Development of a model based on a SPH technique for the study of 3D hydrodynamic problems in presence of a free surface.

SPH is a meshless method based on estimates of the quantities through integral interpolations. The kernel which we use presents a radial form and has a circular support in 2D. Its extension to 3D is thus direct, the expression remaining unchanged on a spherical compact support. The passage to 3D on the paper of this meshless method based on interpolations whose form is identical in 2D and in 3D is therefore straightforward and introduces no additional modelling difficulty contrary to other methods where, for instance, the mesh metrics complexity would largely increase in 3D. Of course, this is especially true for the core of the method, additional difficulties will nonetheless be encountered. Hence, all the numerical properties of the method remain valid in 3D (it has been checked in particular on the interpolation itself, see Colagrossi 2005). The only constraint is to preserve similar particle densities, i.e. particle spacing, and the same radial support extent. Doing so, all the stability/convergence/etc. analysis are identical to the 2D ones, and the resulting numerical properties are exactly the same. Further, the CPU time will consequently remain O(N) where N is the total number of particles.