A combined wave refraction-diffraction numerical model based on the wave energy budget equation is presented in this paper. An operator splitting scheme was used to solve the wave energy equations in which the Eulerian-Lagrangian method was applied to the advection terms to increase numerical stability and the other terms were discretized by finite element method. A wave energy dissipation term was employed to increase numerical accuracy. The numerical results of wave diffraction were compared with analytical results and laboratory results. Laboratory wave measurements under submerged circular and elliptical shoal conditions were selected to validate the computed results as well. Good agreement between computed and laboratory results was observed in general. The wave climates in Pearl River Estuary in China were predicted using the numerical model. The numerical model is efficient for wave refraction-diffraction computation in a large coastal area with complex configuration.
Estuaries are prominent coastal features. Estuaries are of great economics significance to mankind. At these areas, many coastal infrastructures have to be built for economic purposes. Waves and currents are main hydrodynamics in estuaries. In order to simulate sediment transport, make proper plans for shoreline protection and coastal resource management in an estuary, it is essential to have detailed information on the waves. Since Berkhoff (1972) developed the mild slope equation that describes wave refraction-diffraction phenomenon. The mild slope equation has been wildly used in practical engineering problems. The original mild slop equation was an elliptical equation and numerical method for solving it took a relatively long time. In order to solve the mild slope equation more efficiently the parabolic model was applied by Radder (1979), Horikawa, K. (1988), and Lee and Wang (1997).
