Simulation of Three-Dimensional Free-Surface Flows Using Two-Dimensional Multilayer Shallow Water Equations
Year: 2020
Author: Saida Sari, Thomas Rowan, Mohammed Seaid, Fayssal Benkhaldoun
Communications in Computational Physics, Vol. 27 (2020), Iss. 5 : pp. 1413–1442
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
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2019-0036
Communications in Computational Physics, Vol. 27 (2020), Iss. 5 : pp. 1413–1442
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 30
Keywords: Multilayer shallow water equations incompressible hydrostatic flows Eulerian-Lagrangian scheme finite volume solver projection method.