| Based on integral equation for two dimensional Laplace quation, a nonlinear time domain numerical model for wave transformation is given in this paper. The numerical method is applied to analyse the linear wave and nonlinear wave deformations caused by inclined water bottom. It is also used to solve fully nonlinear potential flow equations with a free surface by use of a HOBEM(higher-order boundary element method) and a mixed Eulerian-Lagrangian time updating based on second-order explicit Taylor series expansions with adaptive time steps. Nonlinear periodic waves can be generated at one end; and reflecting or absorbing boundary conditions specified at the other end.Quasi-spline boundary elements are used on the free surface and three-node quadratic elements on the other boundaries. The clap wave-generating is simulated and time-updating method is used to imporove the numerical results. Firstly, a solitary wave is computed, which shows a good agreement with analytical result. Secondly, linear wave propagation in the inclined area is analyzed, the wave deformation results is in accord with theoretical rules, which validated the wave deformation theory. Finally, nonlinear wave propagation in the inclined area is analyzed, the results indicate that the deformation rule of nonlinear wave can be calculated by linear wave theory when the wave have a steady form. |
