Numerical Simulation Of Nonlinear Wave Propagation

Considering the nonlinear dispersion random 3-D of water waves, the nonlinear wave mathematical model, which based on the model of water wave propagation for slowly varying topography water level current and combined diffraction-refraction, are established in this paper. In addition, the suitable algorithm methods and applicable relative depth are studied.Based on the control equations, the available difference methods and iterative algorithm are established, the suitable initial conditions and boundary conditions are confirmed. The numerical simulations of long waves and various groups of nonlinear wave element from deep water to shallow water, the comparing of analytic solutions and numerical results of linear wave propagation in the concurrent and countercurrent are carried out in this paper. These several verification tests show the difference methods and iterative algorithm are stable. In the meanwhile, the accuracy tests of the numerical methods are analyzed.In addition, the systematic comparing analyses show that the numerical results on the Berkhoff topography of nonlinear wave are well consistent with experimental results than linear wave. The comparisons of the numerical results of linear and nonlinear wave without currents indicate that the nonlinear characters are obvious from deep water to shallow water. It is shown that, the nonlinear influence of water waves should be taken into account, it's very important.By the wave numerical simulation with varying current velocities, several verifications are performed to examine the accuracy of linear and nonlinear wave models, such as the stability and the consistency between numerical results and experimental results.