A large-scale wave-current coupled module with wave diffraction effect on unstructured meshes

Based on the extended mild-slope equation, a large-scale wave module is developed. By combining the eikonal equation and the modified wave action equation, the wave model can account for diffraction in most situations such as in the lee of islands and breakwaters, and using unstructured meshes provides great flexibility for modelling the wave in the complex geomorphology of barriers and islands, also allowing for refinement of the grid resolution within computationally important domains. The numerical implementation of the module is based on the explicit second-order upwind finite-volume schemes in geographic space, the Flux-Corrected Transport (FCT) algorithm in frequency space and the implicit Crank-Nicolson method in directional space. The three-dimensional hydrodynamic module is then modified to couple with the wave model, where the wave readily provides the depth-dependent radiation stress and the wave-induced turbulence coefficient for the current fields, and the wave propagation takes into account the current-induced advection, refraction and diffraction of wave energy and the effect of water level. The applicability of the proposed model to calculate Snell’s Law, wave transformation over the breakwaters and the elliptic shoal, wave propagation over the rip current field and the undertow on a sloping beach is evaluated. Numerical results show that the present model makes better predictions of the near-shore wave propagation and complex three-dimensional (3D) near-shore circulation driven by the waves, considering analytical solutions and experimental values.