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Pré-Publication, Document De Travail Année : 2017

Laminar shallow viscoplastic fluid flowing through an array of vertical obstacles

Pierre Saramito
Andrew Harris
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Résumé

A new Bingham-Darcy shallow depth approximation flow model is proposed in this paper. This model is suitable for a laminar shallow viscoplastic fluid flowing on a general topography and crossing an array of vertical obstacles. An analogous porous medium is first introduced for reducing the array of obstacles. It bases on a continuum model similar to the Brinkman equations, where the usual Darcy model is extended for viscoplastic Bingham fluids. Next, a specific asymptotic analysis of this Bingham-Darcy porous medium in the case of shallow depth flows leads to a new reduced model. The resulting highly nonlinear parabolic equation in terms of the flow height only is efficiently solved by a Newton method, without any regularization. The numerical predictions compares both qualitatively and quantitatively well with both some experimental measurements and full tridimensional simulations. Finally , a new experiment for a viscoplastic flow over an inclined plane through a network of obstacle is proposed and numerical simulations are provided for future comparisons with experiments.
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Dates et versions

hal-01646766 , version 1 (23-11-2017)
hal-01646766 , version 2 (19-03-2018)

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  • HAL Id : hal-01646766 , version 1

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Noé Bernabeu, Pierre Saramito, Andrew Harris. Laminar shallow viscoplastic fluid flowing through an array of vertical obstacles. 2017. ⟨hal-01646766v1⟩
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