Simulation of astrophysical flows is of particular importance as many objects and processes of astronomical interest such as stars and nebulae involve gases. Fluid computer models are often coupled with radiative transfer, (Newtonian) gravity, nuclear physics and (general) relativity to study highly energetic phenomena such as supernovae, relativistic jets, active galaxies and gamma-ray bursts and are also used to model stellar structure, planetary formation, evolution of stars and of galaxies, and exotic objects such as neutron stars, pulsars, magnetars and black holes. Computer simulations are often the only means to study stellar collisions, galaxy mergers, as well as galactic and black hole interactions.