Numerical Simulations of Black Hole Accretion Flows

We model the structure and evolution of black hole accretion disks, and their neighboring regions, using numerical simulations. The numerics is governed by the equations of general relativistic magneto-hydrodynamics (GRMHD). In particular, such 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, more persistent type of the jet phenomena, are blazars, emitted from the centers of galaxies. Long-lasting, detailed computations are essential to properly determine the physics of these explosions, and confront the theoretical models with any potential observables. From the point of view of numerical methods and computational 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 at each time-step, to advance the conserved quantities from one time step to the next. Second, the efficiency of computations intrinsically depends on the code parallelization methods, which may use various techniques. Third, the analysis of results is possible via the post-processing of the computed time-dependent physical quantities, and visualization of the flow properties. This is done via implementing various packages and libraries that are standardized in the field of computational astrophysics and supported by community developers. In the present paper, we discuss the physical picture of the cosmic sources which are modeled using numerical framework. We also describe several technical issues, in the particular context of our own experience with the performance 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.