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Journal of Computational Mathematics

Numerical simulations of hydraulic jumps with the Shear Shallow Water model
Argiris I. Delis1; Hervé Guillard2; Yih-Chin Tai3
1 School of Production Engineering and Management, Technical University of Crete, University Campus, Chania, Crete, Greece
2 Inria Sophia Antipolis Méditerranée and Côte d’Azur University, LJAD, CNRS, France
3 Departement of Hydraulic and Ocean Engineering, National Cheng Kung University, Tainan 701, Taiwan
The SMAI Journal of computational mathematics, Volume 4 (2018), pp. 319-344.

An extension and numerical approximation of the shear shallow water equations model, recently proposed in [25], is considered in this work. The model equations are able to describe the oscillatory nature of turbulent hydraulic jumps and as such correct the deficiency of the classical non-linear shallow water equations in describing such phenomena. The model equations, originally developed for horizontal flow or flows occurring over small constant slopes, are straightforwardly extended here for modeling flows over non-constant slopes and numerically solved by a second-order well-balanced finite volume scheme. Further, a new set of exact solutions to the extended model equations is derived and several numerical tests are performed to validate the numerical scheme and its ability to predict the oscillatory nature of hydraulic jumps under different flow conditions.

Published online:
DOI: 10.5802/smai-jcm.37
Keywords: Shear Shallow Water model, Shallow Water equations, Turbulent Hydraulic jumps, Free surface flows, Finite Volumes, Well-balancing
Argiris I. Delis 1; Hervé Guillard 2; Yih-Chin Tai 3

1 School of Production Engineering and Management, Technical University of Crete, University Campus, Chania, Crete, Greece
2 Inria Sophia Antipolis Méditerranée and Côte d’Azur University, LJAD, CNRS, France
3 Departement of Hydraulic and Ocean Engineering, National Cheng Kung University, Tainan 701, Taiwan
License: CC-BY-NC-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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     title = {Numerical simulations of hydraulic jumps with the {Shear} {Shallow} {Water} model},
     journal = {The SMAI Journal of computational mathematics},
     pages = {319--344},
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Argiris I. Delis; Hervé Guillard; Yih-Chin Tai. Numerical simulations of hydraulic jumps with the Shear Shallow Water model. The SMAI Journal of computational mathematics, Volume 4 (2018), pp. 319-344. doi : 10.5802/smai-jcm.37. https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.37/

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