Laminar shallow viscoplastic fluid flowing through an array of vertical obstacles
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.
Origine : Fichiers produits par l'(les) auteur(s)
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