Smoothed Particle Hydrodynamics: Turbulence and MHD

TL;DR

This paper demonstrates that Smoothed Particle Hydrodynamics (SPH) effectively simulates supersonic turbulence and MHD phenomena in astrophysics, showing high accuracy and agreement with grid-based methods, while also discussing recent algorithmic improvements.

Contribution

The paper provides high-resolution SPH simulations of turbulence and MHD, validating the method against grid-based results and exploring the limitations of vector potential formulations in SPMHD.

Findings

SPH results agree with grid-based simulations on turbulence spectra.

Density-weighted velocity shows Kolmogorov-like scaling.

Vector potential approach in SPMHD has significant issues.

Abstract

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.