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

Turner, Matthew, Bridges, Thomas and Alemi Ardakani, H (2017) Lagrangian particle path formulation of multilayer shallow-water flows dynamically coupled to vessel motion Journal of Engineering Mathematics, 106 (1). pp. 75-106.

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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 :
Alemi Ardakani, H
Date : 23 January 2017
Funders : Engineering and Physical Sciences Research Council (EPSRC)
DOI : 10.1007/s10665-016-9893-3
Copyright Disclaimer : © The Author(s) 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Uncontrolled Keywords : Dynamic; Lagrangian particle path; Multilayer; Sloshing; Two-layer
Related URLs :
Depositing User : Symplectic Elements
Date Deposited : 05 Dec 2016 12:44
Last Modified : 11 Dec 2018 11:22

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