The matter of astrophysical objects (
, a star or a galaxy) can often be approximated as a gas or fluid,
, the equations of fluid dynamics are adequate to describe the astrophysical phenomena. Hereafter, for simplification, the word fluid will be used as a synonym for both fluid and gas. Because most astrophysical conditions are inaccessible in the laboratory, and as astrophysical fluid motion may occur on time scales long compared to the life span of humans or deep inside astrophysical objects, numerical simulation is the only means to study such fluid motion. In this respect numerical simulations play a more important role in astrophysics then in most other branches of physics: astronomers are passive ‘observers’ of what Nature decides to show them. The study of astrophysical fluid flows is further complicated by the effects of self-gravity, which must be considered in many astrophysical flow problems, by the enormous range of length scales and time scales to be covered in the simulations, and by a variety of other physical effects which must be taken into account frequently. The latter include radiation transport (of photons or neutrinos), heat conduction, radiative cooling, ionization and recombination of atoms, magnetic fields, energy generation by thermonuclear reactions, flow velocities near the speed of light, and strong gravitational fields.