An analytical solution of Shallow Water system coupled to Exner equation

Creators: Berthon, Christophe; Cordier, Stéphane; Le, Minh; Delestre, Olivier

Others:: Laboratoire de Mathématiques Jean Leray (LMJL) ; Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST) ; Université de Nantes (UN)-Université de Nantes (UN)-Centre National de la Recherche Scientifique (CNRS); Mathématiques - Analyse, Probabilités, Modélisation - Orléans (MAPMO) ; Université d'Orléans (UO)-Centre National de la Recherche Scientifique (CNRS); Bureau de Recherches Géologiques et Minières (BRGM) (BRGM); Laboratoire Jean Alexandre Dieudonné (JAD) ; Université Nice Sophia Antipolis (1965 - 2019) (UNS) ; COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS); Institut Jean le Rond d'Alembert (DALEMBERT) ; Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)

Description

In this paper, an exact smooth solution for the equations modeling the bedload transport of sediment in Shallow Water is presented. This solution is valid for a large family of sedimentation laws which are widely used in erosion modeling such as the Grass model or those of Meyer-Peter & Muller. One of the main interest of this solution is the derivation of numerical benchmarks to valid the approximation methods.

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An analytical solution of Shallow Water system coupled to Exner equation

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