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 re liability of astrophysical jet simulations in axial symmetry. We consider b oth pure hydrodynamic jets and jets with a dynamically significant magnetic field. The setups were chosen to match the setups of two other publication s, and recomputed with the MHD code NIRVANA. We show that NIRVANA and the t wo other codes give comparable, but not identical results. We explain the d ifferences by the different application of artificial viscosity in the thre e codes and numerical details, which can be summarized in a resolution effe ct, in the case without magnetic field: NIRVANA turns out to be a fair code of medium efficiency. It needs approximately twice the resolution as the c ode by Lind (Lind et al. 1989) and half the resolution as the code by Kossl (Kossl & Muller 1988). We find that some global properties of a hydrodynam ical jet simulation, like e.g. the bow shock velocity, converge at 100 poin ts per beam radius (ppb) with NIRVANA. The situation is quite different aft er switching on the toroidal magnetic field: in this case, global propertie s converge even at 10 ppb. In both cases, details of the inner jet structur e and especially the terminal shock region are still insufficiently resolve d, even at our highest resolution of 70 ppb in the magnetized case and 400 ppb for the pure hydrodynamic jet. The magnetized jet even suffers from a f atal retreat of the Mach disk towards the in ow boundary, which indicates t hat this simulation does not converge, in the end. This is also in definite disagreement with earlier simulations, and challenges further studies of t he problem with other codes. In the case of our highest resolution simulati on, we can report two new features: first, small scale Kelvin-Helmholtz ins tabilities are excited at the contact discontinuity next to the jet head. T his slows down the development of the long wavelength Kelvin-Helmholtz inst ability and its turbulent cascade to smaller wavelengths. Second, the jet h ead develops Rayleigh-Taylor instabilities which manage to entrain an incre asing amount of mass from the ambient medium with resolution. This region e xtends in our highest resolution simulation over 2 jet radii in the axial d irection.