Numerical simulations of granular free-surface flows using smoothed particle hydrodynamics

This paper presents a two-dimensional SPH model designed to simulate free-surface flows of dense granular materials. Smoothed particle hydrodynamics (SPH) is a mesh-free numerical method based on a Lagrangian discretization of the continuum mass and momentum conservation equations. The rheology of dense granular materials is modelled using a new local constitutive law recently proposed by Jop et al. (Nature, 2006). Of the viscoplastic class, this law is characterized by an apparent viscosity depending both on the local strain rate and local pressure. Validation test cases of the model in steady and unsteady configurations are presented. For steady cases (vertical chute flow and uniform free-surface layers on inclines), excellent agreement with analytical predictions is obtained. In the unsteady case, the simulations satisfactorily capture the dynamics of gravity-driven surges observed in experiments, including behaviours that are very specific to granular materials. Among the various parameters involved in the computations, the influence of SPH particle configuration within the flow and of the threshold viscosity used in the regularization of the constitutive yield criterion are particularly discussed.