Ricerc@Sapienza

We propose a three-dimensional numerical model for non-hydrostatic free surface flows in which the Navier-Stokes equations are expressed in integral form on a coordinate system in which the vertical coordinate is varying in time. By a time-dependent coordinate transformation, the irregular time varying physical domain is transformed into a uniform fixed computational domain, in which the equations of motion are numerically integrated by a shock-capturing scheme based on WENO reconstruction and an approximate HLL Riemann Solver. The proposed model is used to simulate free surface elevation and three-dimensional velocity fields induced by normally incident waves on a beach with submerged breakwaters. The three-dimensional numerical results are compared with experimental measurements and with the numerical results obtained by a depth-averaged horizontal two-dimensional model. This comparison shows that features of three-dimensionality in the fluid flow induced by wave-structure interaction, as the undertow, can be correctly simulated by the proposed non-hydrostatic three-dimensional model.