Numerical Simulation Of Coastal Waves Using Boussinesq-type Equations And Its Application

In this paper, a numerical model with fine grids is established and conducted to simulate the whole processes of coastal surface water wave, including wave making, shoaling, refraction, diffraction, reflection, breaking and energy dissipation due to the effect of topography and various hydraulic structures. The model was based on Boussinesq-type equations, which include the effect of nonlinear and frequency dispersion.Based on the mass conservation equation and potential theory, the extended form of Boussinesq equations is derived by using the velocity at an arbitrary water depth as the independent variable, and several terms are added into governing equations to simulate the effect of bottom friction, wave breaking and subgrid turbulent mixing. A Predictor-Corrector finite difference scheme was employed to solve the extended equations numerically. In order to verify the accuracy and applicability of the model, several numerical results from the model are compared with available physical experiment data. Comparisons show that numerical results agreed well with experimental data. Moreover, numerical results from Mild-slope equation are also compared with results from the model. Index method, in which boundary conditions are considered in details according to different shoreline types (beach or breakwater, slope or vertical wall, etc.), is reduced to deal with complex boundary conditions. Finally, the utility of the model to a real coastal area is shown by applying it to a fishing port.