Complex material flow problems: a multi-scale model hierarchy and particle methods
Material flow simulation is in increasing need of multi-scale models. On the one hand, macroscopic flow models are used for large-scale simulations with a large number of parts. On the other hand, microscopic models are needed to describe the details of the production process. In this paper, we present a hierarchy of models for material flow problems ranging from detailed microscopic, discrete element method type, models to macroscopic models using scalar conservation laws with non-local interaction terms. Numerical simulations are presented at all levels of the hierarchy, and the results are compared to each other for several test cases.
KeywordsDEM material flow simulation Diffusive limits Hydrodynamic limits Interacting particles Mean field equations
- 1.Hoher S, Schindler P, Göttlich S, Schleper V, Röck S (2011) System dynamic models and real-time simulation of complex material flow systems. In: ElMaraghy HA (ed) Enabling manufacturing competitiveness and economic sustainability 2012, Part 3, pp 316–321Google Scholar
- 3.Reinhart G, Lacour F (2009) Physically based virtual commissioning of material flow intensive manufacturing plants. In: Zaeh MF, ElMaraghy HA (eds) 3rd international conference on Changeable, Agile, Reconfigurable and Virtual production (CARV 2009), pp 377–387Google Scholar
- 16.Braun W, Hepp K (1977) The Vlasov dynamics and its fluctuations in the 1/N limit of interacting classical particles. Commun Math Phys 56:101–113Google Scholar
- 17.Neunzert H (1977) The Vlasov equation as a limit of Hamiltonian classical mechanical systems of interacting particles. Trans Fluid Dyn 18:663–678Google Scholar