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

Shallow Water Mechanical Shock Wave

doi: 10.21656/1000-0887.380078
Funds:  The National Natural Science Foundation of China(11472076;51609034);China Postdoctoral Science Foundation(2016M590219)
  • Received Date: 2017-04-05
  • Rev Recd Date: 2017-06-13
  • Publish Date: 2017-08-15
  • The hydraulic jump problem was studied by means of the displacement method and the Lagrangian coordinates. The discussion and the numerical example show that, under the fundamental assumption that the horizontal displacement is independent of the vertical coordinate, the hydraulic jump is not a type of strong discontinuous solution because of the kinetic energy of the vertical motion, but a continuous solution which fluctuates near the discontinuity. The strong discontinuity can be seen as the limit of the continuous solution.
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  • [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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