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Efficient numerical schemes for viscoplastic avalanches. Part 1: The 1D case.

Opened Access Efficient numerical schemes for viscoplastic avalanches. Part 1: The 1D case.


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Autor: Fernández-Nieto, Enrique D.
Gallardo, José M.
Vigneaux, Paul
Departamento: Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
Fecha: 2014
Publicado en: Journal of Computational Physics, 264, pp. 55–90
Tipo de documento: Artículo
Resumen: 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 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 accoun...
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DOI: 10.1016/

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