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Journal Articles ESAIM: Mathematical Modelling and Numerical Analysis Year : 2021

Asymptotic derivation and simulations of a non-local Exner model in large viscosity regime

Abstract

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.
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Dates and versions

hal-03312836 , version 1 (02-08-2021)

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Emmanuel Audusse, Léa Boittin, Martin Parisot. Asymptotic derivation and simulations of a non-local Exner model in large viscosity regime. ESAIM: Mathematical Modelling and Numerical Analysis, 2021, 55 (4), pp.1635-1668. ⟨10.1051/m2an/2021031⟩. ⟨hal-03312836⟩
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