A non-local model for heterogeneous material flow on conveyor belts

TL;DR

This paper develops a finite volume scheme for a non-local macroscopic model of heterogeneous material flow on conveyor belts, extending previous scalar results to systems with boundary considerations and validating with numerical tests.

Contribution

It introduces a new finite volume approximation for a non-local system modeling heterogeneous material flow, including boundary effects, and proves convergence of the scheme.

Findings

Numerical results agree well with microscopic simulations.

The scheme effectively handles flux discontinuities.

Extension from scalar to system models with boundary considerations.

Abstract

In this paper, a finite volume approximation scheme is used to solve a non-local macroscopic material flow model in two space dimensions, accounting for the presence of boundaries in the non-local terms. Based on a previous result for the scalar case, we extend the setting to a system of heterogeneous material on bounded domains. We prove the convergence of the approximate solutions constructed using the Roe scheme with dimensiona splitting, where the major challenge lies in the treatment of the discontinuity occurring in the flux function. Numerical tests show a good agreement with microscopic simulations.