基于高阶边界元的三维数值波浪港池--波浪破碎的模拟

在势流理论的框架内,采用高阶边界元方法和混合欧拉-拉格朗日法,实现了对三维波浪破碎过程的数值模拟.数值模型使用可调节时间步长的基于二阶显式泰勒展开的混合欧拉-拉格郎日时间步进来求解自由表面的演化过程.在所使用的边界元方法中,采用16节点三次滑移四边形单元来表示,这种单元在单元内具有高阶的精度同时在单元之间具有良好的连续性.给出了孤立波的传播和周期性非线性波浪沿缓坡传播的计算结果,表明数值模型具有良好的稳定性.

Three dimensional numerical wave tank using HOBEM --simulation of breaking waves

This paper presents a study on mathematical modeling of breaking waves using the high order boundary element method(HOBEM) and the hybrid Eulerian-Lagrangian method for three dimensional potential flows with the free surface.A three dimensional numerical wave tank with a gentle beach based on a high order boundary element method is developed,which can be used to simulate the propagation of solitary waves and nonlinear periodic waves.The model solves fully nonlinear potential flow equations with a free surface using a HOBEM and a hybrid Eulerian-Lagrangian time updating,which is based on second-order explicit Taylor series expansions with adaptive time steps.In the HOBEM,boundary geometry and field variables are represented by 16-node cubic 'sliding' quadrilateral elements. These elements provide higher order accuracy in themselves and good inter-element continuity.The results show that the present NWT can simulate the propagation of a solitary wave and nonlinear periodic waves over gentle beaches efficiently with good stability.