Among the meshless numerical method, the SPH method (Smooth Particle Hydrodynamics) has been now theoretically studied and developed in order to allow numerous applications in fluid mechanics. It has been first introduced by Lucy (1977) and formalized by Gingold and Monaghan (1977, 1983) initially for astrophysical applications. Monaghan has proposed many important developments (see a list of references in this text).