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保辛水波动力学

钟万勰 吴锋 孙雁 姚征

钟万勰, 吴锋, 孙雁, 姚征. 保辛水波动力学[J]. 应用数学和力学, 2018, 39(8): 855-874. doi: 10.21656/1000-0887.390062
引用本文: 钟万勰, 吴锋, 孙雁, 姚征. 保辛水波动力学[J]. 应用数学和力学, 2018, 39(8): 855-874. doi: 10.21656/1000-0887.390062
ZHONG Wanxie, WU Feng, SUN Yan, YAO Zheng. Symplectic Water Wave Dynamics[J]. Applied Mathematics and Mechanics, 2018, 39(8): 855-874. doi: 10.21656/1000-0887.390062
Citation: ZHONG Wanxie, WU Feng, SUN Yan, YAO Zheng. Symplectic Water Wave Dynamics[J]. Applied Mathematics and Mechanics, 2018, 39(8): 855-874. doi: 10.21656/1000-0887.390062

保辛水波动力学

doi: 10.21656/1000-0887.390062
基金项目: 国家自然科学基金(11472076;51609034;51278298);中央高校基本科研业务费(DUT17RC(3)069)
详细信息
    作者简介:

    钟万勰(1934—),男,教授,中科院院士(通讯作者. E-mail: zwoffice@dlut.edu.cn);吴锋(1985—),男,副教授(E-mail: vonwu@dlut.edu.cn);孙雁(1965—),女,副教授(E-mail: sunyan@sjtu.edu.cn);姚征(1978—),男,副教授(E-mail: yaozheng@dlmu.edu.cn).

  • 中图分类号: O352;O353.2

Symplectic Water Wave Dynamics

Funds: The National Natural Science Foundation of China(11472076;51609034;51278298)
  • 摘要: 初步介绍了基于位移表示的水波动力学理论,给出了线性水波、浅水波的位移周期行波解.提出保辛摄动法,计算一般水深周期行波解,并通过数值算例验证了算法的正确性.该研究注重水波的动力学属性,可以直接给出质点粒子的轨迹,模拟出水面尖锐的周期行波解.
  • [1] 梅强中. 水波动力学[M]. 北京: 科学出版社, 1984.(MEI Qiangzhong. Water Wave Dynamics [M]. Beijing: Science Press, 1984.(in Chinese))
    [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 Wanxie, 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 Wanxie. Symplectic Solution Methodologyin Applied Mechanics [M]. Beijing: Higher Education Press, 2006.(in Chinese))
    [4] 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, 2006,21(4): 486-493.(ZHONG Wanxie, CHEN Xiaohui. Solving shallow water waves with the displacement method[J]. Journal of Hydrodynamics,2006,21(4): 486-493.(in Chinese))
    [5] 钟万勰, 吴锋. 力-功-能-辛-离散: 祖冲之方法论[M]. 大连: 大连理工大学出版社, 2016.(ZHONG Wanxie, WU Feng. Force-Work-Energy-Symplecticity-Discretization: ZU Chongzhi’s Methodology [M]. Dalian: Dalian University of Technology Press, 2016.(in Chinese))
    [6] 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.(WU Feng, ZHONG Wanxie. 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.(in Chinese))
    [7] 吴锋. 基于位移的水波数值模拟: 辛方法[M]. 大连: 大连理工大学, 2017.(WU Feng. Numerical Modeling of Water Waves Based on Displacement: Symplectic Method [M]. Dalian: Dalian University of Technology Press, 2017.(in Chinese))
    [8] WEYL H. The Classical Groups: Their Invariants and Representations [M]. Princeton, New Jersey: Princeton University Press, 1939.
    [9] 冯康, 秦孟兆. 哈密尔顿系统的辛几何算法[M]. 杭州: 浙江科学技术出版社, 2004.(FENG Kang, QIN Mengzhao. Symplectic Geometric Algorithms for Hamiltonian Systems [M]. Hangzhou: Zhejiang Science and Technology Press, 2004.(in Chinese))
    [10] 吴云岗, 陶明德. 水波动力学基础[M]. 上海: 复旦大学出版社, 2011.(WU Yungang, TAO Mingde. The Foundation of Hydrodynamic [M]. Shanghai: Fudan University Press, 2011.(in Chinese))
    [11] 钟万勰, 吴锋, 孙雁. 浅水机械激波[J]. 应用数学和力学, 2017,38(8): 845-852.(ZHONG Wanxie, WU Feng, SUN Yan. Shallow water mechanical shock wave[J]. Applied Mathematics and Mechanics,2017,38(8): 845-852.(in Chinese))
    [12] STOKER J J. Water Waves: the Mathematical Theory With Applications [M]. New York: Interscience Publishers Ltd, 1957.
    [13] 吴锋, 孙雁, 姚征, 等. 椭圆余弦波的位移法分析[J]. 计算机辅助工程, 2018,27(2): 1-5.(WU Feng, SUN Yan, YAO Zheng, et al. Analysis on cnoidal wave using the displacement method[J]. Computer Aided Engineering,2018,27(2): 1-5.(in Chinese))
    [14] ADRIAN C. Nonlinear Water Waves With Applications to Wave-Current Interactions and Tsunamis [M]. New York: Society for Industrial & Applied Mathematics, 2011.
    [15] CONSTANTIN A. The trajectories of particles in Stokes waves[J]. Inventiones Mathematicae,2006,166(3): 523-535.
    [16] CONSTANTIN A, ESCHER J. Particle trajectories in solitary water waves[J]. Bulletin of the American Mathematical Society,2007,44(3): 423-431.
    [17] 吴锋, 钟万勰. 浅水动边界问题的位移法模拟[J]. 计算机辅助工程, 2016,25(2): 5-13.(WU Feng, ZHONG Wanxie. Simulation on moving boundaries of shallow water using displacement method[J]. Computer Aided Engineering,2016,25(2): 5-13.(in Chinese))
    [18] 姚征, 钟万勰. 位移法浅水波方程解及其特性[J]. 计算机辅助工程, 2016,25(2): 21-25.(YAO Zheng, ZHONG Wanxie. Solutions and characteristics of shallow water equation based on displacement method[J]. Computer Aided Engineering,2016,25(2): 21-25.(in Chinese))
    [19] 吴锋, 钟万勰. 不平水底浅水波问题的位移法[J]. 水动力学研究与进展, 2016,31(5): 549-555.(WU Feng, ZHONG Wanxie. Displacement method for the shallow water wave problems with uneven bottoms[J]. Chinese Journal of Hydrodynamics,2016,31(5): 549-555.(in Chinese))
    [20] WU Feng, ZHONG Wanxie. On displacement shallow water wave equation and symplectic solution[J]. Computer Methods in Applied Mechanics and Engineering,2017,318: 431-455.
    [21] WU F, YAO Z, ZHONG W. Fully nonlinear (2+1)-dimensional displacement shallow water wave equation[J]. Chinese Physics B,2017,26(5): 253-258.
    [22] WU F, ZHONG W. A shallow water equation based on displacement and pressure and its numerical solution[J]. Environmental Fluid Mechanics,2017,17(5): 1-28.
    [23] 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.(WU Feng, ZHONG Wanxie. Simulation of water waves based on the inter-belt finite element method[J]. Applied Mathematics and Mechanics,2015,36(12): 1219-1227.(in Chinese))
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出版历程
  • 收稿日期:  2018-02-09
  • 修回日期:  2018-04-11
  • 刊出日期:  2018-08-15

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