Wave overtopping over a sea dike

This paper describes a solver on the simulation of overtopping of water waves over sloping and vertical structures in a numerical wave tank (NWT). It involves a time-implicit cell-staggered approximately factored VOF finite volume (FV) approach for solution of unsteady incompressible Navier–Stokes (NS) equations with a free surface on nonuniform Cartesian cut-cell grids. The Godunov-type high-order upwind schemes are introduced for discretization of the convective fluxes, while the coupling of the pressure with the velocity is realized by a projection method. The effects of turbulence are incorporated with a subgrid-scale (SGS) model. A novel VOF solver is proposed for the capture of a free surface undergoing severe topological deformation related with breaking waves. Only an approximation for the free-surface boundary conditions neglects the viscous stress but surface tension is modelled as a body force. A blend of second- and fourth-order artificial damping terms is designed for enhancement of the numerical stability. Additionally, the cut-cell techniques are utilized for handling an arbitrary geometry, and an absorbing-generating boundary condition for a wave generator is applied. The calculated results are represented in terms of the surface elevation versus time at certain locations and the velocity fields created by regular and irregular waves. Furthermore, the convergence behavior, the grid refinement effects, the study of different SGS models, the surface tension and Reynolds number effects and the role of a turbulence model under breaking waves are discussed, including a comparison with measurements available.