Volume 55, Number 4, July-August 2021
|Page(s)||1635 - 1668|
|Published online||02 August 2021|
Asymptotic derivation and simulations of a non-local Exner model in large viscosity regime
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: firstname.lastname@example.org
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.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.