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水波的界带有限元

吴锋 钟万勰

吴锋, 钟万勰. 水波的界带有限元[J]. 应用数学和力学, 2015, 36(12): 1219-1227. doi: 10.3879/j.issn.1000-0887.2015.12.001
引用本文: 吴锋, 钟万勰. 水波的界带有限元[J]. 应用数学和力学, 2015, 36(12): 1219-1227. doi: 10.3879/j.issn.1000-0887.2015.12.001
WU Feng, ZHONG Wan-xie. Simulation of Water Waves Based on the Inter-Belt Finite Element Method[J]. Applied Mathematics and Mechanics, 2015, 36(12): 1219-1227. doi: 10.3879/j.issn.1000-0887.2015.12.001
Citation: WU Feng, ZHONG Wan-xie. Simulation of Water Waves Based on the Inter-Belt Finite Element Method[J]. Applied Mathematics and Mechanics, 2015, 36(12): 1219-1227. doi: 10.3879/j.issn.1000-0887.2015.12.001

水波的界带有限元

doi: 10.3879/j.issn.1000-0887.2015.12.001
基金项目: 国家自然科学基金(面上项目)(11472067)
详细信息
    作者简介:

    吴锋(1985—),男,江苏靖江人,博士(通讯作者. E-mail: wufeng_chn@163.com);钟万勰(1934—),男,浙江德清人,教授,院士(E-mail: zwoffice@dlut.edu.cn).

  • 中图分类号: O353.2

Simulation of Water Waves Based on the Inter-Belt Finite Element Method

Funds: The National Natural Science Foundation of China(General Program)(11472067)
  • 摘要: 研究了水波计算的位移法.采用物质坐标,以位移为基本未知量,考虑小变形条件,引入流函数满足不可压缩条件.于是,分析力学的变分原理可以运用了,界带有限元、正则变换、保辛积分等有效手段可使数值求解方便得多.
  • [1] 兰姆 H. 理论流体动力学[M]. 游镇雄, 牛家玉, 译. 北京: 科学出版社, 1990.(Lamb H. Hydrodynamics [M]. YOU Zhen-xiong, NIU Jia-yu, transl. Beijing: Science Press, 1990.(Chinese version))
    [2] 钟万勰, 姚征. 位移法浅水孤立波[J]. 大连理工大学学报, 2006,46(1): 151-156.(ZHONG Wan-xie, YAO Zheng. Shallow water solitary waves based on displacement method[J]. Journal of Dalian University of Technology,2006,46(1): 151-156.(in Chinese))
    [3] 钟万勰. 应用力学的辛数学方法[M]. 北京: 高等教育出版社, 2006.(ZHONG Wan-xie. Symplectic Solution Methodology in Applied Mechanics [M]. Beijing: Higher Education Press, 2006.(in Chinese))
    [4] 梅强中. 水波动力学[M]. 北京: 科学出版社, 1984.(MEI Qiang-zhong. Dynamics of Water Wave[M]. Beijing: Science Press, 1984.(in Chinese))
    [5] Remoissenet M. Waves Called Solitons [M]. Berlin: Springer, 1996.
    [6] Hairer E, Lubich Ch, Wanner G. Geometric-Preserving Algorithms for Ordinary Differential Equations [M]. Berlin: Springer, 2006.
    [7] 吴锋, 孙雁, 钟万勰. 不可压缩材料分析的界带有限元法[J]. 应用数学和力学, 2013,34(1): 1-9.(WU Feng, SUN Yan, ZHONG Wan-xie. Inter-belt finite element for the analysis of incompressible material problems[J]. Applied Mathematics and Mechanics,2013,34(1): 1-9.(in Chinese))
    [8] 钟万勰, 高强. 辛破茧[M]. 大连: 大连理工大学出版社, 2011.(ZHONG Wan-xie, GAO Qiang. Break the Limitions of Symplectics[M]. Dalian: Dalian University of Technology Press, 2011.(in Chinese))
    [9] 钟万勰, 高强, 彭海军. 经典力学辛讲[M]. 大连: 大连理工大学出版社, 2013.(ZHONG Wan-xie, GAO Qiang, PENG Hai-jun. Classical Mechanics—Its Symplectic Description[M]. Dalian: Dalian University of Technology Press, 2013.(in Chinese))
    [10] 钟万勰, 高强. 约束动力系统的分析结构力学积分[J]. 动力学与控制学报, 2006,4(3): 193-200.(ZHONG Wan-xie, GAO Qiang. Integration of constrained dynamical system via analytical structural mechanics[J].Journal of Dynamics and Control,2006,4(3): 193-200.(in Chinese))
    [11] 高强, 钟万勰. Hamilton系统的保辛-守恒积分算法[J]. 动力学与控制学报, 2009,7(3): 193-199.(GAO Qiang, ZHONG Wan-xie. The symplectic and energy preserving method for the integration of Hamilton system[J].Journal of Dynamics and Control,2009,7(3): 193-199.(in Chinese))
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出版历程
  • 收稿日期:  2015-09-01
  • 修回日期:  2015-10-11
  • 刊出日期:  2015-12-15

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