Sediment transport modelling : Relaxation schemes for Saint-Venant – Exner and three layer models

In this note we are interested in the modelling of sediment transport phenomena. We mostly focus on bedload transport and we do not consider suspension sediment processes. We first propose a numerical scheme for the classical Saint-Venant – Exner model. It is based on a relaxation approach for the whole system and it works with all sediment flux function. The stability of the scheme is investigated and some numerical tests are proposed. We exhibit that this coupled approach is more stable than the splitting approach that is mostly used in industrial softwares. Then we derive an original three layers model in order to overcome the difficulties that are encountered when using the classical Exner approach and we present a related relaxation model.