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A HLLC Riemann solver to compute shallow water equations with topography and friction

Abdou Wahidi Bello, Aurélien Goudjo, Hervé Guillard, Jean‐Antoine Désidéri

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Abstract

We consider the resolution, by a finite-volume method, of the two-dimensional model of the shallow water equations with topography and friction. Thanks to the property of invariance per rotation of the flux of shallow water equations, we show that the study of the 2D case rises from the good resolution of the monodimensional system of the shallow water equations. The numerical implementation is carried out by a finite volume scheme of Godunov type using an Riemann approximate solver of the type HLLC which preserves the positivity height of water and which is well adapted for the treatment of the shock waves. Lastly, numercal examples on academic problems are presented as well as a real case : application of the model to the phenomenon of flood of the town of Cotonou (BENIN) by the risings of the lagoon of Cotonou.

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We consider the resolution, by a finite-volume method, of the two-dimensional model of the shallow water equations with topography and friction. Thanks to the property of invariance per rotation of the flux of shallow water equations, we show that the study of the 2D case rises from the good resolution of the monodimensional system of the shallow water equations. The numerical implementation is carried out by a finite volume scheme of Godunov type using an Riemann approximate solver of the type HLLC which preserves the positivity height of water and which is well adapted for the treatment of the shock waves. Lastly, numercal examples on academic problems are presented as well as a real case : application of the model to the phenomenon of flood of the town of Cotonou (BENIN) by the risings of the lagoon of Cotonou.

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Available abstract

We consider the resolution, by a finite-volume method, of the two-dimensional model of the shallow water equations with topography and friction. Thanks to the property of invariance per rotation of the flux of shallow water equations, we show that the study of the 2D case rises from the good resolution of the monodimensional system of the shallow water equations. The numerical implementation is carried out by a finite volume scheme of Godunov type using an Riemann approximate solver of the type HLLC which preserves the positivity height of water and which is well adapted for the treatment of the shock waves. Lastly, numercal examples on academic problems are presented as well as a real case : application of the model to the phenomenon of flood of the town of Cotonou (BENIN) by the risings of the lagoon of Cotonou.

Key concepts: Riemann solver, Shallow water equations, Finite volume method, Riemann problem, Roe solver, Waves and shallow water, Godunov's scheme, Mathematics

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