The Coupled Numerical Model Of Non-linear Wave In Harbour

The numerical model of non-linear wave in harbor, including the non-coupled and non-linear wave numerical model (only one numerical model), the numerical model combined Boussinesq equations with Laplace equation and the coupled numerical model combined Boussinesq equations with Euler's equations, are studied.The studies on non-coupled and non-linear wave numerical model are following. 1) Second order incident boundary condition on fixed incident boundary is derived for numerical simulations, based on the cnoidal or sinusoidal motions of wave maker paddle, which shows that the prediction with second order incident boundary condition is more accurate than the prediction with first order incident boundary condition. 2) The analytical solution for higher-order Boussinesq equations is derived and its applicable range is discussed. 3) A 2-D fully non-linear numerical model using boundary element method is developed to obtain wave forces acting on rectangular obstacle. 4) The three-dimensional fully non-linear waves are studied in a numerical wave tank using finite element method.The studies on the coupled numerical model combined Boussinesq equations with Laplace equation are following. 1) A 2-D coupled numerical model, which is the combination Boussinesq equations solved by finite difference method with Laplace equation solved by boundary element method, is established. The matching conditions, the procedure of coupled solution, the length of common domain are discussed. The sem-Lagrangian and the Lagrangian are used to track the free surface. It is shown the computational efficiency of sem-Lagrangian is higher than that of Lagrangian and the accuracy is almost identical. 2) Least Square Method is adopted to calculate second and fourth derivative of depth-averaged horizontal velocity to horizontal coordinate. The maximum error between two and four order formula of horizontal velocity is less than 4% while Kh < 1.26 (K is wave number, h is water depth), herein two order formula of horizontal velocity can be used to calculate the distribution of the horizontal velocity along water depth. 3) A 3-D coupled numerical model combined Boussinesq equations solved by finite difference method with Laplace equation solved by finite element method is developed.The studies on the coupled numerical model combined Boussinesq equations with Euler's equations are following. 1) The 2-D and 3-D coupled numerical modelsare established, which are the combination of Boussinesq equations with Euler's equations solved respectively by finite difference method. Compared with the coupled model that inner domain is governed by Laplace equation, the coupled model that the inner domain is governed by Euler's equations has simple procedure of coupled solution and higher computational efficiency, but limited applicable range.2) A 2-D coupled numerical model, combined Boussinesq equations with Newton's Second Law, is established to calculate the nonlinear wave forces acting on rectangular obstacle against vertical quay in a harbor. The natural frequency of the fluid motions in the gap between rectangular obstacle, seabed and vertical quay wall is derived. It is shown that by the experimental data and numerical results the resonance waves in the gap are induced by the first or higher harmonics of incident waves and the first or higher order horizontal wave forces on rectangular obstacle against vertical quay wall increase largely when the frequency of the harmonics of incident waves is close to the natural frequency of fluid motions in the gap.