Numerical modeling of wave propagation, breaking and run-up on a beach

A numerical method for free-surface flow is presented at the aim of studying water waves in coastal areas. The method builds on the nonlinear shallow water equations and utilizes a non-hydrostatic pressure term to describe short waves. A vertical boundary-fitted grid is used with the water depth divided into a number of layers. A compact finite difference scheme is employed that takes into account the effect of non-hydrostatic pressure with a few number of vertical layers. As a result, the proposed technique is capable of simulating relatively short wave propagation, where both frequency dispersion and nonlinear shoaling play an important role, in an accurate and efficient manner. Mass and momentum are strictly conserved at discrete level while the method only dissipates energy in the case of wave breaking. A simple wet-dry algorithm is applied for a proper calculation of wave run-up on the beach. The computed results show good agreement with analytical and laboratory data for wave propagation, transformation, breaking and run-up within the surf zone.