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

作　　者：Feng WU Wanxie ZHONG 

机构地区：[1]State Key Laboratory of Structural Analysis of Industrial Equipment, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology

出　　处：《Applied Mathematics and Mechanics(English Edition)》2016年第1期1-14,共14页应用数学和力学（英文版）

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

摘　　要：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 spa- tial discretization and the Zu-class method for time integration is created for the SWE- DP. 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 perfor- mance with respect to simulating the long time evolution of the shallow water.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 spa- tial discretization and the Zu-class method for time integration is created for the SWE- DP. 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 perfor- mance with respect to simulating the long time evolution of the shallow water.

关 键 词：shallow water equation （SWE） constrained Hamilton variational principle Zu-class method 

分 类 号：O352[理学—流体力学]