A higher-order σ-coordinate non-hydrostatic model for nonlinear surface waves

A σ‐coordinate non‐hydrostatic model with embedded Boussinesq‐type‐like equations for modeling deep‐water waves

“…In this paper, we integrate the Boussinesq-type-like equations [27] into a -based non-hydrostatic model [23] with the purpose of simulating 3D non-linear deep-water wave evolution. The use of the Boussinesq-type-like equations provides an analytical-based pressure distribution to the top-layer pressure under the staggered model grid system.…”

“…In the following, discretization of the -coordinate non-hydrostatic model is briefly described in Section 3.1 and details can be referred to Young et al [23]. To accurately calculate the mass flux, we employ the so-called N piecewise quadratic functions treatment [8] in the free-surface equation, different from the centered weighting of a staggered grid system in the previous works [23,33].…”

“…To accurately calculate the mass flux, we employ the so-called N piecewise quadratic functions treatment [8] in the free-surface equation, different from the centered weighting of a staggered grid system in the previous works [23,33]. Section 3.2 presents the implementation of the Boussinesq-type-like equations under the -coordinate system.…”

“…To exactly describe the free surface as well as the bottom topography, a boundary-fitted co-ordinate system (see Figure 1) that transforms the time-dependent Cartesian domain (x * − y * − z * −t * ) into a stationary regular domain (x − y − −t) is used [23,32]. The transformation between the Cartesian and co-ordinates is…”

“…non-linear waves are tackled by the use of the higher-order implicit finite difference scheme [23]. In addition, the employment of N piecewise quadratic functions treatment [8] of mass flux and a new adapted top-layer control (ATLC) method in the model effectively resolves the model layer size's dependence on wave number, which is important to deep-water wave groups modeling.…”