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基于二阶时间步进法数值波浪水槽研究

ISSN号：1005-9865
期刊名称：海洋工程
时间：2011.8.8
页码：50-58
分类：TV148[水利工程—水力学及河流动力学]
作者机构：[1]大连理工大学海岸和近海工程国家重点实验室,辽宁大连116024, [2]国家海洋局第二海洋研究所卫星海洋环境动力学国家重点实验室,浙江杭州310012
相关基金：国家自然科学基金资助项目（50921001,11072052）;卫星海洋环境动力学国家重点实验室开放基金资助项目（SOEDl002）;中央高校基本科研业务费专项资金资助项目（DUTl0JN03）
相关项目：无限水深中海洋结构物上的二阶波浪力

关键词：二阶泰勒级数展开, 源造波法, 五阶斯托克斯波, 数值波浪水槽, 高阶边界元, second-order Taylor series expansion, source generation of waves, fifth-order Stokes wave, numerical wave tank, HOBEM

中文摘要：

基于势流理论和时域高阶边界元方法，建立了三维完全非线性数值波浪水槽模型。利用源造波法产生入射波浪，应用五阶斯托克斯波理论给定波浪速度；采用混合欧拉．拉格朗日方法追踪流体瞬时水面，将二阶泰勒级数展开法应用于更新下一时间步的波面和速度势；通过加速势的方法准确计算自由水面速度的法向导数和物面速度势的时间导数。对完全非线性波浪进行了模拟，得到了稳定的波形。当波浪非线性较小时，与四阶Runge-Kutta法（RK4）计算结果和五阶斯托克斯波理论解均吻合良好；随着波浪非线性的增大，计算结果误差逐渐增大。通过数值试验分析，在满足精度要求的基础上，本方法计算时间略大于四阶Runge—Kutta法的四分之一，大大减少了计算量。

英文摘要：

A three-dimensional fully nonlinear numerical wave tank was developed by using a time-domain higher-order boundary element method based on the potential theory. The source generation of waves was adopted to generate input waves. The wave velocity is given by the fifth-order Stokes wave theory. The mixed Eulerian-Lagrangian method was utilized to track and refresh the free surface, based on second-order Taylor series expansion. The acceleration-potential scheme was used for obtaining accurate normal derivative of velocity on the free surface and the time derivative of velocity potential on the body surface. Numerical experiments were carried out to model the fully nonlinear waves. Steady wave profiles are obtained and good agreement between numerical solutions, results from four-order Runge-Kutta （RK4） and analytical solu- tions are obtained for weak nonlinearity. Error of present calculation increases with the increasing of wave nonlinearity. On the basis of meeting the precision requirement, the numerical results show that the present method greatly reduces the computing cost, which is slightly more than one fourth of that from fourth-order Runge-Kutta method.

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