完全非线性聚焦波浪的数值模拟

利用高阶边界元方法求解拉普拉斯方程,建立了模拟完全非线性聚焦波的时域数值模型,其中追踪流体自由表面的方法为满足完全非线性自由水面条件的半混合欧拉-拉格朗日方法,运用四阶Runga-Kutta方法计算每一时间步新的波面高度和速度势,同时通过入射边界给定速度的二阶Stokes解析解产生波浪,并应用镜像格林函数消除水槽两个侧面和底面上的积分。对不同波陡的聚焦波群在水槽中开展了物理模型实验,并把试验结果和数值结果进行了对比,两者吻合得很好,然后对非线性条件下聚焦波的特点进行了研究。

Numerical simulation of fully nonlinear focused wave groups

The propagation of transient wave groups, focused on a point in time and space to produce waves with steepness, is simulated by resolving Laplace equation using the higher-order boundary element method in the time domain, in which the fully nonlinear boundary conditions and semi-mixed Euler-Lagrange method are used to track free surface. The fourth-order Runga-Kutta method is used to comput the wave elevation and velocity potential on the free surface at each time step. The 2nd-order Stokes analytical velocity is given at the incident boundary to generate the input wave. The image Green function is applied in the present study so that the integration on the lateral surfaces and bottom are excluded. The experimental study on the focused wave groups with different wave slopes is carried out in a wave flume. And the numerical solutions are compared with the experimental results. The characters of the nonlinear focused wave groups are studied here.