【作者】 王大国；

【导师】 邹志利；

【作者基本信息】 大连理工大学 ， 港口、海岸及近海工程， 2005， 博士

【摘要】 本文分别以Boussinesq方程,二维和三维Laplace方程,欧拉方程和牛顿第二定律作为基本控制方程,分别从非耦合非线性波浪计算模型(指单独采用一个计算模型:本文指Boussinesq方程,或边界元法解Laplace方程,或有限元法解Laplace方程)、Boussinesq方程与Laplace方程耦合计算模型、Boussinesq方程与欧拉方程耦合计算模型三个方面对港口非线性波浪计算模型展开了研究。 非耦合非线性波浪计算模型:1) 根据造波板做椭圆余弦运动或正弦运动速度,推导出数值模拟波浪水槽时固定入射边界上的二阶波浪入射边界条件,数值计算结果和实验结果的对比表明采用二阶入射边界条件对波面升高的预报比采用一阶入射边界条件对波面升高的预报更为精确;2) 推导了波浪水槽造波板做正弦运动所产生波浪的高阶Boussinesq方程摄动展开解析解,讨论了该解析解的适用范围;3) 对整个波浪水槽应用边界元方法数值模拟了波浪对物体的非线性作用;4) 用有限元法求解三维Laplace方程模拟了三维完全非线性波浪水槽。 Boussinesq方程与Laplace方程耦合计算模型:1) 建立了外域用有限差分法求解Boussinesq方程、内域用边界元法求解Laplace方程的二维耦合计算模型。研究了耦合计算的匹配条件、耦合求解过程和公共区域长度的确定,讨论了内域自由表面条件分别采用半拉格朗日法和拉格朗日法时的区别:用半拉格朗日法的计算效率要比用拉格朗日法的计算效率高,但计算结果精度差别不大;2) 提出了用最小二乘拟合法求Boussinesq方程的二阶、四阶水平速度公式中水深平均速度对水平坐标二阶、四阶的导数,讨论了Boussinesq方程的二阶水平速度公式相对四阶水平速度公式的适用范围:在Kh<1.26(K是波数,h是静水深)时,它们之间的最大误差不超过4%,因此可以用Boussinesq方程的二阶水平速度公式代替Boussinesq方程的四阶水平速度公式计算水平速度沿水深的分布;3) 建立了外域用有限差分法求解Boussinesq方程、内域用有限元法求解Laplace方程的三维耦合计算模型。 Boussinesq方程与欧拉方程耦合计算模型:1) 建立了外域用有限差分法求解Boussinesq方程、内域也用有限差分法求解欧拉方程的二维、三维耦合计算模型。讨论了耦合计算的匹配条件、耦合求解过程。对比了内域用欧拉方程的二维、三维耦合计算模型和内域用Laplace方程的二维、三维耦合计算模型的优缺点:内域用欧拉方程的二维、三维耦合计算模型内域数值求解、整个耦合过程简单,计算效率高,但适用范围窄(只适用于船体为箱体)。2) 对直立码头前固定箱体引起的非线性波浪运动,建立了外域用Boussinesq方程、内域用牛顿第二定律的港口非线性波浪祸合计算模刑二维祸合计算模型。推导了箱体与海底和直立码头之间流体运动的自振频率,从实验和数值两方面研究了间隙内流体运动的共振现象:当入射波浪的基频或高频与间隙内流体运动的自振频率接近时,将会激发起间隙内流体运动的共振现象,使直立码头前物体所受水平力比没有码头时船所受水平增大约一倍。 关键词:有限差分法,边界元法,有限元法,Boussinesq方程,Laplaee方程,欧拉方程,牛顿第二定律,非线性波浪祸合模型更多还原

【Abstract】 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.更多还原