A phase-resolved, depth-averaged non-hydrostatic numerical model for cross-shore wave propagation

In this study, a phase-resolved and depth-averaged non-hydrostatic numerical model (SNH model) is developed. The non-incremental pressure-correction method is employed to solve the equation system in two successive steps. Firstly, an approximate Riemann solver in the framework of finite volume methods is employed to solve the hydrostatic shallow-water equations (SWE) on a collocated grid to obtain provisional solutions. Then, the intermediate solutions is updated by considering the non-hydrostatic pressure effect; a semi-staggered grid is used in this step to avoid predicting checkboard pressure field. A series of benchmark tests are used to validate the numerical model, showing that the developed model is well-balanced and describes the wetting and drying processes accurately. By employing a shock-capturing numerical scheme, the wave-breaking phenomenon is reasonably simulated without using any ad-hoc techniques. Compared with the SWE model, the wave shape can be well-preserved and the numerical predictions are much improved by using the SNH model.