A SPH model for the simulation of free surface granular flows in a dense regime

Smoothed Particle Hydrodynamics (SPH) is a particle-based Lagrangian numerical method, particularly suitable for modeling free surface flows of fluids with different constitutive equations. In this work, a SPH model is developed to solve flow problems of granular matter flowing in a dense regime, featuring a constitutive equation proposed by Pouliquen et al. (2006) and Jop et al. (2006). The problem of resolving the flow close to static conditions has been solved by introducing a weak compressibility for the grains: this leads to a third order algebraic equations to be solved for computing granular material density. A new viscosity regularisation method, suitable for any visco-plastic fluid with varying yield stress has been developed, in order to reproduce stopping flow and static conditions. Validation of the model has been performed by solving the simple uniform granular flow problem, for which the solution is known analytically and by reproducing a set of experimental data on granular columns collapses by Lube et al. (2004) .