Novel methods in recent years have been developed for numerically solving the hydrodynamical and MHD equations relevant to all kinds of astrophysical flows. I will first (briefly) present one such computational technique, where the numerical grid follows the MHD flow using a “moving mesh”. I will then present some astrophysical scenarios for which I have applied this method, including planet formation and high-energy transients such as supernovae and gamma ray bursts.
