Multidimensional relativistic MHD simulations of Pulsar Wind Nebulae: dynamics and emission

Pulsar Wind Nebulae, and the Crab nebula in particular, are the best cosmic laboratories to investigate the dynamics of magnetized relativistic outflows and particle acceleration up to PeV energies. Multidimensional MHD modeling by means of numerical simulations has been very successful at reproducing, to the very finest details, the innermost structure of these synchrotron emitting nebulae, as observed in the X-rays. Therefore, the comparison between the simulated source and observations can be used as a powerful diagnostic tool to probe the physical conditions in pulsar winds, like their composition, magnetization, and degree of anisotropy. However, in spite of the wealth of observations and of the accuracy of current MHD models, the precise mechanisms for magnetic field dissipation and for the acceleration of the non-thermal emitting particles are mysteries still puzzling theorists to date. Here we review the methodologies of the computational approach to the modeling of Pulsar Wind Nebulae, discussing the most relevant results and the recent progresses achieved in this fascinating field of high-energy astrophysics.