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 halos 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 analyze 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 SPH's gradient estimate and the associated subsonic velocity noise
are ultimately responsible for producing inaccurate results in the subsonic
regime. In contrast, SPH's performance is much better for supersonic
turbulence. [Abridged]
