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浅水机械激波

钟万勰 吴锋 孙雁

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. doi: 10.21656/1000-0887.380078
引用本文: 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. doi: 10.21656/1000-0887.380078
ZHONG Wan-xie, WU Feng, SUN Yan. Shallow Water Mechanical Shock Wave[J]. Applied Mathematics and Mechanics, 2017, 38(8): 845-852. doi: 10.21656/1000-0887.380078
Citation: ZHONG Wan-xie, WU Feng, SUN Yan. Shallow Water Mechanical Shock Wave[J]. Applied Mathematics and Mechanics, 2017, 38(8): 845-852. doi: 10.21656/1000-0887.380078

浅水机械激波

doi: 10.21656/1000-0887.380078
基金项目: 国家自然科学基金(11472076;51609034);中国博士后科学基金(2016M590219)
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: wufeng_chn@163.com);孙雁(1965—),女,副教授(E-mail: sunyan@sjtu.edu.cn).

  • 中图分类号: O352

Shallow Water Mechanical Shock Wave

Funds: The National Natural Science Foundation of China(11472076;51609034);China Postdoctoral Science Foundation(2016M590219)
  • 摘要: 采用位移法和Lagrange坐标探索水跃问题.通过分析表明,在水平位移与竖向坐标无关的基本假定下,因垂直运动动能的存在,水跃不会是强间断,而是一个在间断面附近抖动的连续解,强间断是该连续解的极限.
  • [1] Courant R, Friedrichs K O. Supersonic Flow and Shock Waves [M]. New York: Wiely, 1948.
    [2] Stoker J J. Water Waves: the Mathematical Theory With Applications [M]. New York: Interscience Publishers LTD, 1957.
    [3] Remoissenet M.Waves Called Solitons: Concepts and Experiments [M]. 3rd ed. Berlin: Springer, 1996: 60-64.
    [4] 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))
    [5] 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 Method in Applied Mechanics [M]. Beijing: High Education Press, 2006.(in Chinese))
    [6] 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 Wan-xie, WU Feng. Force-Work-Energy-Symplecticity-Discretization—ZU Chongzhi’s Methodology [M]. Dalian: Dalian University of Technology Press, 2016.(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] 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 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.(in Chinese))
    [9] 姚征, 钟万勰. 位移法浅水波方程的解及其特性[J]. 计算机辅助工程, 2016,25(2): 1-4, 13.(YAO Zheng, ZHONG Wan-xie. Solutions and characteristics of shallow water equation based on displacement method[J]. Computer Aided Engineering,2016,25(2): 1-4, 13.(in Chinese))
    [10] 梅强中. 水波动力学[M]. 北京: 科学出版社, 1984.(MEI Qiang-zhong.Water Wave Dynamics [M]. Beijing: Science Press, 1984.(in Chinese))
    [11] 钟万勰, 吴锋, 孙雁. 浅水机械激波[Z/OL]. (2017-6-13)[2017-6-19]. http://blog.sciencenet.cn/blog-1177086-1060491.html.(ZHONG Wan-xie, WU Feng, SUN Yan. Shallow water mechanical shock, wave[Z/OL]. (2017-6-13)[2017-6-19]. http://blog.sciencenet.cn/blog-1177086-1060491.html.(in Chinese))
    [12] 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 Wan-xie. Simulation on moving boundaries of shallow water using displacement method[J]. Computer Aided Engineering,2016,25(2): 5-13.(in Chinese))
    [13] 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 Wan-xie. Displacement method for the shallow water wave problems with uneven bottoms[J]. Chinese Journal of Hydrodynamics,2016,31(5): 549-555.(in Chinese))
    [14] WU Feng, ZHONG Wan-xie. On displacement shallow water wave equation and symplectic solution[J].Computer Methods in Applied Mechanics and Engineering,2017,318: 431-455.
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  • 被引次数: 0
出版历程
  • 收稿日期:  2017-04-05
  • 修回日期:  2017-06-13
  • 刊出日期:  2017-08-15

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