AUDUSSE, Emmanuel; BOITTIN, Léa; PARISOT, Martin

doi:10.1051/m2an/2021031

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AUDUSSE, Emmanuel
Laboratoire Analyse, Géométrie et Applications [LAGA]

BOITTIN, Léa
Numerical Analysis, Geophysics and Ecology [ANGE]

PARISOT, Martin
Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts [CARDAMOM]

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ESAIM: Mathematical Modelling and Numerical Analysis. 2021-07, vol. 55, n° 4, p. 1635-1668

EDP Sciences

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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.< Réduire

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Free surface flow

Shallow water equations

Sediment transport

Entropy dissipation

Non-local effects

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

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