Comparative statistics of selected subgrid-scale models in large eddy
  simulations of decaying, supersonic MHD turbulence
  Large eddy simulations (LES) are a powerful tool in understanding processes
that are inaccessible by direct simulations due to their complexity, for
example, in the highly turbulent regime. However, their accuracy and success
depends on a proper subgrid-scale (SGS) model that accounts for the unresolved
scales in the simulation. We evaluate the applicability of two traditional SGS
models, namely the eddy-viscosity (EV) and the scale-similarity (SS) model, and
one recently proposed nonlinear (NL) SGS model in the realm of compressible MHD
turbulence. Using 209 simulations of decaying, supersonic (initial sonic Mach
number of ~3) MHD turbulence with a shock-capturing scheme and varying
resolution, SGS model and filter, we analyze the ensemble statistics of kinetic
and magnetic energy spectra and structure functions. Furthermore, we compare
the temporal evolution of lower and higher order statistical moments of the
spatial distributions of kinetic and magnetic energy, vorticity, current
density, and dilatation magnitudes. We find no statistical influence on the
evolution of the flow by any model if grid-scale quantities are used to
calculate SGS contributions. In addition, the SS models, which employ an
explicit filter, have no impact in general. On the contrary, both EV and NL
models change the statistics if an explicit filter is used. For example, they
slightly increase the dissipation on the smallest scales. We demonstrate that
the nonlinear model improves higher order statistics already with a small
explicit filter, i.e. a three-point stencil. The results of e.g. the structure
functions or the skewness and kurtosis of the current density distribution are
closer to the ones obtained from simulations at higher resolution. We conclude
that the nonlinear model with a small explicit filter is suitable for
application in more complex scenarios when higher order statistics are
important.
