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.

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

##### doi: 10.3879/j.issn.1000-0887.2015.12.001
Funds:  The National Natural Science Foundation of China(General Program)（11472067）
• Rev Recd Date: 2015-10-11
• Publish Date: 2015-12-15
• Here the displacement method for the simulation of water waves was studied. Under the physical coordinate system, the displacements were taken as the unknown variables. Under the assumption of small deformation, the water incompressibility was satisfied through introduction of the flow function. Hence the variational principle of the analytic mechanics can be applied and the numerical results can be more conveniently got by efficient means of the interbelt finite element method, the canonical transformation and the symplectic conservation integration. 2 numerical examples show the correctness and potential of the proposed method.
•  [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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