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.
Keywords: Free surface flow, shallow water equations, sediment transport, entropy dissipation, non-local effects
@article{M2AN_2021__55_4_1635_0,
author = {Audusse, Emmanuel and Boittin, L\'ea and Parisot, Martin},
title = {Asymptotic derivation and simulations of a non-local {Exner} model in large viscosity regime},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1635--1668},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {4},
doi = {10.1051/m2an/2021031},
mrnumber = {4293496},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2021031/}
}
TY - JOUR AU - Audusse, Emmanuel AU - Boittin, Léa AU - Parisot, Martin TI - Asymptotic derivation and simulations of a non-local Exner model in large viscosity regime JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2021 SP - 1635 EP - 1668 VL - 55 IS - 4 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2021031/ DO - 10.1051/m2an/2021031 LA - en ID - M2AN_2021__55_4_1635_0 ER -
%0 Journal Article %A Audusse, Emmanuel %A Boittin, Léa %A Parisot, Martin %T Asymptotic derivation and simulations of a non-local Exner model in large viscosity regime %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2021 %P 1635-1668 %V 55 %N 4 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2021031/ %R 10.1051/m2an/2021031 %G en %F M2AN_2021__55_4_1635_0
Audusse, Emmanuel; Boittin, Léa; Parisot, Martin. Asymptotic derivation and simulations of a non-local Exner model in large viscosity regime. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 4, pp. 1635-1668. doi: 10.1051/m2an/2021031
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