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Lagrangian particle path formulation of multilayer shallow-water flows dynamically coupled to vessel motion

Turner, MR, Bridges, TJ and Alemi Ardakani, H (2016) Lagrangian particle path formulation of multilayer shallow-water flows dynamically coupled to vessel motion Journal of Engineering Mathematics.

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Abstract

The coupled motion, between multiple inviscid, incompressible, immiscible fluid layers in a rectangular vessel with a rigid lid and the vessel dynamics, is considered. The fluid layers are assumed to be thin and the shallow-water assumption is applied. The governing form of the Lagrangian functional in the Lagrangian Particle Path (LPP) framework is derived for an arbitrary number of layers, while the corresponding Hamiltonian is explicitly derived in the case of two- and three-layer fluids. The Hamiltonian formulation has nice properties for numerical simulations, and a fast, effective and symplectic numerical scheme is presented in the two- and three-layer cases, based upon the implicit-midpoint rule. Results of the simulations are compared with linear solutions and with the existing results of Alemi Ardakani, Bridges & Turner [1] (J. Fluid Struct. 59 432-460) which were obtained using a finite volume approach in the Eulerian representation. The latter results are extended to non-Boussinesq regimes. The advantages and limitations of the LPP formulation and variational discretization are highlighted.

Item Type: Article
Subjects : Mathematics
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
AuthorsEmailORCID
Turner, MRUNSPECIFIEDUNSPECIFIED
Bridges, TJUNSPECIFIEDUNSPECIFIED
Alemi Ardakani, HUNSPECIFIEDUNSPECIFIED
Date : 2016
Copyright Disclaimer : The final publication will be available at Springer via http://link.springer.com/journal/10665
Related URLs :
Depositing User : Symplectic Elements
Date Deposited : 05 Dec 2016 12:44
Last Modified : 05 Dec 2016 12:44
URI: http://epubs.surrey.ac.uk/id/eprint/813037

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