Journal of Engineering Mathematics

, Volume 92, Issue 1, pp 15–29 | Cite as

Complex material flow problems: a multi-scale model hierarchy and particle methods

  • S. GöttlichEmail author
  • A. Klar
  • S. Tiwari


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.


DEM material flow simulation Diffusive limits Hydrodynamic limits Interacting particles  Mean field equations 



This work was supported by the German research foundation, DFG grants KL 1105/20-1, GO 1920/3-1 and the BMBF Project KinOpt.


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MannheimMannheimGermany
  2. 2.Fraunhofer Institute ITWMFraunhofer-Platz 1KaiserslauternGermany
  3. 3.Department of MathematicsTU KaiserslauternKaiserslauternGermany

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