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On the Exner model and non-local approximations: modeling, analysis and numerical simulations

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 schema based on a staggered discretization is proposed for the full model, sediment and water.
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https://hal.archives-ouvertes.fr/hal-03001671
Contributor : Martin Parisot <>
Submitted on : Tuesday, November 24, 2020 - 10:08:28 AM
Last modification on : Tuesday, December 8, 2020 - 3:34:19 AM

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NonLocalExner_V1.0_HAL.pdf
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  • HAL Id : hal-03001671, version 1

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Emmanuel Audusse, Léa Boittin, Martin Parisot. On the Exner model and non-local approximations: modeling, analysis and numerical simulations. 2020. ⟨hal-03001671⟩

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