State-of-the-art of classical SPH for free-surface flows

Smoothed Particle Hydrodynamics (SPH) is the most widely established mesh-free method which has been used in several fields as astrophysics, solids mechanics and fluid dynamics. In the particular case of computational fluid dynamics, the model is beginning to reach a maturity that allows carrying out detailed quantitative comparisons with laboratory experiments. Here the state-of-the-art of the classical SPH formulation for free-surface flow problems is described in detail. This is demonstrated using dam-break simulations in 2-D and 3-D. The foundations of the method will be presented using different derivations based on the method of interpolants and on the moving least-squares approach. Different methods to improve the classic SPH approach such as the use of density filters and the corrections of the kernel function and its gradient are examined and tested on some laboratory cases.