对称格林函数简化计算的数学推导  

Mathematical derivation of simplified calculation of symmetrical Green function

作　　者：杨鹏 叶梦熊[2] 李金成[2] 何景异 杜兆伟[2] YANG Peng;YE Mengxiong;LI Jincheng;HE Jingyi;DU Zhaowei(School of Mechanics and Electrics Engineering,Hainan University,Haikou 570228,China;Wuhan Second Ship Design and Research Institute,Wuhan 430205,China)

机构地区：[1]海南大学机电学院,海南海口570228 [2]武汉第二船舶设计研究所,湖北武汉430205

出　　处：《中国舰船研究》2018年第A01期22-28,共7页Chinese Journal of Ship Research

基　　金：国家重点基础研究发展计划(973计划)资助项目(2013CB036105)

摘　　要：[目的]为了减少利用边界元法计算大型浮体运动的水动力系数时的面元数量,并提高计算速度,[方法]针对具有对称面的浮体,利用其在求解奇点源强时系数矩阵可以看成循环矩阵的特性,提出对称格林函数的简化计算方法。[结果]利用该方法可以显著地加快对称浮体在波浪中运动的水动力系数求解过程:对于具有1个对称面的浮体,源强系数矩阵只需求解1/2的元素,同时线性方程组的求解时间降为原来的1/4;对于具有2个对称面的浮体,源强系数矩阵只需求解1/4的元素,同时线性方程组的求解时间缩短为原来的1/16。[结论]数值计算结果表明给出的对称性简化方法是有效的,能够极大地提高计算效率。[Objectives]This paper studies the way to reduce the elements used for calculating the hydrodynamic coefficient for movement of a large floating body with boundary element method and to quicken the calculation.[Methods]Based on the characteristic of the symmetrical floating body that the coefficient matrix can be considered as a circulant matrix during solvement of source intensity of singular point,a simplified calculation method of symmetrical Green function is proposed.Besides,detailed mathematical derivation is carried out and the physical meanings are explained.[Results]It is found that,through this method,the process of solving the hydrodynamic coefficient for wave movement of symmetrical floating body can be quickened significantly.For the floating body with one symmetrical plane,it only needs to solve half of the elements of the coefficient matrix of source intensity;meanwhile the time of solving linear equations is reduced by one quarter.And for the floating body with two symmetrical planes,it only needs to solve a quarter of elements of the coefficient matrix of source intensity;meanwhile the time of solving linear equations is reduced by one sixteenth.[Conclusions]The numerical results show that the proposed symmetrical simplification method is effective,and can greatly improve the calculation efficiency.

关 键 词：对称面浮体 格林函数 循环矩阵 

分 类 号：U661.1[交通运输工程—船舶及航道工程]