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.

Keywords: Shear Shallow Water model, Shallow Water equations, Turbulent Hydraulic jumps, Free surface flows, Finite Volumes, Well-balancing

@article{SMAI-JCM_2018__4__319_0, author = {Argiris I. Delis and Herv\'e Guillard and Yih-Chin Tai}, title = {Numerical simulations of hydraulic jumps with the Shear Shallow Water model}, journal = {The SMAI journal of computational mathematics}, publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles}, volume = {4}, year = {2018}, pages = {319-344}, doi = {10.5802/smai-jcm.37}, language = {en}, url={smai-jcm.centre-mersenne.org/item/SMAI-JCM_2018__4__319_0/} }

Delis, Argiris I.; Guillard, Hervé; Tai, Yih-Chin. 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/item/SMAI-JCM_2018__4__319_0/

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