Smoothed particle hydrodynamics

In this review of SPH we describe advances made in the last few years. SPH is now seen as one of the simplest of the meshless numerical methods. Despite its simplicity it is a proven, robust tool for investigating fluid dynamics with of without gravity. One of the desirable features of SPH is that the resolution can vary with both space and time. This has now been extended to include variation with direction. The dissipation terms have been improved and their relation to Riemann solutions clarified. For relativistic blast waves and similar problems SPH gives results comparable to the best Riemann and FCT methods. New applications include impact and fragmentation, dusty gases, and nearly incompressible fluids. A wide range of problems in planetesimal formation and collision, engineering and geophysics can now be studied using SPH.