【作者】 熊志强；

【导师】 陶建华；

【作者基本信息】 天津大学 ， 流体力学， 2007， 硕士

【摘要】 Boussinesq方程是用于描述非线性色散波在浅水中传播的方程,以Boussinesq方程为基础的数学模型可以模拟近岸海域复杂地形上波浪传播的非线性变形,如折射、绕射、反射、浅化等现象。数值造波方法是该数学模型的一个关键技术,研究数值造波方法和无反射边界处理具有重要的理论意义和实用价值。本文综述了各类Boussinesq方程在色散性、非线性、浅化性等方面的改进,以及数值造波方法和无反射边界处理的研究进展。为方便研究数学模型和数值造波方法,建立了Madsen和S?rensen(1992)形式的Boussinesq方程为基础的一维数学模型。模型中采用了高精度紧致差分格式离散方程,使用了“窄缝法”处理动边界,并引入了能量耗散项处理波浪破碎问题。数值造波方法分别采用了入射边界上造波和域内源项造波,开边界则采用吸收边界和辐射边界相结合的方法进行数值消波处理。入射边界上造波建立了线性造波机、椭圆余弦造波机和能处理造波板二次反射的可吸收式造波机;域内源项造波研究了线源造波和区域源造波方法,由理论推导证明了域内造波源函数中的波速应使用能量速度,即群速度。为了分析和比较不同的数值造波方法,分别对小振幅波、孤立波和椭圆余弦波进行了模拟,数值试验结果与理论解析解符合良好,边界处理效果也令人满意。更多还原

【Abstract】 Boussinesq equation is a nonlinear dispersion waves equation in shallow water. The numerical models based on Boussinesq equation could simulate nonlinear wave deformations on uneven bottom, such as refraction, diffraction, reflection, shoaling etc. The numerical wave generation method is a key technology of the models. It is also significant to the study of wave generation and absorbing boundary.In this paper, the improvement of the dispersive property, dissipative property, shoaling for kinds of Boussinesq equations, and the study of the numerical wave generation and absorbing boundary are reviewed. In order to investigate the model and the numerical wave generation method further, 1D models based on the extended Boussinesq equation of Madsen & S?rensen(1992) are set up. The compact difference scheme is applied in Boussinesq equation. The slot method is used to treat the moving boundary. A simple eddy viscosity-type model is added for wave breaking model.Numerical wave paddle and source function method are used to generate waves. The open boundary, which combines the sponge layer and radiation boundary, is set to permit incident waves to be transmitted freely. Linear wave maker, cnoidal wave maker and absorbing wave maker are built up. Theoretical derivations of the line and distributed source function methods show that the energy transport which equals the group velocity should be used in the model. The numerical model is applied to simulate sinusoidal, solitary and cnoidal waves. The numerical results agree well with the analytical solutions and experimental data. The sponge layer for open boundary is good.更多还原