Fully Nonlinear Modeling Wave Transformation over Fringing Reefs Using Shock-Capturing Boussinesq Model

摘要

A numerical model, which solves the horizontal two-dimensional fully nonlinear Boussinesq equations using a well-balanced shock-capturing scheme, is developed and used to investigate wave transformation in a fringing reef environment. The governing equations are first reformulated into a conservative form, and a Godunov-type finite volume method is then used to deal with the convective parts, while the remaining terms are discretized using the finite difference method. Special attention focuses on obtaining a well-balanced state between numerical flux and the source term to model moving wet-dry fronts accurately. The third-order Runge-Kutta scheme with the strong stability preserving property and adaptive time step is used for time marching. After being validated against the analytical solution of exact solitary wave propagation, the proposed model is run to simulate solitary wave transformation over two-dimensional and three-dimensional reefs, and the computed results are in satisfactory agreement with the experimental data.