Some considerations on the Bouchaud–Cates–Ravi–Edwards model for granular flow

We discuss some features of the BCRE model. Under some conditions, we show that it can be understood as a mapping from a two-dimensional to a one-dimensional problem. We then propose some modifications that (a) guarantee mass conservation (which is not assured in its original form) and (b) correct undesired features that appear when there are irregularities in the surface of the static phase. We also show that a similar model can be deduced both from the principle of mass conservation (first equation) and from a simple thermodynamic argument (from which the exchange equation can be obtained). Finally, we solve the model numerically, using different velocity profiles and studying the effects of different parameters.