Numerical Wave Generation In Boussinesq Equation Models

Boussinesq equation is a nonlinear dispersion waves equation in shallow water. The numerical models based on Boussinesq equation could simulate nonlinear wave deformations on uneven bottom, such as refraction, diffraction, reflection, shoaling etc. The numerical wave generation method is a key technology of the models. It is also significant to the study of wave generation and absorbing boundary.In this paper, the improvement of the dispersive property, dissipative property, shoaling for kinds of Boussinesq equations, and the study of the numerical wave generation and absorbing boundary are reviewed. In order to investigate the model and the numerical wave generation method further, 1D models based on the extended Boussinesq equation of Madsen & S?rensen(1992) are set up. The compact difference scheme is applied in Boussinesq equation. The slot method is used to treat the moving boundary. A simple eddy viscosity-type model is added for wave breaking model.Numerical wave paddle and source function method are used to generate waves. The open boundary, which combines the sponge layer and radiation boundary, is set to permit incident waves to be transmitted freely. Linear wave maker, cnoidal wave maker and absorbing wave maker are built up. Theoretical derivations of the line and distributed source function methods show that the energy transport which equals the group velocity should be used in the model. The numerical model is applied to simulate sinusoidal, solitary and cnoidal waves. The numerical results agree well with the analytical solutions and experimental data. The sponge layer for open boundary is good.