Simulation of wave run-up by means of the exact solution of the wet/dry Riemann problem

An innovative method for the simulation of the hydrodynamics in the swash zone, related to the wave run-up phenomenon, is presented. This method applies the exact solution of the Riemann problem over a dry bed to correctly evaluate the celerity of water waves propagating over the shore, and so to precisely track the coastline location. The simulations of velocity and wave fields outside the surf zone, inside the surf zone and in the swash zone, are carried out by means of a numerical model which solves 3D motion equations expressed in integral form, with a vertical coordinate that varies in time in order to follow the free surface evolution. Several numerical validation tests are carried out, in order to verify the capability of the method to track the coastline.