ABSTRACT
This chapter provides an overview of some techniques currently in use within astrophysics that the reader can use as a starting point for further literature study. It focuses on the finite volume method, which is used by a range of widely available hydrodynamics packages currently deployed in astrophysics research. With the advent of powerful computers, computational fluid dynamics (CFD) has become an important tool in the toolkit of the (astro-)physicists or engineer. As an area of research CFD actually predates computers, if it is taken to describe a systematic algorithmic approach to solving Euler's equation through discretization and approximation. In CFD, the readers are trying to find a numerical solution to the partial differential equation that models the evolution of the state vector. A fixed mesh approach to CFD reflects a Eulerian framing of the problem. The chapter discusses finite difference and finite volume methods on a fixed mesh.
