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

This work is devoted to numerical modeling and simulation of flows of granular materials, with application 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 two-dimensional setting with a free surface. The regularization method is used to deal with the singularity of the rheological law, together with a finite element approximation. An arbitrary Lagrangian Eulerian formulation is used for the displacement of the domain, with special treatments applied to prevent the free surface from folding over itself. We perform numerical simulations of the collapse and spreading of both trapezoidal and rectangular granular columns over horizontal rigid beds and horizontal erodible beds made of the same material. We compare our results (evolution of the free surface, velocity profiles and static-flowing interface) with those predicted by an augmented Lagrangian formulation and with laboratory measurements. The different approaches provide similar results.