A Coupled Model For Numerical Study Of Coastal Water Waves

The enhanced Boussinesq equation (EB model) has been widely used as a mathematical model for nonlinear wave propagation and transformation in nearshore waters. EB model is known to be of advantages when a coastal hydrodynamic problem defined on large domain must be treated with high accuracy. Since EB model assumed the vertical structure of the velocity and the pressure of the wave induced flow, it becomes invalid in a number of situations such as in the vicinity of a structure with complex geometry. On the other hand, a mathematical model based on the Navier—Stokes equation for incompressible fluid flows in porous media can resolve complex flow caused by a local wave event, the computational effort required is tremendous. Hence, it can be applied only to problems with a dimension of several wavelengths. The present study is to combine the advantages of both the EB model and the NSPMF model, so as to effectively solve nonlinear wave motion with structures in presence in large domains. The first part of the study is on the development of the EB model. Based on Nwogu's equations, a finite difference scheme is proposed and the numerical method is shown to be valid for nonlinear dispersive waves over gentle slope. A predictor-corrector method is used for the temporal discretization while the special discretization is based on central schemes but with a careful consideration to avoid numerical dispersion and numerical dissipation. Sommerfeld radiation condition is combined with a Sponge layer to deal with open boundaries. Regular and irregular wave propagation over a submerged breakwater is studied by the present method and the numerical results are shown to agree with the available experimental data very well. The second part of the present study is on the development of the NSPMF model. The model is based on the basic equations for incompressible fluid flows in porous medium. The kinematics' condition of the free surface is described with the VOF function. Temporal discretization of the governing equations is based on the SMAC method and the special discretization is based on the finite volume method. Reconstruction of the free surface from the VOF function is by Yongs' nine-point method. The wave transformation and breaking over a slope is simulated to verify the numerical model.The third part of the present study is to establish a matching method so that the EB model and the NSPMF model can be coupled to solve a problem with large definition domain and with complex local phenomena as well. The coupled numerical model is employed to compute the nonlinear transformation of the regular and irregular wave over a submerged breakwater and the numerical result is found to be satisfactory when compared with experimental data.