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A well-balanced finite volume-augmented lagrangian method for an integrated Herschel-Bulkley model

 

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Opened Access A well-balanced finite volume-augmented lagrangian method for an integrated Herschel-Bulkley model
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Author: Acary-Robert, C.
Fernández-Nieto, Enrique D.
Narbona-Reina, Gladys
Vigneaux, Paul
Department: Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
Date: 2012
Published in: Journal of Scientific Computing, 53(3), 608-641
Document type: Article
Abstract: We are interested in the derivation of an integrated Herschel-Bulkley model for shallow flows, as well as in the design of a numerical algorithm to solve the resulting equations. The goal is to simulate the evolution of thin sheet of viscoplastic materials on inclined planes and, in particular, to be able to compute the evolution from dynamic to stationary states. The model involves a variational inequality and it is valid from null to moderate slopes. The proposed numerical scheme is well balanced and involves a coupling between a duality technique (to treat plasticity), a fixed point method (to handle the power law) and a finite volume discretization. Several numerical tests are done, including a comparison with an analytic solution, to confirm the well balanced property and the ability to cope with the various rheological regimes associated with the Herschel-Bulkley constitutive law.
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Format: PDF

URI: http://hdl.handle.net/11441/32223

DOI: http://dx.doi.org/10.1007/s10915-012-9591-x

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