Short gamma ray bursts are presumably results of binary neutron star mergers, which lead to the formation of a stellar mass black hole, surrounded by a remnant matter. The strong magnetic fields help collimate jets of plasma, launched along the axis of the black hole rotation. We study the structure and evolution of the accreting plasma in the short GRBs and we model the formation of the base of a relativistic, Poynting-dominated jets. Our numerical models are based on the general relativistic MHD, axisymmetric simulations. We discuss the origin of variability in the GRB jet emission, which timescales are related to the action of the magneto-rotational instability in the accreting plasma. We also estimate the value of a maximum achievable Lorentz factor in the jets produced by our simulations, and reached at the large distances, where the gamma ray emission is produced.

Relativistic jets associated with long/soft gamma-ray bursts are formed and initially propagate in the interior of the progenitor star. Because of the subsequent loss of their external pressure support after they cross the stellar surface, these flows can be modeled as moving around a corner. A strong steady-state rarefaction wave is formed, and the sideways expansion is accompanied by a rarefaction acceleration. We investigate the efficiency and the general characteristics of this mechanism by integrating the steady-state, special relativistic, magnetohydrodynamic equations, using a special set of partial exact solutions in planar geometry (r self-similar with respect to the "corner"). We also derive analytical approximate scalings in the ultrarelativistic cold/magnetized, and hydrodynamic limits. The mechanism is more effective in magnetized than in purely hydrodynamic flows. It substantially increases the Lorentz factor without much affecting the opening of the jet; the resulting values of their product can be much grater than unity, allowing for possible breaks in the afterglow light curves. These findings are similar to the ones from numerical simulations of axisymmetric jets by Komissarov et al and Tchekhovskoy et al, although in our approach we describe the rarefaction as a steady-state simple wave and self-consistently calculate the opening of the jet that corresponds to zero external pressure.

We construct and analyze a model of the relativistic steady-state magnetohydrodynamic (MHD) rarefaction that is induced when a planar symmetric flow (with one ignorable Cartesian coordinate) propagates under a steep drop of the external pressure profile. Using the method of self-similarity we derive a system of ordinary differential equations that describe the flow dynamics. In the specific limit of an initially homogeneous flow we also provide analytical results and accurate scaling laws. We consider that limit as a generalization of the previous Newtonian and hydrodynamic solutions already present in the literature. The model includes magnetic field and bulk flow speed having all components, whose role is explored with a parametric study.

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.