In this paPer the author studies Buttke’s velicity reformulation of the incompressible Euler equation, and the symPlectic integration of the Hamiltonian system obtained by discretizing the vehicity equation.The autho...In this paPer the author studies Buttke’s velicity reformulation of the incompressible Euler equation, and the symPlectic integration of the Hamiltonian system obtained by discretizing the vehicity equation.The author shows that he linearized velicity equation is hyperbolic only in the weak sense and she analyzes the characteristics of the linea-rized velicity equation for the variable coefficient case. The author will briefiy describe the symplectic schemes: one is the imPlicit midpoint scheme, and tanother a fourthorder implicit scheme. Also, the author shows a computational result obtained by redistributing the Lagrangian points at flxed times.展开更多
In this paper the author applies the implicit midpoint scheme (IM) to her Hamiltonian system for large time, with the fixed time step (t) to be 0.1. Two velicitieswhose initial data diner by a gradient yield the same ...In this paper the author applies the implicit midpoint scheme (IM) to her Hamiltonian system for large time, with the fixed time step (t) to be 0.1. Two velicitieswhose initial data diner by a gradient yield the same velocity field for all time: the author has verified this in a numerical experiment using the IM scheme, up to t = 2.展开更多
基金NSFC(No.10901074)Natural Science Foundation of Jiangxi Province(No.2008GQS0054)+3 种基金Foundation of Department of Education Jiangxi Province(No.GJJ09147)Young Growth Foundation of Jiangxi Normal University(No.3182)Innovation Foundation in 2010 for Graduate Students(No.YJS2010009)Natural Science Foundation of Anhui Province(No.090416227)
文摘In this paPer the author studies Buttke’s velicity reformulation of the incompressible Euler equation, and the symPlectic integration of the Hamiltonian system obtained by discretizing the vehicity equation.The author shows that he linearized velicity equation is hyperbolic only in the weak sense and she analyzes the characteristics of the linea-rized velicity equation for the variable coefficient case. The author will briefiy describe the symplectic schemes: one is the imPlicit midpoint scheme, and tanother a fourthorder implicit scheme. Also, the author shows a computational result obtained by redistributing the Lagrangian points at flxed times.
文摘In this paper the author applies the implicit midpoint scheme (IM) to her Hamiltonian system for large time, with the fixed time step (t) to be 0.1. Two velicitieswhose initial data diner by a gradient yield the same velocity field for all time: the author has verified this in a numerical experiment using the IM scheme, up to t = 2.
