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Adaptation of f-wave finite volume methods to the two-layer shallow-water equations in a moving vessel with a rigid-lid

Ardakani, HA, Bridges, TJ and Turner, MR (2015) Adaptation of f-wave finite volume methods to the two-layer shallow-water equations in a moving vessel with a rigid-lid Journal of Computational and Applied Mathematics, 296. pp. 462-479.

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Abstract

A numerical method is proposed to solve the two-layer inviscid, incompressible and immiscible 1D shallow-water equations in a moving vessel with a rigid-lid with different boundary conditions based on the high-resolution f-wave finite volume methods due to Bale et al. (2002). The method splits the jump in the fluxes and source terms including the pressure gradient at the rigid-lid into waves propagating away from each grid cell interface. For the influx–efflux boundary conditions the time dependent source terms are handled via a fractional step approach. In the linear case the numerical solutions are validated by comparison with the exact analytical solutions. Numerical solutions presented for the nonlinear case include shallow-water sloshing waves due to prescribed surge motion of the vessel.

Item Type: Article
Subjects : Mathematics
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
NameEmailORCID
Ardakani, HA
Bridges, TJT.Bridges@surrey.ac.uk
Turner, MRM.Turner@surrey.ac.uk
Date : 26 October 2015
Funders : Engineering and Physical Sciences Research Council (EPSRC)
DOI : 10.1016/j.cam.2015.09.026
Copyright Disclaimer : © 2016. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Uncontrolled Keywords : Two-layer shallow-water equations; Finite volume methods; Wave propagation; Sloshing
Depositing User : Symplectic Elements
Date Deposited : 24 Mar 2016 12:48
Last Modified : 13 Mar 2019 09:45
URI: http://epubs.surrey.ac.uk/id/eprint/810244

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