Smoothed Particle Hydrodynamics: Turbulence and MHD
  In this paper we discuss recent applications of the Smoothed Particle
Hydrodynamics (SPH) method to the simulation of supersonic turbulence in the
interstellar medium, as well as giving an update on recent algorithmic
developments in solving the equations of magnetohydrodynamics (MHD) in SPH.
Using high resolution calculations (up to 134 million particles), we find
excellent agreement with grid-based results on a range of measures including
the power spectrum slope in both the velocity field and the density-weighted
velocity rho^(1/3) v, the latter showing a Kolmogorov-like k^-5/3 scaling as
proposed by Kritsuk et al. (2007). We also find good agreement on the
statistics of the Probability Distribution Function (PDF) and structure
functions, independently confirming the scaling found by Schmidt, Federrath &
Klessen (2008). On Smoothed Particle Magnetohydrodynamics (SPMHD) we have
recently wasted a great deal of time and effort investigating the vector
potential as an alternative to the Euler potentials formulation, in the end
concluding that using the vector potential has even more severe problems than
the standard (B-field based) SPMHD approach.
