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.
