A numerical study of a two-layer model for the growth of granular matter in a silo
For researchers studying granular flow, this provides numerical methods for a specific model, but the work is incremental.
The paper numerically solves a two-layer model for granular matter growth in a silo, showing that heap profiles evolve towards similarity solutions in finite time.
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.