有限深水域中三维频域自由面格林函数及其导数的计算方法  

Algorithm for Three-dimensional Free-surface Green Function in Frequency Domain at Finite Water Depth and Its Derivatives

作　　者：徐潜龙 李晔[1] XU Qianlong;LI Ye(School of Naval Architecture,Ocean&Civil Engineering,Shanghai Jiao Tong University,Shanghai 200240,China)

机构地区：[1]上海交通大学船舶海洋与建筑工程学院,上海200240

出　　处：《计算物理》2021年第1期35-46,共12页Chinese Journal of Computational Physics

基　　金：国家自然科学基金(51761135012)资助项目。

摘　　要：三维频域自由面格林函数及其偏导数的数值计算是海洋结构物水动力分析的难点。本文对有限水深格林函数及其偏导数的数值算法作出两点改进:(1)对原函数的级数表达式进行变形,提出适用于数值计算的形式,解决高频率情况下级数解的计算失真问题;(2)对Gauss-Laguerre积分法作出改进,解决高频率大水深情况下积分解的数值溢出问题。计算结果表明:本文提出的改进算法可以有效提高有限水深格林函数及其偏导数的数值精度,对于研究较大吃水的浮体或潜体的高频垂荡问题具有重要意义。Numerical evaluation of three-dimensional free-surface Green function in frequency domain and its partial derivatives is a main difficulty in hydrodynamic analyses of marine structures.We proposed two improvements in traditional algorithms of Green function and its partial derivatives.Firstly,we transformed series expressions of Green function and its partial derivatives into expressions that were applicable in numerical evaluation.The improved algorithm is able to prevent series solutions from numerical distortion.Secondly,we improved Gauss-Laguerre algorithm to make sure it is effective at high frequencies and in large water depths.Numerical results indicate that the algorithms improved effectively numerical accuracy of Green function and its partial derivatives.It is significant for heave radiation problems of floating or submerged bodies with large draft at high frequencies.

关 键 词：有限水深 格林函数 级数法 高频失真 Gauss-Laguerre积分法 

分 类 号：O241[理学—计算数学]