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

Emmanuel Audusse 1, 2, Christophe Chalons 3, 4, Olivier Delestre 5, 6, Nicole Goutal 7, Magali Jodeau 7, Jacques Sainte-Marie 8, 9, Jan Giesselmann 10, Georges Sadaka 11

(2012-01-20)

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 coupled numerical scheme for the classical Saint-Venant -- Exner model. It is based on a relaxation approach and it works with all sediment flux function. 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 write a related relaxation model.

1:	Laboratoire Analyse, Géométrie et Application (LAGA)
	CNRS : UMR7539 – Université Paris XIII - Paris Nord – Université Paris VIII - Vincennes Saint-Denis
2:	BANG (INRIA Rocquencourt)
	INRIA – Laboratoire Jacques-Louis Lions
3:	Laboratoire d'Énergétique Moléculaire et Macroscopique, Combustion (EM2C)
	CNRS : UPR288 – Ecole Centrale Paris
4:	Laboratoire Jacques-Louis Lions (LJLL)
	CNRS : UMR7598 – Université Pierre et Marie Curie [UPMC] - Paris VI
5:	Mathématiques - Analyse, Probabilités, Modélisation - Orléans (MAPMO)
	Université d'Orléans – CNRS : UMR7349
6:	Laboratoire Jean Alexandre Dieudonné (JAD)
	CNRS : UMR6621 – Université Nice Sophia Antipolis [UNS]
7:	Laboratoire d'Hydraulique Saint-Venant / Saint-Venant Laboratory for Hydraulics (Saint-Venant)
	Université Paris-Est Créteil Val-de-Marne (UPEC) – Ecole des Ponts ParisTech – EDF – CETMEF
8:	MACS (INRIA Rocquencourt)
	INRIA
9:	Centre d'Études Techniques Maritimes et Fluviales (CETMEF)
	CETMEF
10:	Department of Mathematics [Stuttgart]
	University of Stuttgart
11:	Laboratoire Amiénois de Mathématique Fondamentale et Appliquée (LAMFA)
	CNRS : UMR6140 – Université de Picardie Jules Verne

Subject

:

Mathematics/Numerical Analysis

Keyword(s): Sediment transport modelling – shallow water flows – Exner equation – relaxation schemes

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From: Emmanuel Audusse <>

Submitted on: Monday, 27 February 2012 11:14:30

Updated on: Thursday, 8 March 2012 15:33:49