A two-dimensional depth-integrated non-hydrostatic numerical model for nearshore wave propagation

•A 2D depth-averaged non-hydrostatic model is developed based on a FVM SWE solver.•The model is verified to be accurate, robust and well-balanced.•The model describes wave dispersivity and wetting and drying processes well.•The wave breaking and reverse wave breaking processes are modeled well.•The splitting error of the model is verified to be negligible.

In this study, we develop a shallow-water depth-integrated non-hydrostatic numerical model (SNH model) using a hybrid finite-volume and finite-difference method. Numerical discretization is performed using the non-incremental pressure-correction method on a collocated grid. We demonstrate that an extension can easily be made from an existing finite-volume method and collocated-grid based hydrostatic shallow-water equations (SWE) model to a non-hydrostatic model. A series of benchmark tests are used to validate the proposed numerical model. Our results demonstrate that the proposed model is robust and well-balanced, and it captures the wet-dry fronts accurately. A comparison between the SNH and SWE models indicates the importance of considering the wave dispersion effect in simulations when the wave amplitude to water depth ratio is large.