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| 完全非线性深水波的数值模拟 |
| Numerical simulation of fully nonlinear deep-water waves |
| 投稿时间：2009-10-11 修订日期：2010-12-07 |
| DOI： |
| 中文关键词: 造波板运动 数值变深水槽 完全非线性 高阶边界元 深水波 |
| 英文关键词:Wave maker motion numerical wave tank fully nonlinear HOBEM deep water waves |
| 基金项目:国家高技术研究发展计划（863计划）;国家自然科学基金项目（面上项目，重点项目，重大项目） |
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| 中文摘要: |
| 基于势流理论，并结合深水波质点运动从水面向下呈e指数衰减的特性，建立了完全非线性数值变深水槽模型，通过实时模拟活塞式造波机运动来产生波浪。采用时域高阶边界元法进行模拟，利用混合欧拉-拉格朗日方法和四阶Runge-Kutta方法追踪流体瞬时水面，应用镜像格林函数消除了水槽两个侧面的积分，在水槽末端布置人工阻尼层消除反射波浪。利用GMRES加速算法，提高了计算效率。利用所建模型对深水波进行了模拟研究，得到了稳定的波形，在造波板运动幅值较小时，与线性解析结果吻合良好，当造波板运动幅值较大时，体现出波浪的非线性特性。同时利用所建模型研究了造波板所在位置（上部台阶）水深对生成波浪高度的影响，由此可以选择合适的造波板所在位置水深及造波板运动幅值来得到所需要的深水波浪。 |
| 英文摘要: |
| Based on potential theory and the particle velocity decreasing exponentially with the increasing of water depth for the deep-water waves, a fully nonlinear numerical variable deep wave flume model was developed. Waves generated by a piston wave maker were real-time simulated. The model is developed by using a time domain higher-order boundary element method (HOBEM). A mixed Eulerian-Lagrangian technique and a 4th-order Runge-Kutta scheme are utilized to track the free surface. Image Green function is used in the whole fluid domain so that the integration on the lateral surfaces are excluded. An artificial damping layer is distributed at the end of the flume to eliminate wave reflection. The GMRES accelerated algorithm is utilized to improve calculation efficiency. Numerical experiments are carried out to model the deep water waves. Steady wave profiles are obtained and good agreements between numerical solutions and analytical solutions are obtained for the small motion amplitude of the wave maker. The wave nonlinear features are shown for the large motion amplitude. Numerical experiments are also carried out to study the effect on the generated wave height due to the water depth at the up step. According to the proposed numerical simulation, the suitable water depth at the up step and the motion amplitude of the wave maker can be derived to get the required wave in deep water. |
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