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

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 b...

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Detalhes bibliográficos
Autores: Acary-Robert, C., Fernández Nieto, Enrique Domingo, Narbona Reina, Gladys, Vigneaux, Paul
Tipo de documento: artigo
Estado:Versión enviada para evaluación y publicación
Data de publicação:2012
País:España
Recursos:Universidad de Sevilla (US)
Repositório:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/32223
Acesso em linha:http://hdl.handle.net/11441/32223
https://doi.org/10.1007/s10915-012-9591-x
Access Level:Acceso aberto
Palavra-chave:variational inequality
finite volume
well balanced
Herschel-Bulkley
viscous shallow water
avalanche
Descrição
Resumo: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.