JOURNAL OF COMPUTATIONAL PHYSICS | 卷:264 |
Efficient numerical schemes for viscoplastic avalanches. Part 1: The 1D case | |
Article | |
Fernandez-Nieto, Enrique D.1  Gallardo, Jose M.2  Vigneaux, Paul3  | |
[1] Univ Seville, ETS Arquitectura, Dept Matemat Aplicada 1, E-41012 Seville, Spain | |
[2] Univ Malaga, Dept Anal Matemat, E-29071 Malaga, Spain | |
[3] Ecole Normale Super Lyon, Unitee Math Pures & Appliquees, F-69364 Lyon 07, France | |
关键词: Viscoplastic; Shallow water; Well-balanced; Finite volume; Variational inequality; Bingham; | |
DOI : 10.1016/j.jcp.2014.01.026 | |
来源: Elsevier | |
【 摘 要 】
This paper deals with the numerical resolution of a shallow water viscoplastic flow model. Viscoplastic materials are characterized by the existence of a yield stress: below a certain critical threshold in the imposed stress, there is no deformation and the material behaves like a rigid solid, but when that yield value is exceeded, the material flows like a fluid. In the context of avalanches, it means that after going down a slope, the material can stop and its free surface has a non-trivial shape, as opposed to the case of water (Newtonian fluid). The model involves variational inequalities associated with the yield threshold: finite-volume schemes are used together with duality methods (namely Augmented Lagrangian and Bermudez-Moreno) to discretize the problem. To be able to accurately simulate the stopping behavior of the avalanche, new schemes need to be designed, involving the classical notion of well-balancing. In the present context, it needs to be extended to take into account the viscoplastic nature of the material as well as general bottoms with wet/dry fronts which are encountered in geophysical geometries. We derived such schemes and numerical experiments are presented to show their performances. (C) 2014 Elsevier Inc. All rights reserved.
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