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Constrained Hamilton variational principle for shallow water problems and Zu-class symplectic algorithm

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Abstract

In this paper, the shallow water problem is discussed. By treating the incompressible condition as the constraint, a constrained Hamilton variational principle is presented for the shallow water problem. Based on the constrained Hamilton variational principle, a shallow water equation based on displacement and pressure (SWE-DP) is developed. A hybrid numerical method combining the finite element method for spatial discretization and the Zu-class method for time integration is created for the SWEDP. The correctness of the proposed SWE-DP is verified by numerical comparisons with two existing shallow water equations (SWEs). The effectiveness of the hybrid numerical method proposed for the SWE-DP is also verified by numerical experiments. Moreover, the numerical experiments demonstrate that the Zu-class method shows excellent performance with respect to simulating the long time evolution of the shallow water.

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Authors and Affiliations

  1. State Key Laboratory of Structural Analysis of Industrial Equipment, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, Dalian, 116023, Liaoning Province, China

    Feng Wu & Wanxie Zhong

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  1. Feng Wu
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  2. Wanxie Zhong
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Correspondence to Wanxie Zhong.

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Project supported by the National Natural Science Foundation of China (No. 11472067)

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Wu, F., Zhong, W. Constrained Hamilton variational principle for shallow water problems and Zu-class symplectic algorithm. Appl. Math. Mech.-Engl. Ed. 37, 1–14 (2016). https://doi.org/10.1007/s10483-016-2051-9

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  • DOI: https://doi.org/10.1007/s10483-016-2051-9

Keywords

Chinese Library Classification

2010 Mathematics Subject Classification

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