A numerical study of a two-layer model for the growth of granular matter in a silo

TL;DR

This paper numerically investigates a two-layer model for granular matter growth in silos, demonstrating how similarity solutions can be characterized and showing the evolution of heap profiles over time.

Contribution

It introduces numerical methods to analyze similarity solutions in a two-layer granular growth model and demonstrates the finite-time evolution of heap profiles.

Findings

Similarity quasi-static solutions can be numerically characterized.

Heap profiles evolve in finite time towards similarity solutions.

Finite difference scheme effectively models the dynamical growth process.

Abstract

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.