A non-hydrostatic model for water waves in nearshore region

Based on uniform grid, a depth integrated non-hydrostatic model for coastal water flow is presented. The numerical implementation of the model is split into hydrostatic step and non-hydrostatic step. In the hydrostatic step, an efficient finite volume scheme is used to solve the fully nonlinear shallow water equations, where the hydrostatic reconstruction approach and the implicit treatment of the bottom friction are used to ensure the properties of well balance, conservation and non-negative water depth, and moving shoreline is also efficiently handled. In the non-hydrostatic step, the predicted solutions from hydrostatic step are corrected by the contribution of the dynamic pressure, which is obtained by solving Possion equations using finite difference method. A simple criterion is introduced to identify breaking waves and the governing equations are then switched off to the fully nonlinear equations, which admit breaking waves as a shock. Some numerical tests are conducted for model validation.