A higher-order non-hydrostatic model for simulating wave propagation over irregular bottoms

A higher-order non-hydrostatic model is developed to simulate the wave propagation over irregular bottoms based on a vertical boundary-fitted coordinate system. In the model, an explicit projection method is adopted to solve the unsteady Euler equations. Advection terms are integrated explicitly with the MacCormack's scheme, with a second-order accuracy in both space and time. Two classical examples of surface wave propagation are used to demonstrate the capability of the model. It is found that the model with only two vertical layers could accurately simulate the motion of waves, including wave shoaling, nonlinearity, dispersion, refraction, and diffraction phenomena.