ABSTRACT
In contrast to the basic stellar structure problem outlined in the previous chapter, in many problems in astrophysics the assumption of spherical symmetry is not adequate to describe the situation nor is the assumption of hydrostatic equilibrium. For example, the expansion of a supernova remnant into a nonuniform interstellar medium, the collapse of an interstellar cloud and its breakup into a binary system, the evolution of a disk that develops spiral waves as a result of gravitational instability, or the development of structure in the early universe after the Big Bang — all these problems require a three-dimensional hydrodynamic treatment. For some problems the situation can be reduced down to two space dimensions and the numerical techniques are the same, so in order to simplify matters this chapter concentrates on two-dimensional solutions to hydrodynamic problems on a grid. The methods discussed here can be generalized to three-dimensional problems in a straightforward manner.
