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Two-dimensional sediment transport models in shallow water equations. A second order finite volume approach on unstructured meshes. (English) Zbl 1228.76091
Summary: In this paper, we study the numerical approximation of bedload sediment transport due to shallow layer flows. The hydrodynamical component is modeled by a 2D shallow water system and the morphodynamical component by a solid transport discharge formula that depends on the hydrodynamical variables. The coupled system can be written as a nonconservative hyperbolic system. To discretize it, first we consider a Roe-type first order scheme as well as a variant based on the use of flux limiters. These first order schemes are then extended to second order accuracy by means of a new MUSCL-type reconstruction operator on unstructured meshes. Finally, some numerical tests are presented.

MSC:
76M12 Finite volume methods applied to problems in fluid mechanics
76T20 Suspensions
76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing
76A05 Non-Newtonian fluids
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