Abstract
Highly supersonic, compressible turbulence is thought to be of tantamount
importance for star formation processes in the interstellar medium (ISM).
Likewise, cosmic structure formation is expected to give rise to subsonic
turbulence in the intergalactic medium (IGM), 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 quite badly fails 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. 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. This casts doubt about the
reliability of SPH for simulations of cosmic structure formation, especially if
turbulence in clusters of galaxies is indeed significant. In contrast, SPH's
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. Abridged
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