A multi-layer non-hydrostatic model for wave breaking and run-up

Abstract

In this paper, a multi-layer non-hydrostatic model is developed to simulate wave breaking and run-up. The model uses explicit projection method to solve the three dimensional (3D) Navier–Stokes equations (NSE). The nonlinear free surface boundary condition is employed to track the free surface. A momentum conservative scheme is used to discretize the advection terms in momentum equations, which enables the model to efficiently resolve discontinuous flow, involving breaking waves and hydraulic jumps. A new grid arrangement is presented to accurately include the non-hydrostatic pressure effect, which is very important to describe dispersive waves. To capture the moving shoreline, a novel wet–dry algorithm is incorporated in the model. Comparisons between numerical results and analytical or experimental data are presented. It is shown that the proposed model without the use of predefined criteria is capable of accurately simulating both breaking waves and wave run-up in 2D or 3D dimensions.