A 3D non-hydrostatic model for simulating coastal wave transformations: shoaling, diffraction, and refraction

This research develops a 3D non-hydrostatic model to simulate complex free-surface flows, including wave propagation under various conditions. The model discretizes the full 3D Reynolds-averaged Navier-Stokes (RANS) equations using the finite volume method on a staggered computational grid. The grid combines orthogonal cells in the horizontal plane with a curvilinear system conforming to bed and water surface boundaries vertically. The governing equations are solved via a time-splitting pressure-correction approach. Initially, intermediate velocities are computed by addressing advection-diffusion terms, the dynamic pressure gradient, and the water surface gradient in the momentum equations. This is achieved through a time-splitting method with tailored techniques for each component. Subsequently, the provisional velocity fields and pressure correction gradients are incorporated into the continuity equation. A Poisson equation governing pressure correction is then derived. The study introduces a modification to the 3D non-hydrostatic pressure distribution in the surface layer within the pressure correction method, streamlining its implementation compared to similar approaches. With this modification, the model can simulate short-wave propagation in three dimensions using only a few vertical layers. Furthermore, a new approach is implemented for estimating horizontal velocities at vertical velocity locations, reducing computational complexity by increasing the sparsity of the system matrix. The 3D numerical model is validated through simulations of various scenarios. The high level of agreement with experimental and analytical results highlights the model as a reliable and efficient tool for simulating coastal wave processes in practical scenarios.