Particle Methods in Astrophysical Fluid Dynamics

Particle methods play an important role in the study of a wide variety ofastrophysical fluid dynamics problems. The different methods currently in useare all variants of the so-called Smoothed Particle Hydrodynamics (SPH) schemeintroduced by Lucy and Gingold & Monaghan more than twenty years ago. Thispaper presents a complete introduction to SPH in its modern form, and discussessome of the main numerical properties of the scheme. In particular, theconvergence properties of SPH are studied, as a function of the number ofparticles N and the number of interacting neighbors N_n, using a simpleanalysis based on sound waves. It is shown that consistency of SPH (i.e.,convergence towards a physical solution) requires both N -> infinity and N_n ->infinity, with the smoothing length h -> 0, i.e., N_n/N -> 0.Comment: 13 pages, to appear in proceedings of the 5th International Conference on Computational Physics (ICCP5), held in Kanazawa, Japan, Oct 11-13, 1999 (special issue of Progress of Theoretical Physics