| Issue |
ESAIM: M2AN
Volume 55, Number 4, July-August 2021
|
|
|---|---|---|
| Page(s) | 1635 - 1668 | |
| DOI | https://doi.org/10.1051/m2an/2021031 | |
| Published online | 02 August 2021 | |
Asymptotic derivation and simulations of a non-local Exner model in large viscosity regime
1
Université Paris 13, Laboratoire d’Analyse, Géométrie et Applications, 99 av. J.-B. Clément, F-93430 Villetaneuse, France.
2
Inria, ANGE team, 2 rue Simone Iff, F-75012 Paris, France.
3
CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, Paris, France.
4
Sorbonne Université, UPMC Univ. Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, Paris, France.
* Corresponding author: martin.parisot@inria.fr
Received:
12
November
2020
Accepted:
30
June
2021
The present paper deals with the modeling and numerical approximation of bed load transport under the action of water. A new shallow water type model is derived from the stratified two-fluid Navier–Stokes equations. Its novelty lies in the magnitude of a viscosity term that leads to a momentum equation of elliptic type. The full model, sediment and water, verifies a dissipative energy balance for smooth solutions. The numerical resolution of the sediment layer is not trivial since the viscosity introduces a non-local term in the model. Adding a transport threshold makes the resolution even more challenging. A scheme based on a staggered discretization is proposed for the full model, sediment and water.
Mathematics Subject Classification: 35L65 / 65C20 / 86A05
Key words: Free surface flow / shallow water equations / sediment transport / entropy dissipation / non-local effects
© The authors. Published by EDP Sciences, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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