Two-dimensional simulation by regularization of free surface viscoplastic flows with Drucker-Prager yield stress and application to granular collapse

Christelle Lusso 1 Alexandre Ern 1, 2 François Bouchut 3 Anne Mangeney 4, 5 Maxime Farin 4 Olivier Roche 6
1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
2 SERENA - Simulation for the Environment: Reliable and Efficient Numerical Algorithms
Inria de Paris
3 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
4 IPGP - Institut de Physique du Globe de Paris
5 ANGE - Numerical Analysis, Geophysics and Ecology
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt
6 LMV - Laboratoire Magmas et Volcans
Abstract : This work is devoted to numerical modeling and simulation of granular flows relevant to geophysical flows such as avalanches and debris flows. We consider an incompressible viscoplastic fluid, described by a rheology with pressure-dependent yield stress, in a 2D setting with a free surface. We implement a regularization method to deal with the singularity of the rheological law, using a mixed finite element approximation of the momentum and incompressibility equations, and an arbitrary Lagrangian Eulerian (ALE) formulation for the displacement of the domain. The free surface is evolved by taking care of its deposition onto the bottom and of preventing it from folding over itself. Several tests are performed to assess the efficiency of our method. The first test is dedicated to verify its accuracy and cost on a one-dimensional simple shear plug flow. On this configuration we setup rules for the choice of the numerical parameters. The second test aims to compare the results of our numerical method to those predicted by an augmented Lagrangian formulation in the case of the collapse and spreading of a granular column over a horizontal rigid bed. Finally we show the reliability of our method by comparing numerical predictions to data from experiments of granular collapse of both trapezoidal and rectangular columns over horizontal rigid or erodible granular bed made of the same material. We compare the evolution of the free surface, the velocity profiles, and the static-flowing interface. The results show the ability of our method to deal numerically with the front behavior of granular collapses over an erodible bed.
Keywords : Drucker–Prager pressure-dependent yield stress Viscoplastic flows granular collapse ALE method regularization free surface
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Christelle Lusso, Alexandre Ern, François Bouchut, Anne Mangeney, Maxime Farin, et al.. Two-dimensional simulation by regularization of free surface viscoplastic flows with Drucker-Prager yield stress and application to granular collapse. Journal of Computational Physics, Elsevier, 2017, 333, pp.387-408. ⟨10.1016/j.jcp.2016.12.036⟩. ⟨hal-01133786v2⟩

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