In the present paper, we examine the convergence behavior and inter-codereliability of astrophysical jet simulations in axial symmetry. We considerboth, pure hydrodynamic jets and jets with a dynamically significant magneticfield. The setups were chosen to match the setups of two other publications,and recomputed with the MHD code NIRVANA. We show that NIRVANA and the twoother codes give comparable, but not identical results. We find that someglobal properties of a hydrodynamical jet simulation, like e.g. the bow shockvelocity, converge at 100 points per beam radius (ppb) with NIRVANA. Thesituation is quite different after switching on the toroidal magnetic field: Inthis case, global properties converge even at 10 ppb. In both cases, details ofthe inner jet structure and especially the terminal shock region are stillinsufficiently resolved, even at our highest resolution of 70 ppb in themagnetized case and 400 ppb for the pure hydrodynamic jet. In the case of ourhighest resolution simulation, we can report two new features: First, smallscale Kelvin-Helmholtz instabilities are excited at the contact discontinuitynext to the jet head. This slows down the development of the long wavelengthKelvin-Helmholtz instability and its turbulent cascade to smaller wavelengths.Second, the jet head develops Rayleigh-Taylor instabilities which manage toentrain an increasing amount of mass from the ambient medium with resolution.This region extends in our highest resolution simulation over 2 jet radii inthe axial direction.
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