  The problem of filling a silo of given bounded cross-section with granular
matter can be described by the two-layer model of Hadeler and Kuttler [8]. In
this paper we discuss how similarity quasi-static solutions for this model can
be numerically characterized by the direct finite element solution of a
semidefinite elliptic Neumann problem. We also discuss a finite difference
scheme for the dynamical model through which we can show that the growing
profiles of the heaps in the silo evolve in finite time towards such similarity
solutions.
