时域自由面格林函数在半无限长垂直柱面上的解析积分研究  

Analytical Integration of Transient Free Surface Green Function over the Hemi-Infinite Vertical Cylinder

作　　者：李志富 吴斌 任慧龙[2] 石玉云 LI Zhi-fu;WU Bin;REN Hui-long;SHI Yu-yun(School of Naval Architecture and Ocean Engineering,Jiangsu University of Science and Technology,Zhenjiang 212003,China;College of Shipbuilding Engineering,Harbin Engineering University,Harbin 150001,China)

机构地区：[1]江苏科技大学船舶与海洋工程学院,江苏镇江212003 [2]哈尔滨工程大学船舶与海洋工程学院,哈尔滨150001

出　　处：《船舶力学》2020年第12期1530-1539,共10页Journal of Ship Mechanics

基　　金：国家自然科学基金资助项目(51709131)。

摘　　要：本文引入一虚拟控制面,将流体域划分为内部流体域和外部流体域两个子域。在内部流体域应用Rankine作为积分核,从而适用于复杂的自由面条件和浮体表面条件;在外部流体域应用时域自由面格林函数作为积分核,从而自动满足远方辐射条件。控制面的形状选取为无限深圆柱面,从而可以将控制面上速度势及其法向导数展开为Fourier-Laguerre级数。进一步地,控制面上关于自由面格林函数的空间积分可以进行解析计算。此种做法的好处是可以避免传统点源积分带来的数值发散问题。最后,对由控制面上解析积分导出的系数进行了数值计算和分析,发现积分系数随时间振荡衰减,成功避免了传统点源积分的数值发散问题。The coupling of Rankine source and transient free surface Green function is done with the help of a control surface,which separates the fluid region into two sub-domains.The Rankine source is used in the interior domain while the transient free surface Green function is applied in the exterior domain to find the relationships between the velocity potential and its normal derivatives.The control surface is chosen as a hemi-infinite cylinder,and the velocity potential defined on the control surface is expressed as the Fourier series in the horizontal direction and Laguerre series in the vertical direction.Then the integration of the transient free surface Green function over the control surface is computed analytically,which is important for the moderate or high speed problems.Numerical computations are carried out for the coefficients arising from the analytical integration of the transient free surface Green function over the control surface,and the properties of the coefficients are analyzed.

关 键 词：船舶运动 RANKINE源 自由面格林函数 FOURIER级数 Laguerre级数 

分 类 号：U675.91[交通运输工程—船舶及航道工程]