and highly supersonic turbulence. We find that the widely employed standard formulation of SPH yields problematic results in the subsonic regime. Instead of building up a Kolmogorov-like turbulent cascade, large-scale eddies are quickly damped close to the driving scale and decay into small-scale velocity noise. Reduced viscosity settings improve the situation, but the shape of the dissipation range differs compared with expectations for a Kolmogorov cascade. In contrast, our moving-mesh technique does yield power-law scaling laws for the power spectra of velocity, vorticity and density, consistent with expectations for fully developed isotropic turbulence. We show that large errors in SPHs gradient estimate and the associated subsonic velocity noise are ultimately responsible for producing inaccurate results in the subsonic regime. In contrast, SPHs performance is much better for supersonic turbulence, as here the flow is kinetically dominated and characterized by a network of strong shocks, which can be adequately captured with SPH. When compared to fixed grid Eulerian simulations of turbulence, our moving mesh approach shows qualitatively very similar results, although with somewhat better resolving power at the same number of cells, thanks to reduced advection errors and the automatic adaptivity of the AREPO code.