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浅水问题的约束Hamilton变分原理及祖冲之类保辛算法

吴锋 钟万勰

吴锋, 钟万勰. 浅水问题的约束Hamilton变分原理及祖冲之类保辛算法[J]. 应用数学和力学, 2016, 37(1): 1-13. doi: 10.3879/j.issn.1000-0887.2016.01.001
引用本文: 吴锋, 钟万勰. 浅水问题的约束Hamilton变分原理及祖冲之类保辛算法[J]. 应用数学和力学, 2016, 37(1): 1-13. doi: 10.3879/j.issn.1000-0887.2016.01.001
WU Feng, ZHONG Wan-xie. The Constrained Hamilton Variational Principle for Shallow Water Problems and the Zu-Type Symplectic Algorithm[J]. Applied Mathematics and Mechanics, 2016, 37(1): 1-13. doi: 10.3879/j.issn.1000-0887.2016.01.001
Citation: WU Feng, ZHONG Wan-xie. The Constrained Hamilton Variational Principle for Shallow Water Problems and the Zu-Type Symplectic Algorithm[J]. Applied Mathematics and Mechanics, 2016, 37(1): 1-13. doi: 10.3879/j.issn.1000-0887.2016.01.001

浅水问题的约束Hamilton变分原理及祖冲之类保辛算法

doi: 10.3879/j.issn.1000-0887.2016.01.001
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: O352

The Constrained Hamilton Variational Principle for Shallow Water Problems and the Zu-Type Symplectic Algorithm

Funds: The National Natural Science Foundation of China(General Program)(11472067)
  • 摘要: 针对浅水流问题,将不可压缩条件作为约束处理,提出一种约束Hamilton变分原理,并利用该变分原理,推出一种基于位移和压强的浅水方程(SWE-DP).针对SWE-DP,构造了一种结合有限元和祖冲之类算法的混合数值方法.通过数值算例,将SWE-DP与两个现有的浅水方程进行了数值比较,从而验证了SWE-DP的可靠性,并验证了针对SWE-DP构造的数值算法的正确性.此外,数值算例还显示出祖冲之类算法在对浅水波进行长时间仿真时,具有很好的表现.
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    [8] 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 Wang-xie.Symplectic Solution Methodology in Applied Mechanics [M]. Beijing: Higher Education Press, 2006.(in Chinese))
    [9] FENG Kang, QIN Meng-zhao.Symplectic Geometric Algorithms for Hamiltonian Systems [M]. Heidelberg, Berlin: Springer, 2010.
    [10] 钟万勰, 陈晓辉. 浅水波的位移法求解[J]. 水动力学研究与进展(A辑), 2006,21(4): 486-493.(ZHONG Wan-xie, CHEN Xiao-hui. Solving shallow water waves with the displacement method[J].Journal of Hydrodynamics(Ser A),2006,21(4): 486-493.(in Chinese))
    [11] 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))
    [12] 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,〖STHZ〗4(3): 193-200.(in Chinese))
    [13] 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))
    [14] 吴锋, 钟万勰. 基于祖冲之类方法具有保辛性[J]. 计算力学学报, 2015,32(4): 447-450.(WU Feng, ZHONG Wan-xie. The Zu-type method is symplectic[J].Chinese Journal of Computational Mechanics,2015,32(4): 447-450.(in Chinese))
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  • 被引次数: 0
出版历程
  • 收稿日期:  2015-09-30
  • 修回日期:  2015-12-01
  • 刊出日期:  2016-01-16

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