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Multisymplectic formulation of fluid dynamics using the inverse map

Cotter, C J, Holm, D D and Hydon, Peter E (2007) Multisymplectic formulation of fluid dynamics using the inverse map Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 463 (2086). pp. 2671-2687.


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We construct multisymplectic formulations of fluid dynamics using the inverse of the Lagrangian path map. This inverse map, the ‘back-to-labels’ map, gives the initial Lagrangian label of the fluid particle that currently occupies each Eulerian position. Explicitly enforcing the condition that the fluid particles carry their labels with the flow in Hamilton's principle leads to our multisymplectic formulation. We use the multisymplectic one-form to obtain conservation laws for energy, momentum and an infinite set of conservation laws arising from the particle relabelling symmetry and leading to Kelvin's circulation theorem. We discuss how multisymplectic numerical integrators naturally arise in this approach.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Cotter, C J
Holm, D D
Hydon, Peter
Date : 30 July 2007
DOI : 10.1098/rspa.2007.1892
Additional Information : This is the authors' preprint of an article published in its final form in Proc. Roy. Soc. Lond. A 463: 2671-2687
Depositing User : Mr Adam Field
Date Deposited : 27 May 2010 14:41
Last Modified : 06 Jul 2019 05:07

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