The computational effort involves the use of modern shock-capturing schemes exploited at very high effective resolutions. Our implementation in the AMRVAC code allows various schemes for hydro and magnetohydrodynamic applications. The governing equations of relativistic (magneto)hydrodynamics need accurate numerical treatment, fully obeying their conservation law nature in four-dimensional space-time. To make predictions for the long-term behavior of astrophysical jet flows, the use of parallelized, grid-adaptive software is a requirement, optimally exploiting modern high performance computing platforms. I will discuss the octree-based automated grid refinement (AMR) strategy, its parallel implementation, and provide quantitative information on its performance on some typical applications. For the visualization of the AMR computations, we exploit the open-source Paraview visualization package (www.paraview.org). I will present some modern examples of computational, plasma-astrophysical research, aimed at gaining more insight in the relativistic jet. In particular, I will highlight recent results on the classification of the radio source galaxies according to the properties of the external medium and of the central engine.
In the second part, I will present some work on Gamma Ray Bursts. Indeed a strong optical and radio flares often appear in the afterglow phase of Gamma-Ray Bursts (GRBs). It has been proposed that colliding ultra-relativistic shells can produce these flares. Such consecutive shells can be formed due to the variability in the central source of a GRB. We perform high resolution 1D and 2D numerical simulations of late collisions between two ultra-relativistic shells in order to explore these events. We find steeply rising flare like behavior for small jet opening angles and more gradual rebrightenings for large opening angles. Synchrotron self-absorption is found to strongly influence the onset and shape of the radio flare.