An efficient and accurate non‐hydrostatic model with embedded Boussinesq‐type like equations for surface wave modeling

A novel approach that embeds the Boussinesq‐type like equations into an implicit non‐hydrostatic model (NHM) is developed. Instead of using an integration approach, Boussinesq‐type like equations with a reference velocity under a virtual grid system are introduced to analytically obtain an analytical form of pressure distribution at the top layer. To determine the size of vertical layers in the model, a top‐layer control technique is proposed and the reference location is employed to optimize linear wave dispersion property. The efficiency and accuracy of this NHM with Boussinesq‐type like equations (NHM‐BTE) are critically examined through four free‐surface wave examples. Overall model results show that NHM‐BTE using only two vertical layers is capable of accurately simulating highly dispersive wave motion and wave transformation over irregular bathymetry. Copyright © 2008 John Wiley & Sons, Ltd.