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Numerical schemes for viscoplastic avalanches


We talk about 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 Bermúdez-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. More details in: Journal of Computational Physics (2014) 264, p 55-90
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hal-01019923 , version 1 (07-07-2014)


  • HAL Id : hal-01019923 , version 1


Paul Vigneaux. Numerical schemes for viscoplastic avalanches. 2me Ecole du GdR CNRS EGRIN, Jun 2014, Domaine de Chalès, France. ⟨hal-01019923⟩
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