Modelling the dynamics of granular matter

This work presents a new model for the movement, the erosion and the deposition of granular matter along a sloping bed. It is a synthesis of the Hadeler–Kuttler and of the Savage–Hutter models. The result is a 3 × 3 system of balance laws able to describe the deposition–erosion dynamics, as in the former model, while being compliant with the dynamics, as in the latter one. First, the basic analytical properties of the new model are described. Then several numerical simulations allow to compare the different models. Whenever the slope of the bed changes, sign and deposition–erosion phenomena are relevant, the present model appears to provide better descriptions of granular matter behaviour.