Numerical simulations of gamma-ray burst explosions

Gamma-ray bursts are a complex, non-linear system that evolves very rapidly through stages of vastly different conditions. They evolve from scales of few hundred kilometers where they are very dense and hot to cold and tenuous on scales of parsecs. As such, our understanding of such a phenomenon can truly increase by combining theoretical and numerical studies adopting different numerical techniques to face different problems and deal with diverse conditions. In this review, we will describe the tremendous advancement in our comprehension of the bursts phenomenology through numerical modeling. Though we will discuss studies mainly based on jet dynamics across the progenitor star and the interstellar medium, we will also touch upon other problems such as the jet launching, its acceleration, and the radiation mechanisms. Finally, we will describe how combining numerical results with observations from Swift and other instruments resulted in true understanding of the bursts phenomenon and the challenges still lying ahead.