Plenary Lecture - A multi-scale model hierarchy for material flow problems

Abstract: Efficient simulation and optimization of material flow processes are key components of modern production systems and digital factories. While microscopic particle models provide a detailed description of individual interactions, their computational cost becomes prohibitive for large-scale industrial applications. This talk presents a hierarchy of mathematical models for material flow on conveyor belts, bridging microscopic particle dynamics and macroscopic continuum descriptions.

Starting from an interacting particle system based on Newtonian mechanics, a sequence of formal limit procedures leads to a two-dimensional nonlocal conservation law describing the evolution of the material density. The model combines a prescribed transport velocity induced by the conveyor belt with a density-dependent nonlocal interaction term that captures congestion and collision avoidance. Particular emphasis is placed on the mathematical analysis of the resulting PDE model, including the existence and uniqueness of entropy solutions, stability estimates, and the convergence of efficient finite-volume discretization schemes.

The predictive capability of the macroscopic model is demonstrated through extensive validation against experimental data for both cylindrical and cubical parts. The simulations accurately reproduce density evolution, outflow characteristics, and positioning while requiring significantly less computational effort than microscopic particle simulations for large numbers of transported objects. Finally, extensions towards hybrid modeling and data-driven approaches are discussed, highlighting the flexibility of the proposed multi-scale framework for industrial material flow applications.

Speaker: Simone Göttlich (Scientific Computing Research Group (SciCom), University of Mannheim)
Date and Time: Wednesday, September 30, 2026 | 09:30 - 10:30
Venue: NTI Lecture Hall