k-e RANS model for the numerical simulation

of turbulent shallow water flows


R. Abdellaoui1*, I. Elmahi1

1 Equipe EMSN, ENSAO, Complexe Universitaire, B.P. 669, 60000 Oujda, Maroc.

* Corresponding author. E-mail:  r.abdellaoui@gmail.com

Received: 01 June  2014; revised version accepted: 26 October 2014



     In this work, a Reynolds Averaged Navier-Stokes (RANS) model is adopted in a finite volume method for the numerical computation of turbulent shallow water flows on unstructured meshes. The governing equations are those of 2D Saint-Venant, they include the slope variations, the friction terms and the eddy viscosity. The effects of turbulence are incorporated in the system by considering the k-e model. The convective fluxes are approximated using a modified Roe scheme that incorporates in its reconstruction the sign of the Jacobian matrix of the system. The diffusion terms are discretized using a Green-Gauss type reconstruction. The performance of the solver is illustrated over two test cases: the mixing layer problem in shallow water flows and the flow in an open channel with a bend of 90°.


Keywords: Saint-Venant equations; Turbulence; RANS Model; Finite volumes; Unstructured meshes; Mixing layer; Open channel with a bend of 90°.



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