极限波浪运动特性的非线性数值模拟

Nonlinear numerical simulation on the extreme-wave kinematics

利用时域高阶边界元方法建立了模拟极限波浪运动的完全非线性数值模型,其中自由水面满足完全非线性自由水面条件。采用半混合欧拉-拉格朗日方法追踪流体瞬时水面,运用四阶Runge-Kutta方法更新下一时间步的波面和速度势,同时应用镜像格林函数消除水槽两个侧面和底面上的积分。研究中利用波浪聚焦的方法产生极限波浪,并且在水槽中开展了物理模型实验,将测点试验数据与数值结果进行了对比,两者吻合得很好。对极限波浪运动的非线性和流域内速度分布进行了研究。

A fully-nonlinear numerical model based on the time-domain higher-order boundary element method （HOBEM） is established to simulate the kinematics of extreme waves. In the model, the fully- nonlinear free surface boundary conditions are satisfied and the semimixed Euler-Lagrange method is used to track free surface; the fourth-order Runge-Kutta method is used to refresh the wave elevation and the velocity potential on the free surface at each time step; the image Green function is used so that the integration on the lateral surfaces and bottom are excluded. The extreme waves are generated by the method of wave focusing. The physical experiments are carried out in a wave flume. On the horizontal velocity of the gauge, the numerical solutions are agreed well with experimental results. The characteristics of the nonlinear extreme-wave kinematics and the velocity distribution are studied here.