深水波频域格林函数及其高阶导数算法研究  

Algorithm for infinite depth water wave Green function and its high order derivatives

作　　者：段文洋[1] 余冬华[2] 沈艳[2] 

机构地区：[1]哈尔滨工程大学船舶工程学院,哈尔滨150001 [2]哈尔滨工程大学理学院,哈尔滨150001

出　　处：《船舶力学》2016年第1期10-22,共13页Journal of Ship Mechanics

基　　金：国家自然科学基金项目(NSFC Project)(51079032;51409065)

摘　　要：文章研究了无限水深自由面格林函数一种新的算法,该算法将计算域重新划分为五个子区域,在每一个子区域内只涉及级数展开,没有使用插值表及数值积分,与现有格林函数算法相比,不仅给出一阶导数值,而且能高效地计算二阶导数,这在格林函数微分方程求解及高阶面元法中非常有用。数值结果表明,该方法计算速度快且一阶导数和二阶导数的计算精度达到10^(-9)。A new algorithm for infinite depth case free surface frequency Green function is proposed. The calculation domain was re-divided into five subareas. In each subarea, this algorithm used series expansion without interpolation table and numerical quadrature. Compared with existing algorithms of Green function,the new algorithm can compute first order derivative and second order derivative efficiently. They are very necessary in Green function differential equation and high-order panel method. The numerical result shows that the algorithm has highly efficient and its calculation precision of first and second order derivatives can reach to 10^-9.

关 键 词：GREEN函数 自由面 高阶导数 数值逼近 

分 类 号：U661.1[交通运输工程—船舶及航道工程]