A Comparison between Grid and Particle Methods on Small-scale Dynamo Amplification of Magnetic Fields in Supersonic Turbulence

We have performed simulations of driven, supersonic, magnetohydrodynamic turbulence following the growth and saturation of an initially weak magnetic field via small-scale dynamo amplification. The results are compared between two different numerical methods and codes: smoothed particle magnetohydrodynamics (SPMHD) with the PHANTOM code, and the grid-based code FLASH. We find that the growth rate of FLASH is largely insensitive to the numerical resolution, whereas PHANTOM shows a resolution dependence that arises from the scaling of the numerical dissipation terms. The saturation level of the magnetic energy in both codes is about 2–4% of the mean kinetic energy, increasing with higher magnetic Reynolds numbers. PHANTOM yields higher mean magnetic energy at saturation than FLASH at comparable resolution. The time-averaged saturated magnetic spectra have a similar shape between the two methods, though PHANTOM contains twice as much energy on large scales. Both codes show PDFs of magnetic field strength that are log-normal during the growth phase, which become lopsided as the magnetic field saturates. We find encouraging agreement between gridand particle methods for ideal MHD, concluding that SPMHD is able to reliably simulate the small-scale dynamo. Quantitative agreement on growth rates can only be achieved by including explicit, physical terms for viscosity and resistivity, because those are the terms that primarily control the growth rate and saturation level of the turbulent dynamo.