Jet simulations extending radially self-similar MHD models
  We perform a numerical simulation of magnetohydrodynamic radially self-similar jets, whose prototype is the Blandford & Payne analytical example. The reached final steady state is valid close to the rotation axis and also at large distances above the disk where the classical analytical model fails to provide physically acceptable solutions. The outflow starts with a sub-slow magnetosonic speed which subsequently crosses all relevant MHD critical points and corresponding magnetosonic separatrix surfaces. The characteristics are plotted together with the Mach cones and the super-fast magnetosonic outflow satisfies MHD causality. The final solution remains close enough to the analytical one which is thus shown to be topologically stable and robust for various boundary conditions. 
J. Gracia, N. Vlahakis, K. Tsinganos