Resumen
We model the structure and evolution of black hole accretion disks using numerical simulations. The numerics is governed by the equations of general relativistic magneto-hydrodynamics (GRMHD). Accretion disks and outflows can be found at the base of very energetic ultra-relativistic jets produced by cosmic explosions, so called gamma-ray bursts (GRBs). Another type of phenomena are blazars, with jets emitted from the centers of galaxies.Long-lasting, detailed computations are essential to determine the physics of these explosions, and confront the theory with potential observables. From the point of view of numerical methods and techniques, three ingredients need to be considered. First, the numerical scheme must work in a conservative manner, which is achieved by solving a set of non-linear equations to advance the conserved quantities from one time step to the next. Second, the efficiency of computations depends on the code parallelization methods. Third, the analysis of results is possible via the post-processing of computed physical quantities, and visualization of the flow properties. This is done via implementing packages and libraries that are standardized in the field of computational astrophysics and supported by community developers.In this paper, we discuss the physics of the cosmic sources. We also describe our numerical framework and some technical issues, in the context of the GRMHD code which we develop. We also present a suite of performance tests, done on the High-Performance Computer cluster (HPC) in the Center for Mathematical Modeling of the Warsaw University.