A comparison between grid and particle methods on the small-scale dynamo in magnetised supersonic turbulence

TL;DR

This study compares grid and particle methods in simulating the small-scale dynamo in highly supersonic turbulence, showing both approaches can reproduce key dynamo features but differ in growth rates due to numerical dissipation.

Contribution

It demonstrates for the first time that smoothed particle magnetohydrodynamics can successfully model the small-scale dynamo in supersonic turbulence, aligning with grid-based methods.

Findings

Both codes agree on magnetic energy spectra and saturation levels.

The dynamo growth rate varies with resolution and code, influenced by numerical dissipation.

Differences in shock capturing schemes affect the effective Prandtl number.

Abstract

We perform a comparison between the smoothed particle magnetohydrodynamics (SPMHD) code, Phantom, and the Eulerian grid-based code, Flash, on the small-scale turbulent dynamo in driven, Mach 10 turbulence. We show, for the first time, that the exponential growth and saturation of an initially weak magnetic field via the small-scale dynamo can be successfully reproduced with SPMHD. The two codes agree on the behaviour of the magnetic energy spectra, the saturation level of magnetic energy, and the distribution of magnetic field strengths during the growth and saturation phases. The main difference is that the dynamo growth rate, and its dependence on resolution, differs between the codes, caused by differences in the numerical dissipation and shock capturing schemes leading to differences in the effective Prandtl number in Phantom and Flash.