Some recent models and simulations for granular flows

par François Bouchut (CNRS & Université Paris-Est)

mardi 27 sept. 2016, 14:00 → 15:00 Europe/Paris

4e étage, salle 435 (UMPA, ENS Lyon - Site Monod)

Granular materials are always involved in erosion processes on the Earth's surface such as sub-aerial and submarine landslides that occur in mountainous, volcanic, seismic and coastal areas. The geophysical and mechanical description of the behavior of these materials has received a lot of attention the last decade, and a good overview of the current knowledge can be found in [1]. Still many fundamental questions remain open. In particular, when describing granular materials by non-Newtonian fluids, relevant constitutive rheological relations remain to be set up. A striking property of granular materials is the ability to behave like a solid when the grains are blocked one against the other, or like a fluid when they just slide. This twofold behavior is usually represented by viscoplastic models with yield stress. Then the description of the solid/fluid interface (also called static/flowing interface) is a key issue to evaluate the quality of the models. Recent studies of the author's group yield an explicit description of this interface, that is valid under certain asymptotic assumptions [2,3,4]. The results from this model can be compared to two-dimensional simulations of viscoplastic models and to data issued from laboratory experiments [5,6,7]. Another issue is to establish models describing wet granular materials, which means that the material is surrounded by fluid, what happens usually in landslides. The rheological behavior of such a mixture is a difficult problem, but we however established recently a thin-layer model that is able to describe the dilating/contracting behavior of the mixture [8,9]. [1] B. Andreotti, Y. Forterre, and O. Pouliquen, Granular media, between fluid and solid, Cambridge University Press, 2013. [2] F. Bouchut, I.R. Ionescu, and A. Mangeney, An analytic approach for the evolution of the static/flowing interface in viscoplastic granular flows, Comm. Math. Sci. 14 (2016). [3] C. Lusso, F. Bouchut, A. Ern, and A. Mangeney, A simplified model for static/flowing dynamics in thin-layer flows of granular materials with yield, preprint (2015). [4] C. Lusso, F. Bouchut, A. Ern, and A. Mangeney, Explicit solutions to a free interface model for the static/flowing transition in thin granular flows, preprint (2015). [5] I.R. Ionescu, A. Mangeney, F. Bouchut, and O. Roche, Viscoplastic modeling of granular column collapse with pressure-dependent rheology, J. Non-Newtonian Fluid Mech. 219 (2015), 1-18. [6] C. Lusso, A. Ern, F. Bouchut, A. Mangeney, M. Farin, and O. Roche, Two-dimensional simulation by regularization of free surface viscoplastic flows with Drucker-Prager yield stress and application to granular collapse, preprint (2016). [7] N. Martin, I.R. Ionescu, A. Mangeney, F. Bouchut, M. Farin, Continuum viscoplastic simulation of a granular column collapse on large slopes: $\mu(I)$ rheology and lateral wall effects, preprint (2016). [8] F. Bouchut, E.D. Fernandez-Nieto, A. Mangeney, and G. Narbona-Reina, A two-phase shallow debris flow model with energy balance, ESAIM: Math. Modelling Numer. Anal. 49 (2015), 101-140. [9] F. Bouchut, E.D. Fernandez-Nieto, A. Mangeney, and G. Narbona-Reina, A two-phase two-layer model for fluidized granular flows with dilatancy effects, J. Fluid Mech. 801 (2016), 166-221.