Particle methods in astrophysical fluid dynamics

Particle methods play an important role in the study of a wide variety of astrophysical fluid dynamics problems. The different methods currently in use are all variants of the so-called Smoothed Particle Hydrodynamics (SPH) scheme introduced by Lucy and Gingold & Monaghan more than twenty years ago. This paper presents a complete introduction to SPH in its modern form, and discusses some of the main numerical properties of the scheme. In particular, the convergence properties of SPH are studied, as a function of the number of particles N and the number of interacting neighbors N_N, using a simple analysis based on sound waves. It is shown that consistency of SPH (i.e., convergence towards a physical solution) requires both N → ∞ and N_N → ∞, with the smoothing length h → 0, i.e., N_N/N → 0.