Interactions of breaking waves with a current over cut cells

By design of the external and internal wave–current generators, the objective of this paper is to extend our efficient Navier–Stokes solver [T. Li, P. Troch, J. De Rouck, Wave overtopping over a sea dike, J. Comput. Phys. 198 (2004) 686–726] for modelling of interactions between breaking waves and a current over a cut-cell grid, based on a dynamic subgrid-scale (SGS) model. This solver is constructed by a novel VOF finite volume approach, coupled with surface tension. When studying waves following a positive current, our external generator creates the combined inflow motions of waves and a current, which is viewed as one type of wavy inflow conditions. For cases of waves against strong currents, our internal generator describes the opposing current, by incorporating the source function to the continuity and momentum equations as a net driving force, acting on the fluid elements lying within the finite thickness source region. The outgoing waves downstream are dissipated with a breaking-type wave absorber placed in the tank extremity. Five test cases recommended are of distinctly different applications of interest, characterized by overtopping of following waves over sloping and vertical structures. the grid refinement effects, the results in 2D and 3D are in close agreement with the experimental data available in terms of the surface wave. Additionally, the performance of convergence in computations is also investigated, including full discussion for waves on beaches between 2D and 3D. By visualization of the motions that describe the physics of turbulence, it has been shown that our solver can capture most of the significant features in wave–current interactions varying with three different current speeds (positive, zero, negative).