  To ensure that magnetohydrodynamical (MHD) turbulence simulations accurately
reflect the physics, it is critical to understand numerical dissipation. Here
we determine the hydrodynamic and magnetic Reynolds number (Re and Rm) as a
function of linear grid resolution N, in MHD simulations with purely numerical
viscosity and resistivity (implicit large eddy simulations; ILES). We quantify
the numerical viscosity in the subsonic and supersonic regime, via simulations
with sonic Mach numbers of Mach=0.1 and Mach=10, respectively. We find
Re=(N/N_Re)^p_Re, with p_Re=[1.2,1.4] and N_Re=[0.8,1.7] for Mach=0.1, and
p_Re=[1.5,2.0] and N_Re=[0.8,4.4] for Mach=10, and we find Rm=(N/N_Rm)^p_Rm,
with p_Rm=[1.3,1.5] and N_Rm=[1.1,2.3] for Mach=0.1, and p_Rm=[1.2,1.6] and
N_Rm=[0.1,0.7] for Mach=10. The resulting magnetic Prandtl number (Pm=Rm/Re) is
consistent with a constant value of Pm=1.3+/-1.1 for Mach=0.1, and Pm=2.0+/-1.4
for Mach=10. We compare our results with an independent study in the subsonic
regime and find excellent agreement in p_Re and p_Rm, and agreement within a
factor of ~2 for N_Re and N_Rm (due to differences in the codes and solvers).
We compare these results to the target Re and Rm set in direct numerical
simulations (DNS, i.e., using explicit viscosity and resistivity) from the
literature. This comparison and our ILES relations can be used to determine
whether a target Re and Rm can be achieved in a DNS for a given N. We conclude
that for the explicit (physical) dissipation to dominate over the numerical
dissipation, the target Reynolds numbers must be set lower than the
corresponding numerical values.
