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A variational free‐Lagrange method for shallow water
Author(s) -
Dixon Matthew F.,
Ringler Todd
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200701087
Subject(s) - lagrange multiplier , action (physics) , property (philosophy) , variational principle , mathematics , extension (predicate logic) , principle of least action , exploit , free energy principle , waves and shallow water , energy (signal processing) , conservation of energy , computer science , mathematical optimization , mathematical analysis , classical mechanics , physics , philosophy , statistics , computer security , epistemology , quantum mechanics , thermodynamics , programming language
This article presents a variational free‐Lagrange (VFL) method for rotating shallow water. This method was first derived by Augenbaum [2] who discretised Hamilton's action principle with a free‐Lagrange data structure. The novel feature of our approach is to exploit the geometric structure preserved by the VFL method to the effect of conserving energy over long‐time simulations. Numerical results demonstrate this property and motivate the extension of this approach to other variational formulations of climate models. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)