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 ...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.展开更多
Singular system has great relationship with gauge field theory,condensed matter theory and some other research areas.Based on the mixed integer and Riemann-Liouville fractional derivatives,the fractional singular syst...Singular system has great relationship with gauge field theory,condensed matter theory and some other research areas.Based on the mixed integer and Riemann-Liouville fractional derivatives,the fractional singular system is studied.Firstly,the fractional constrained Hamilton equation and the fractional inherent constraint are presented.Secondly,Lie symmetry and conserved quantity are analyzed,including determined equation,limited equation,additional limited equation and structural equation.And finally,an example is given to illustrate the methods and results.展开更多
Noether theorems for two fractional singular systems are discussed.One system involves mixed integer and Caputo fractional derivatives,and the other involves only Caputo fractional derivatives.Firstly,the fractional p...Noether theorems for two fractional singular systems are discussed.One system involves mixed integer and Caputo fractional derivatives,and the other involves only Caputo fractional derivatives.Firstly,the fractional primary constraints and the fractional constrained Hamilton equations are given.Then,the fractional Noether theorems of the two fractional singular systems are established,including the fractional Noether identities,the fractional Noether quasi-identities and the fractional conserved quantities.Finally,the results obtained are illustrated by two examples.展开更多
基金Project supported by the National Natural Science Foundation of China(No.11472067)
文摘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.
基金the National Natural Science Foundation of China(12172241,11802193,11972241)the Natural Science Foundation of Jiangsu Province(BK20191454)the"Qinglan Project"of Jiangsu Province。
文摘Singular system has great relationship with gauge field theory,condensed matter theory and some other research areas.Based on the mixed integer and Riemann-Liouville fractional derivatives,the fractional singular system is studied.Firstly,the fractional constrained Hamilton equation and the fractional inherent constraint are presented.Secondly,Lie symmetry and conserved quantity are analyzed,including determined equation,limited equation,additional limited equation and structural equation.And finally,an example is given to illustrate the methods and results.
基金Supported by the National Natural Science Foundation of China(12172241,12002228,12272248,11972241)Qing Lan Project of Colleges and Universities in Jiangsu Province
文摘Noether theorems for two fractional singular systems are discussed.One system involves mixed integer and Caputo fractional derivatives,and the other involves only Caputo fractional derivatives.Firstly,the fractional primary constraints and the fractional constrained Hamilton equations are given.Then,the fractional Noether theorems of the two fractional singular systems are established,including the fractional Noether identities,the fractional Noether quasi-identities and the fractional conserved quantities.Finally,the results obtained are illustrated by two examples.
