In this contribution I discuss how recent advances in numerical techniques and computational power can be applied to problems in astrophysical fluid mechanics. As a case in point some results of simulations of radio relics are presented which have provided strong support for a model that explains the origin of these peculiar objects. Radio relics are extended radio sources which do not appear to be associated with any radio galaxy. Here a model is presented which explains the origin of these relics in terms of old plasma that has been compressed by a shock wave. Having taken into account synchrotron, inverse Compton and adiabatic energy losses and gains, the relativistic electron population was evolved in time and synthetic radio maps were made which reproduce the observations remarkably well. Finally, some other examples are discussed where hydrodynamical simulations have proven very useful for astrophysical problems.

Introduction

With the advent of powerful computers and more accurate algorithms, simulations of astrophysical fluids have become increasingly useful. Most fields of astrophysics, such as solar physics, star formation, stellar evolution and cosmology have benefitted greatly from hydrodynamical simulations and hopes for further advances are high.

Essentially, there are two main approaches to the numerical solution of the equations of hydrodynamics: Finite-grid simulations and Smoothed Particle Hydrodynamics (SPH). In the former approach the equations are discretised on a computational mesh before they are solved. The latter method avoids the notion of a mesh and employs particles to track the fluid.