A finite element model for wave refraction, diffraction, reflection and dissipation

A finite element model is developed to calculate wave refraction, diffraction, reflection and dissipation. The governing equation is a two-dimensional depth-integrated linear wave equation which considers the effects of topographical variation and energy dissipation. The bathymetric variation consists of a slowly varying component and a fast, small amplitude varying component. In the governing equation, the energy dissipation term may be formulated for different physical mechanisms such as bottom friction, and wave breaking. Wave diffraction and reflection are caused by the appearance of structures. The effects of energy absorbing boundaries are also examined. Numerical results are verified with analytical solutions including harbor oscillations and wave diffraction by a circular cyclinder with absorbing boundaries. Numerical results are also used to compare with experimental data for wave propagation over a shoal in a wave tank.