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 I?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 et al. (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.