Volume 27, Issue 5
Simulation of Three-Dimensional Free-SurfaceFlows Using Two-Dimensional Multilayer Shallow Water Equations

Saida Sari, Thomas Rowan, Mohammed Seaid & Fayssal Benkhaldoun

Commun. Comput. Phys., 27 (2020), pp. 1413-1442.

Published online: 2020-03

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  • 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.

  • Keywords

Multilayer shallow water equations, incompressible hydrostatic flows, EulerianLagrangian scheme, finite volume solver, projection method.

  • AMS Subject Headings

65M08, 35L53, 76B15, 74J40, 76B07

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

sari@math.univ-paris13.fr (Saida Sari)

thomas.rowan@durham.ac.uk (Thomas Rowan)

m.seaid@durham.ac.uk (Mohammed Seaid)

fayssal@math.univ-paris13.fr (Fayssal Benkhaldoun)

  • BibTex
  • RIS
  • TXT
@Article{CiCP-27-1413, author = {Sari , Saida and Rowan , Thomas and Seaid , Mohammed and Benkhaldoun , Fayssal }, title = {Simulation of Three-Dimensional Free-SurfaceFlows Using Two-Dimensional Multilayer Shallow Water Equations}, journal = {Communications in Computational Physics}, year = {2020}, volume = {27}, number = {5}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2019-0036}, url = {http://global-sci.org/intro/article_detail/cicp/15775.html} }
TY - JOUR T1 - Simulation of Three-Dimensional Free-SurfaceFlows Using Two-Dimensional Multilayer Shallow Water Equations AU - Sari , Saida AU - Rowan , Thomas AU - Seaid , Mohammed AU - Benkhaldoun , Fayssal JO - Communications in Computational Physics VL - 5 SP - 1413 EP - 1442 PY - 2020 DA - 2020/03 SN - 27 DO - http://dor.org/10.4208/cicp.OA-2019-0036 UR - https://global-sci.org/intro/cicp/15775.html KW - Multilayer shallow water equations, incompressible hydrostatic flows, EulerianLagrangian scheme, finite volume solver, projection method. AB -

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.

Saida Sari, Thomas Rowan, Mohammed Seaid & Fayssal Benkhaldoun. (2020). Simulation of Three-Dimensional Free-SurfaceFlows Using Two-Dimensional Multilayer Shallow Water Equations. Communications in Computational Physics. 27 (5). 1413-1442. doi:10.4208/cicp.OA-2019-0036
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