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Simulation of Three-Dimensional Free-SurfaceFlows Using Two-Dimensional Multilayer Shallow Water Equations

Sari, Saida; Rowan, Thomas; Seaid, Mohammed; Benkhaldoun, Fayssal

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Authors

Saida Sari

Thomas Rowan

Fayssal Benkhaldoun



Abstract

We present an efficient and conservative Eulerian-Lagrangian method for solving two-dimensional hydrostatic multilayer shallow water flows with mass exchange between the vertical layers. The method consists of a projection finite volume method for the Eulerian stage and a method of characteristics to approximate the numerical fluxes for the Lagrangian stage. The proposed method is simple to implement, satisfies the conservation property and it can be used for multilayer shallow water equations on non-flat bathymetry including eddy viscosity and Coriolis forces. It offers a novel method of calculating stratified vertical velocities without the use of the Navier-Stokes equations. Numerical results are presented for several examples and the obtained results for a free-surface flow problem are in close agreement with the analytical solutions. We also test the performance of the proposed method for a test example of wind-driven flows with recirculation

Citation

Sari, S., Rowan, T., Seaid, M., & Benkhaldoun, F. (2020). Simulation of Three-Dimensional Free-SurfaceFlows Using Two-Dimensional Multilayer Shallow Water Equations. Communications in computational physics, 27(5), 1413-1442. https://doi.org/10.4208/cicp.oa-2019-0036

Journal Article Type Article
Acceptance Date May 15, 2019
Online Publication Date Mar 31, 2020
Publication Date 2020
Deposit Date Oct 26, 2021
Publicly Available Date Nov 13, 2024
Journal Communications in computational physics.
Print ISSN 1815-2406
Electronic ISSN 1991-7120
Publisher Global Science Press
Peer Reviewed Peer Reviewed
Volume 27
Issue 5
Pages 1413-1442
DOI https://doi.org/10.4208/cicp.oa-2019-0036
Public URL https://durham-repository.worktribe.com/output/1230108

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