relation: where is the density change and the velocity vector. In practice a value of c smaller than the real one is adopted to avoid time steps too small in the time integration scheme. Generally a numerical speed of sound is adopted such that density variation smaller than 1% are allowed. This is the so-called weak-compressibility assumption. This corresponds to a Mach number smaller than 0.1, which implies: where the maximum velocity needs to be estimated, for e.g. by Torricelli's law or an educated guess. Since only small density variations occur, a linear equation of state can be adopted: Usually the weakly-compressible schemes are affected by a high-frequency spurious noise on the pressure and density fields. This phenomenon is caused by the nonlinear interaction of acoustic waves and by fact that the scheme is explicit in time and centered in space . Through the years, several techniques have been proposed to get rid of this problem. They can be classified in three different groups: the schemes that adopt density filters, the models that add a diffusive term in the continuity equation, the schemes that employ Riemann solvers to model the particle interaction. Density filter technique The schemes of the first group apply a filter directly on the density field to remove the spurious numerical noise. The most used filters are the MLS (moving least squares) and the Shepard filter which can be applied at each time step or every n time steps. The more frequent is the use of the filtering procedure, the more regular density and pressure fields are obtained. On the other hand, this leads to an increase of the computational costs. In long time simulations, the use of the filtering procedure may lead to the disruption of the hydrostatic pressure component and to an inconsistency between the global volume of fluid and the density field. Further, it does not ensure the enforcement of the dynamic free-surface boundary condition. Diffusive term technique A different way to smooth out the density and pressure field is to add a diffusive term inside the continuity equation (group 2) : The first schemes that adopted such an approach were described in Ferrari and in Molteni where the diffusive term was modeled as a Laplacian of the density field. A similar approach was also used in Fatehi and Manzari . In Antuono et al. a correction to the diffusive term of Molteni was