A second-order well-balanced Lagrange-projection scheme for Shallow Water Exner equations in 1D and 2D
Résumé
The present work is devoted to the numerical approximation of the Shallow water Exner system in both one and two dimensions, where the Exner equation expresses the evolution in time of the bed sediment. In particular the Grass formula is taken into account to model the solid transport discharge contributions. The numerical scheme is based on the Lagrange-projection formalism which consists in splitting the mathematical model into the acoustic and transport system. In particular, the Exner equation is taken into account only at the transport level; both a decoupled and weakly coupled formulation are proposed. The method is designed in such a way to satisfy the well-balanced property as well. Details to reach the second-order of accuracy are given; numerical results are shown to validate the numerical schemes.
Domaines
Mathématiques [math]
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