船舶与海洋工程

时域格林函数的新实用数值计算方法

  • 张腾 ,
  • 任俊生 ,
  • 李志富 ,
  • 白伟伟
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  • (1.大连海事大学 航海学院,辽宁 大连 116026;2.江苏科技大学 船海学院,江苏 镇江 212003)
张腾(1991—),男,博士生,研究方向:船舶水动力.

收稿日期: 2017-05-04

  修回日期: 2017-06-07

  网络出版日期: 2017-05-27

基金资助

国家高技术研究发展计划(863计划)资助项目(2015AA016404);国家自然科学基金资助项目(51109020;51779029);交通部应用基础研究项目(2014329225370);海洋公益性行业科研专项经费项目(201505017-4).

A new and practical numerical calculation method for time-domain Green function

  • ZHANG Teng ,
  • REN Jun-sheng ,
  • LI Zhi-fu ,
  • BAI Wei-wei
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  • (1.Navigation College,Dalian Maritime University, Dalian 116026,China;2.Marine Engineering,Jiangsu University of Science and Technology,Zhenjiang 212003,China)

Received date: 2017-05-04

  Revised date: 2017-06-07

  Online published: 2017-05-27

摘要

针对求解无限水深时域格林函数时大、小区域划分界限不明确,数值精度无法保证的问题,在大、小时间区域交界处,采用精细时程积分法对满足时域格林函数的四阶常微分方程进行数值计算.完成对时域格林函数节点制表后,提出基于精细积分法求解常微分方程的节点间插值的计算时域格林函数新方法.数值计算结果表明,本文提出的方法可有效提高时域格林函数的数值计算精度,为计算船舶水动力奠定了可靠的基础.

本文引用格式

张腾 , 任俊生 , 李志富 , 白伟伟 . 时域格林函数的新实用数值计算方法[J]. 大连海事大学学报, 2018 , 44(1) : 1 -8 . DOI: 10.16411/j.cnki.issn1006-7736.2018.01.001

Abstract

Aiming at the problems of unclear dividing line between short time interval region and long time interval region and the numerical accuracy, the precise time integration method was used to solve the fourthorder ordinary differential equations of timedomain Green function in the junction between long time interval region and short time interval region. Once the node tabulation for the timedomain Green function was obtained, a new method for computing the time domain Green’s function based on the precise integration method was proposed to solve the interpolation between nodes in ordinary differential equations. Numerical calculation results show that the proposed method can effectively improve the numerical accuracy of timedomain Green function which lays a reliable foundation for calculating ship’s hydrodynamics.

 

参考文献

[1]BECK R F,LIAPIS S.Transient motions of floating bodies at zero forward speed[J].Journal of Ship Research, 1987,31(3):164-176.
[2]NEWMAN J N.The approximation of free-surface Green functions[R].Retirement meeting for Professor F.Ursell, 1992:107–135.
[3]黄德波.时域Green函数及其导数的数值计算[J].中国造船,1992(4):16-25.
HUANG De-bo.Approximation of time-domain free surface function and its spatial derivatives[J].Shipbuilding of China,1992(4):16-25.(in Chinese)
[4]CLEMENT A H.An ordinary differential equation for the Green function of time-domain free-surface hydrodynamics[J].Journal of Engineering Mathematics,1998, 33(2), 201–217.
[5]朱海荣.船舶与海洋结构物运动的三维时域方法及应用[D].上海:上海交通大学,2009.
ZHU Hai-rong.Three dimensional time domain approach and application for ship motions[D].Shanghai:Shanghai Jiao Tong University,2009.(in Chinese)
[6]申亮,朱仁传,缪国平,等.深水时域格林函数的实用数值计算[J].水动力学研究与进展,2007,22(3): 380-386.
SHEN Liang,ZHU Ren-chuan,MIAO Guo-ping,et al.A practical numerical method for deep water time-domain Green function[J].Journal of Hydrodynamics,2007,22(3):380-386.(in Chinese)
[7]孙雷.船兴波及其对结构物作用的研究[D].大连:大连理工大学,2009.
SUN Lei.A study of ship-generated waves and its effects on structures[D].Dalian:Dalian University of Technology,2009.(in Chinese)
[8]LI Zhi-fu,REN Hui-long,TONG Xiao-wang,et al.A precise computation method of transient free surface Green function[J]. Ocean Engineering,2015,105:318–326.
[9]钟万勰.结构动力方程的精细时程积分法[J].大连理工大学学报,1994,34(2):131-136.
ZHONG Wan-xie.On precise time-integration method for structural dynamics[J].Journal of Dalian University of Technology,1994,34(2):131-136.(in Chinese)
[10]叶恒奎.三维时域波动函数的一种数值处理方法[J].华中理工大学学报, 1994, 22(4): 58-63.
YE Heng-kui.A numerical calculating method for the 3-D time dependent wave function[J].Journal Huazhong University of Science and Technology,1994,22(4):58-63.(in Chinese)
[11] DUAN Wen-yang, DAI Yi-shan. New derivation of ordinary differential equations for transient free-surface Green functions [J]. Ocean Engineering, 2001, 15(4): 499–507.
[12]CHUANG J M,QIU W,PENG H. On the evaluation of time-domain Green function[J]. Ocean Engineering, 2007, 34(7): 962–969.
[13]WEHAUSEN J V, LAITONE E V. Surface waves[M]// Encyclopaedia of Physics.Berlin:Springer Berlin Heidelberg,1960:446-778.

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