Reliability of astrophysical jet simulations in 2D: On inter-code reliability and numerical convergence

In the present paper, we examine the convergence behavior and inter-code reliability of astrophysical jet simulations in axial symmetry. We consider both, pure hydrodynamic jets and jets with a dynamically significant magnetic field. 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 two other codes give comparable, but not identical results. We find that some global properties of a hydrodynamical jet simulation, like e.g. the bow shock velocity, converge at 100 points per beam radius (ppb) with NIRVANA. The situation is quite different after switching on the toroidal magnetic field: In this case, global properties converge even at 10 ppb. In both cases, details of the inner jet structure and especially the terminal shock region are still insufficiently resolved, even at our highest resolution of 70 ppb in the magnetized case and 400 ppb for the pure hydrodynamic jet. In the case of our highest resolution simulation, we can report two new features: First, small scale Kelvin-Helmholtz instabilities are excited at the contact discontinuity next to the jet head. This slows down the development of the long wavelength Kelvin-Helmholtz instability and its turbulent cascade to smaller wavelengths. Second, the jet head develops Rayleigh-Taylor instabilities which manage to entrain an increasing amount of mass from the ambient medium with resolution. This region extends in our highest resolution simulation over 2 jet radii in the axial direction.