A hyperbolic model for granular flow

We present a model that describes the motion of some granular material sliding along a slope. During this movement, both erosion and deposition may take place, depending on the speed of the sliding material. Analytically, this model consists of a hyperbolic system of partial differential equations. In the 1D case, the resulting system of balance laws displays interesting behavior. Its convective part gives rise to a 3 x 3 globally well defined Riemann Problem, in spite of the appearance of vacuum and of the lack of strict hyperbolicity. Several numerical integrations show various features of this model.