Granular matter in a silo

A dynamic model for slow accumulation of granular matter, with standing and rolling layers, is adapted to the geometry of a silo with vertical walls and bounded cross section. For sources constant in time the typical behavior of a rising level of matter with constant surface profile is described by a similarity solution. This solution can be characterized by a nonlinear boundary value problem. For the case of a circular silo with central point source and the corresponding 1D problem of an interval with central point source the profiles of the standing and rolling layers are explicitly computed. The computed shapes agree qualitatively with experimental observations and seem better justified than results based on the assumption of constant speed of the rolling layer.