A shoreline boundary condition for a highly nonlinear Boussinesq model for breaking waves

A physically based strategy was used to model swash zone hydrodynamics forced by breaking waves within a Boussinesq type of model. The position and the velocity of the shoreline were determined continuously in space by solving the physically based equations of the shoreline motion; moreover, a fixed grid method, with a wet-dry interface, was adopted for integrating the Boussinesq model. The numerical stability of the model was improved by means of an extrapolation method. To validate the proposed methodology, the classical analytical solution for the shoreline motion of a monochromatic wave train over a plane beach was considered. The comparison between the analytical and numerical horizontal shoreline movements provided a very good agreement. Several other tests on the run-up of non-breaking and breaking waves were performed as well. These tests showed that the proposed model was always in fairly good agreement with the experimental data, even in complex hydrodynamic situations like those forced by breaking solitary waves. In particular, in comparison with other state-of-the art shoreline models, in all the analyzed cases the proposed model allowed much better predictions of the shoreline velocity to be obtained.