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

doi:10.1007/s10483-016-2051-9

Applied Mathematics and Mechanics (English Edition) ›› 2016, Vol. 37 ›› Issue (1): 1-14.doi: https://doi.org/10.1007/s10483-016-2051-9

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

Feng WU, Wanxie ZHONG

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

Received:2015-10-06 Revised:2015-11-02 Online:2016-01-01 Published:2016-01-01
Contact: Wanxie ZHONG E-mail:zwx34224@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (No. 11472067)

Abstract

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.

Key words: Zu-class method, constrained Hamilton variational principle, shallow water equation (SWE)

2010 MSC Number:

76B15

Feng WU, Wanxie ZHONG. Constrained Hamilton variational principle for shallow water problems and Zu-class symplectic algorithm. Applied Mathematics and Mechanics (English Edition), 2016, 37(1): 1-14.

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

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