2016
DOI: 10.1016/j.cam.2016.02.053
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Explicit, parallel Poisson integration of point vortices on the sphere

Abstract: Point vortex models are frequently encountered in conceptual studies in geophysical fluid dynamics, but also in practical applications, for instance, in aeronautics. In spherical geometry, the motion of vortex centres is governed by a dynamical system with a known Poisson structure. We construct Poisson integration methods for these dynamics by splitting the Hamiltonian into its constituent vortex pair terms. From backward error analysis, the method is formally known to provide solutions to a modified Poisson … Show more

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Cited by 4 publications
(6 citation statements)
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“…Point vortices have been studied extensively in [ 41 43 ]. We work on a spherical domain [ 44 48 ], viewing the vortex position as a vector in R 3 with unit norm. The equations of motion have a Lie–Poisson structure 1 2 where the Hamiltonian is given by 2 2 and each Γ i represents the circulation of a single point vortex.…”
Section: Application To Reduced Modelling Of Point Vorticesmentioning
confidence: 99%
See 4 more Smart Citations
“…Point vortices have been studied extensively in [ 41 43 ]. We work on a spherical domain [ 44 48 ], viewing the vortex position as a vector in R 3 with unit norm. The equations of motion have a Lie–Poisson structure 1 2 where the Hamiltonian is given by 2 2 and each Γ i represents the circulation of a single point vortex.…”
Section: Application To Reduced Modelling Of Point Vorticesmentioning
confidence: 99%
“…A numerical integrator for the point vortex system is constructed as in Myerscough & Frank [ 48 ] based on splitting the differential equations into integrable subproblems (see related ideas in [ 53 , 54 ]). The backward error analysis of symplectic integrators has an analogous development for Poisson systems, implying approximate conservation of the Hamiltonian [ 8 ].…”
Section: Application To Reduced Modelling Of Point Vorticesmentioning
confidence: 99%
See 3 more Smart Citations