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

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