  In gravitationally stratified fluids, length scales are normally much greater
in the horizontal direction than in the vertical one. When modelling these
fluids it can be advantageous to use the hydrostatic approximation, which
filters out vertically propagating sound waves and thus allows a greater
timestep. We briefly review this approximation, which is commonplace in
atmospheric physics, and compare it to other approximations used in
astrophysics such as Boussinesq and anelastic, finding that it should be the
best approximation to use in context such as radiative stellar zones, compact
objects, stellar or planetary atmospheres and other contexts. We describe a
finite-difference numerical scheme which uses this approximation, which
includes magnetic fields.
