Extended Discrete Element Method

The extended discrete element method (XDEM) is a numerical technique that extends the dynamics of granular material or particles as described through the classical discrete element method (DEM) (Cundall and Allen) by additional properties such as the thermodynamic state, stress/strain or electro-magnetic field for each particle. Contrary to a continuum mechanics concept, the XDEM aims at resolving the particulate phase with its various processes attached to the particles. While the discrete element method predicts position and orientation in space and time for each particle, the extended discrete element method additionally estimates properties such as internal temperature and/or species distribution or mechanical impact with structures.

Molecular dynamics developed in the late 1950s by Alder et al. and early 1960s by Rahman may be regarded as a first step toward the extended discrete element method, although the forces due to collisions between particles were replaced by energy potentials e.g. Lennard-Jones potentials of molecules and atoms as long range forces to determine interaction.

Similarly, the fluid dynamic interaction of particles suspended in a flow were investigated. The drag forces exerted on the particles by the relative velocity by them and the flow were treated as additional forces acting on the particles. Therefore, these multiphase flow phenomena including a solid e.g.~particulate and a gaseous or fluid phase resolve the particulate phase by discrete methods, while gas or liquid flow is described by continuous methods, and therefore, is labelled the combined continuum and discrete model (CCDM) as applied by Kawaguchi et al., Hoomans, Xu 1997 and Xu 1998. Due to a discrete description of the solid phase, constitutive relations are omitted, and therefore, leads to a better understanding of the fundamentals. This was also concluded by Zhu 2007 et al. and Zhu 2008 et al. during a review on particulate flows modelled with the CCDM approach. It has seen a mayor development in last two decades and describes motion of the solid phase by the Discrete Element Method (DEM) on an individual particle scale and the remaining phases are treated by the Navier-Stokes equations. Thus, the method is recognized as an effective tool to investigate into the interaction between a particulate and fluid phase as reviewed by Yu and Xu, Feng and Yu and Deen et al. Based on the CCDM methodology the characteristics of spouted and fluidised beds are predicted by Gryczka et al.

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