COMPARING NUMERICAL METHODS FOR ISOTHERMAL MAGNETIZED SUPERSONIC TURBULENCE

Abstract

We employ simulations of supersonic super-Alfvenic turbulence decay as a\nbenchmark test problem to assess and compare the performance of nine\nastrophysical MHD methods actively used to model star formation. The set of\nnine codes includes: ENZO, FLASH, KT-MHD, LL-MHD, PLUTO, PPML, RAMSES, STAGGER,\nand ZEUS. We present a comprehensive set of statistical measures designed to\nquantify the effects of numerical dissipation in these MHD solvers. We compare\npower spectra for basic fields to determine the effective spectral bandwidth of\nthe methods and rank them based on their relative effective Reynolds numbers.\nWe also compare numerical dissipation for solenoidal and dilatational velocity\ncomponents to check for possible impacts of the numerics on small-scale density\nstatistics. Finally, we discuss convergence of various characteristics for the\nturbulence decay test and impacts of various components of numerical schemes on\nthe accuracy of solutions. We show that the best performing codes employ a\nconsistently high order of accuracy for spatial reconstruction of the evolved\nfields, transverse gradient interpolation, conservation law update step, and\nLorentz force computation. The best results are achieved with divergence-free\nevolution of the magnetic field using the constrained transport method, and\nusing little to no explicit artificial viscosity. Codes which fall short in one\nor more of these areas are still useful, but they must compensate higher\nnumerical dissipation with higher numerical resolution. This paper is the\nlargest, most comprehensive MHD code comparison on an application-like test\nproblem to date. We hope this work will help developers improve their numerical\nalgorithms while helping users to make informed choices in picking optimal\napplications for their specific astrophysical problems.\n