Shivakumar, Lakshmi MalvadiFederrath, Christoph2025-05-232025-05-230035-8711ORCID:/0000-0002-0706-2306/work/184104799http://www.scopus.com/inward/record.url?scp=85218449312&partnerID=8YFLogxKhttps://hdl.handle.net/1885/733752849For magnetohydrodynamical (MHD) turbulence simulations to accurately capture the underlying physics, we must understand numerical dissipation. Here, we quantify numerical viscosity and resistivity in the subsonic and supersonic turbulence regimes, with Mach numbers M = 0.1 and 10, respectively. We find that the hydrodynamic (Re) and magnetic Reynolds numbers (Rm) on the turbulence driving scale turb in a cubic domain of side length L with a total of N3 resolution elements are well described by Re = [2(N/NRe)(turb/L)]pRe and Rm = [2(N/NRm)(turb/L)]pRm . We provide two sets of fit values of (NRe, pRe, NRm, pRm): one with pRe and pRm fixed at their theoretical values, and the other one allowing all four parameters to vary. The sets for M = 0.1 are (1.57+0.10 −0.12, 4/3, 1.55+0.45 −0.14, 4/3) and (0.83+0.09 −0.08, 1.20+0.02 −0.02, 4.19+2.95 −4.05, 1.60+0.18 −0.33), respectively. For M = 10, they are (3.55+0.78 −0.56, 3/2, 1.03+0.12 −0.11, 3/2) and (10.46+0.96 −0.85, 1.90+0.04 −0.04, 0.44+0.61 −0.23, 1.32+0.17 −0.09). The resulting magnetic Prandtl numbers (Pm = Rm/Re) are consistent with constant values of 1.0+0.3 −0.2 for M = 0.1, and 6.2+5.6 −4.8 for M = 10. These results apply when the magnetic energy (Emag) is 10 per cent of the turbulent kinetic energy (Ekin). When Emag/Ekin ∼ 0.1 − 1, Rm is reduced by a factor ∼ 3 (implying an increase in NRm by a factor ∼ 2) for M = 0.1, while Rm for M = 10 and Re (for any M) remain largely unaffected. We compare our Re − N relation with 14 other simulations from the literature, which use a large range of different numerical methods (with and without Riemann solvers, different reconstruction schemes and orders, and smoothed particle hydrodynamics), and find that they all agree with the Re − N relations above to within a factor of three. We further compare these results to target Re and Rm values in simulations using explicit dissipation from the literature. These literature comparisons and our relations allow users to assess what value of Re and Rm can be reached at a given N, ensuring that physical dissipation dominates over numerical dissipation.We thank the referee for their thorough and insightful comments, which have significantly contributed to the clarity, rigour, and generality of this work. CF acknowledges funding provided by the Australian Research Council (Future Fellowship FT180100495 and Discovery Project grants DP230102280 and DP250101526), and the Australia-Germany Joint Research Cooperation Scheme (UA-DAAD). We further acknowledge high-performance computing resources provided by the Leibniz Rechenzentrum and the Gauss Centre for Supercomputing (grants pr32lo, pr48pi, and GCS Large-scale project 10391), the Australian National Computational Infrastructure (grant ek9) and the Pawsey Supercomputing Centre (project pawsey0810) in the framework of the National Computational Merit Allocation Scheme and the ANU Merit Allocation Scheme. The simulation software, FLASH, was in part developed by the Flash Centre for Computational Science at the University of Chicago and the Department of Physics and Astronomy of the University of Rochester.26en© 2025 The Author(s).dynamomagnetic fieldsmethod: numericalMHDturbulence2025-03-0110.1093/mnras/staf16085218449312