A Well-balanced Finite Volume-Augmented Lagrangian Method for an Integrated Herschel-Bulkley Model |
| |
Authors: | C. Acary-Robert E. D. Fernández-Nieto G. Narbona-Reina P. Vigneaux |
| |
Affiliation: | 1. LAMA, Universit?? de Savoie, Campus Scientifique, 73376, Le Bourget-du-Lac, France 2. Dpto. Matem??tica Aplicada I, E.T.S. Arquitectura, Universidad de Sevilla, Avda. Reina Mercedes 2, 41012, Sevilla, Spain 3. Unit?? de Math??matiques Pures et Appliqu??es, Ecole Normale Sup??rieure de Lyon, 46 all??e d??Italie, 69364, Lyon Cedex 07, France
|
| |
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 analytical solution, to confirm the well balanced property and the ability to cope with the various rheological regimes associated with the Herschel-Bulkley constitutive law. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|