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

Abstract

Abstract. 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.

Numerical simulation of the dynamics of sedimentary river beds with a stochastic Exner equation

“…We now describe how we numerically solve the Saint-Venant-Exner system (6). Let us first mention some of the recent works [4,10,24] devoted to the derivation of finite volume methods to handle system (6) at once. Here we do not adopt this strategy and apply a splitting method on a staggered grid in a finite volume -finite difference spirit.…”

Hydrostatic relaxation scheme for the 1D shallow water - Exner equations in bedload transport

“…The idea of this method is follow the paper of Audusse et al (2004) and the book of Bouchut (2004). 45 We apply the local hydrostatic reconstruction to determine a well-balanced scheme from the numerical flux of Audusse et al (2012). According Audusse et al (2004), the hydrostatic reconstruction method is designed to be applied…”

“…Hence, by a relaxation approach of the coupled system of shallow waterExner equations in Audusse et al (2012), the numerical flux F is defined as…”

“…Moreover, the numerical results still need to be verified and validated using analytical solution or data experiment to see the applicability of the scheme. Some models and numerical approaches for sediment transport have been 15 demonstrated Wu & Wang (2007); Capart & Young (1998) ;Simpson & Castelltort (2006); Cao et al (2004); Cordier et al (2011); Audusse et al (2012). Some of them are quite complex because they consider physical characteristics of sediment in detail.…”

“…In addition, their models include some type of sediment such as bedload and suspended load. For example, one 20 of the simple model is called shallow water-Exner equations to study the bedload sediment transport and is introduced in Cordier et al (2011), and Audusse et al (2012).…”