Dimensional Numerical Simulation Of Nonlinear Waves

A nonlinear numerical model for wave transformation is established in time domain based on integral equation transformed from two dimensional Laplace equation. Then the model is applied to compute the linear wave and nonlinear wave deformation in offshore flow field.A new 0-1 combined BEM(Boundary Element Method) is adopted in this thesis to avoid computational errors accumulated with time steps. That is, the constant element for velocity potential, called 0 type element, and linear element for its normal derivative, called 1 type element. Then the whole boundary surface is discretized by such combined elements, so a discretized integral equation is given. Subsequently the free surface is divided by FEM (Finite Element Method) and a linear set of equations is developed based on Bernoulli equation. Finally a set of equations with initiate values for boundary value problem is established where the velocity potential and its normal derivative are unknowns. Because the model includes the effects of both the time and space to the velocity potential of free surface, it can be applied to strong nonlinear wave.As examples, solitary wave is computed in the numerical flume. The results are in good agreement with theoretical ones.