Efficient computation of surf zone waves using the nonlinear shallow water equations with non-hydrostatic pressure

A numerical method for non-hydrostatic, free-surface, irrotational flow governed by the nonlinear shallow water equations including the effects of vertical acceleration is presented at the aim of studying surf zone phenomena. A vertical boundary-fitted grid is used with the water depth divided into a number of layers. A compact finite difference scheme is employed for accurate computation of frequency dispersion requiring a limited vertical resolution and hence, capable of predicting the onset of wave breaking. A novel wet–dry algorithm is applied for a proper handling of moving shoreline. Mass and momentum are strictly conserved at discrete level while the method only dissipates energy in the case of wave breaking. The numerical results are verified with a number of tests and show that the proposed model using two layers without ad-hoc assumptions enables to resolve propagating nonlinear shoaling, breaking waves and wave run-up within the surf and swash zones in an efficient manner.