Geodesic
Numerical simulation of the dynamics of sedimentary river beds with a stochastic Exner equation
Emmanuel Audusse1, 2 ; Sébastien Boyaval3, 4 ; Nicole Goutal3, 5 ; Magali Jodeau5 ; Philippe Ung1, 6
1 Team ANGE, INRIA-Paris-Rocquencourt
2 LAGA, Université Paris XIII, France
3 Université Paris Est, Laboratoire d’Hydraulique Saint-Venant (Ecole des Ponts ParisTech – EDF R&D – CEREMA)
4 INRIA Rocquencourt, France
5 LNHE, EDF R&D
6 MAPMO, Université d’Orléans, France,
ESAIM. Proceedings, Tome 48 (2015), pp. 321-340.

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At the scale of a river reach, the dynamics of the river bed is typically modelled by Exner equation (conservation of the solid mass) with an empirical solid flux of transported sediments, which is a simple deterministic algebraic formula function of i) the sediment physical characteristics (size and mass) and of ii) the averaged hydrodynamical description of the ambient water flow. This model has proved useful, in particular through numerical simulations, for hydraulic engineering purposes (like estimating the mass of sediments that is drained through an open dam). Though, the model is also coarse. And its applicability at various space and time scales remains a question of considerable interest for sedimentologists. In particular, physical experiments from the grain scale to the laboratory scale reveal important fluctuations of the solid flux in given hydrodynamical conditions. This work is a preliminary study of the coupling of a stochastic Exner equation with a hydrodynamical model for large scales. (Stochastic models with a probabilistic solid flux are currently being investigated, but most often only from the viewpoint of theoretical physics at the grain scale.) We introduce a new stochastic Exner model and discuss it using numerical simulations in an appropriate test case.
DOI : 10.1051/proc/201448015

Emmanuel Audusse 1, 2 ; Sébastien Boyaval 3, 4 ; Nicole Goutal 3, 5 ; Magali Jodeau 5 ; Philippe Ung 1, 6

1 Team ANGE, INRIA-Paris-Rocquencourt
2 LAGA, Université Paris XIII, France
3 Université Paris Est, Laboratoire d’Hydraulique Saint-Venant (Ecole des Ponts ParisTech – EDF R&D – CEREMA)
4 INRIA Rocquencourt, France
5 LNHE, EDF R&D
6 MAPMO, Université d’Orléans, France, 
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     author = {Emmanuel Audusse and S\'ebastien Boyaval and Nicole Goutal and Magali Jodeau and Philippe Ung},
     title = {Numerical simulation of the dynamics of sedimentary river beds with a stochastic {Exner} equation},
     journal = {ESAIM. Proceedings},
     pages = {321--340},
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Emmanuel Audusse; Sébastien Boyaval; Nicole Goutal; Magali Jodeau; Philippe Ung. Numerical simulation of the dynamics of sedimentary river beds with a stochastic Exner equation. ESAIM. Proceedings, Tome 48 (2015), pp. 321-340. doi : 10.1051/proc/201448015. http://geodesic.mathdoc.fr/articles/10.1051/proc/201448015/

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