Highly supersonic, compressible turbulence is thought to be of tantamountimportance for star formation processes in the interstellar medium. Likewise,cosmic structure formation is expected to give rise to subsonic turbulence inthe intergalactic medium, which may substantially modify the thermodynamicstructure of gas in virialized dark matter halos and affect small-scale mixingprocesses in the gas. Numerical simulations have played a key role incharacterizing the properties of astrophysical turbulence, but thus farsystematic code comparisons have been restricted to the supersonic regime,leaving it unclear whether subsonic turbulence is faithfully represented by thenumerical techniques commonly employed in astrophysics. Here we focus oncomparing the accuracy of smoothed particle hydrodynamics (SPH) and our newmoving-mesh technique AREPO in simulations of driven subsonic turbulence. Tomake contact with previous results, we also analyze simulations of transsonicand highly supersonic turbulence. We find that the widely employed standardformulation of SPH yields problematic results in the subsonic regime. Insteadof building up a Kolmogorov-like turbulent cascade, large-scale eddies arequickly damped close to the driving scale and decay into small-scale velocitynoise. Reduced viscosity settings improve the situation, but the shape of thedissipation range differs compared with expectations for a Kolmogorov cascade.In contrast, our moving-mesh technique does yield power-law scaling laws forthe power spectra of velocity, vorticity and density, consistent withexpectations for fully developed isotropic turbulence. We show that largeerrors in SPH's gradient estimate and the associated subsonic velocity noiseare ultimately responsible for producing inaccurate results in the subsonicregime. In contrast, SPH's performance is much better for supersonicturbulence. [Abridged]
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