Problem-orientable numerical algorithm for modelling multi-dimensional   radiative MHD flows in astrophysics -- the hierarchical solution scenario
  We present a hierarchical approach for enhancing the robustness of numerical solvers for modelling radiative MHD flows in multi-dimensions. This approach is based on clustering the entries of the global Jacobian in a hierarchical manner that enables employing a variety of solution procedures ranging from a purely explicit time-stepping up to fully implicit schemes. A gradual coupling of the radiative MHD equation with the radiative transfer equation in higher dimensions is possible. Using this approach, it is possible to follow the evolution of strongly time-dependent flows with low/high accuracies and with efficiency comparable to explicit methods, as well as searching quasi-stationary solutions for highly viscous flows. In particular, it is shown that the hierarchical approach is capable of modelling the formation of jets in active galactic nuclei and reproduce the corresponding spectral energy distribution with a reasonable accuracy. 
A. A. Hujeirat