Discrete element method: Difference between revisions

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{{distinguish|finite element method}}

{{More citations needed|date=November 2019}}

A '''discrete element method''' ('''DEM'''), also called a '''distinct element method''', is any of a family of [[numerical analysis|numerical]] methods for computing the motion and effect of a large number of small particles. Though DEM is very closely related to [[molecular dynamics]], the method is generally distinguished by its inclusion of rotational [[Degrees of freedom (statistics)|degrees-of-freedom]] as well as stateful contact, particle deformation and often complicated geometries (including polyhedra). With advances in computing power and numerical algorithms for nearest neighbor sorting, it has become possible to numerically simulate millions of particles on a single processor. Today DEM is becoming widely accepted as an effective method of addressing engineering problems in granular and discontinuous materials, especially in granular flows, powder mechanics, ice and [[rock mechanics]]. DEM has been extended into the [[Extended Discrete Element Method]] taking [[heat transfer]],<ref name="Peng">{{cite journal |last1=Peng |first1=Z. |last2=Doroodchi |first2=E. |last3=Moghtaderi |first3=B. |date=2020 |title=Heat transfer modelling in Discrete Element Method (DEM)-based simulations of thermal processes: Theory and model development |journal=Progress in Energy and Combustion Science |volume=79,100847 |page=100847 |doi=10.1016/j.pecs.2020.100847|s2cid=218967044 }}</ref> [[chemical reaction]]<ref name="Papadikis">{{cite journal |last1=Papadikis |first1=K. |last2=Gu |first2=S. |last3=Bridgwater |first3=A.V. |date=2009 |title=CFD modelling of the fast pyrolysis of biomass in fluidised bed reactors: Modelling the impact of biomass shrinkage |journal=Chemical Engineering Journal |volume=149 |issue=1–3 |pages=417–427|doi=10.1016/j.cej.2009.01.036 |url=https://eprints.soton.ac.uk/149223/1/Paper.pdf }}</ref> and coupling to [[Computational fluid dynamics|CFD]]<ref name="Kafui">{{cite journal |last1=Kafui |first1=K.D. |last2=Thornton |first2=C. |last3=Adams |first3=M.J. |date=2002 |title=Discrete particle-continuum fluid modelling of gas–solid fuidised beds |journal=Chemical Engineering Science |volume=57 |issue=13 |pages=2395–2410|doi=10.1016/S0009-2509(02)00140-9 |bibcode=2002ChEnS..57.2395K }}</ref> and [[Finite element method|FEM]]<ref name="Trivino">{{cite journal |last1=Trivino |first1=L.F. |last2=Mohanty |first2=B. |date=2015 |title=Assessment of crack initiation and propagation in rock from explosion-induced stress waves and gas expansion by cross-hole seismometry and FEM–DEM method |journal=International Journal of Rock Mechanics & Mining Sciences |volume=77 |pages=287–299|doi=10.1016/j.ijrmms.2015.03.036 |bibcode=2015IJRMM..77..287T }}</ref> into account.

Discrete element methods are relatively computationally intensive, which limits either the length of a simulation or the number of particles. Several DEM codes, as do molecular dynamics codes, take advantage of parallel processing capabilities (shared or distributed systems) to scale up the number of particles or length of the simulation. An alternative to treating all particles separately is to average the physics across many particles and thereby treat the material as a [[Continuum mechanics|continuum]]. In the case of [[solid]]-like granular behavior as in [[soil mechanics]], the continuum approach usually treats the material as [[Elasticity (physics)|elastic]] or [[Plasticity (physics)|elasto-plastic]] and models it with the [[finite element method]] or a [[Meshfree methods|mesh free method]]. In the case of liquid-like or gas-like granular flow, the continuum approach may treat the material as a [[fluid]] and use [[computational fluid dynamics]]. Drawbacks to [[Homogenization (chemistry)|homogenization]] of the granular scale physics, however, are well-documented{{Citation needed|date=August 2025}} and should be considered carefully before attempting to use a continuum approach.

==The DEM family==

The various branches of the DEM family are the [[distinct element method]] proposed by [[Peter A. Cundall]] and Otto D. L. Strack in 1979,<ref>{{Cite journal|last1=Cundall|first1=Peter. A.|last2=Strack|first2=Otto D. L.|date=1979|title=Discrete numerical model for granular assemblies|url=http://websrv.cs.umt.edu/classes/cs477/images/0/0e/Cundall_Strack.pdf|journal=Géotechnique|volume=29|issue=1|pages=47–65|doi=10.1680/geot.1979.29.1.47}}</ref> the [[generalized discrete element method]],<ref name="WHM85">{{cite journal |last1=Williams |first1=J. R. |last2=Hocking |first2=G. |last3=Mustoe |first3=G. G. W. |title=The Theoretical Basis of the Discrete Element Method |journal=NUMETA 1985, Numerical Methods of Engineering, Theory and Applications |publisher=A.A. Balkema |___location=Rotterdam |date=January 1985|url=https://docs.google.com/document/d/1ljujwjib2h2NwYksdh9wONZhEpNljGQdAmehXANFJw4}}</ref> the [[Discontinuous Deformation Analysis|discontinuous deformation analysis]] (DDA) {{harv|Shi|1992}} and the finite-discrete element method concurrently developed by several groups (e.g., [[Ante Munjiza|Munjiza]] and [[Roger Owen (mathematician)|Owen]]). The general method was originally developed by Cundall in 1971 to problems in rock mechanics.

Williams<ref name="WHM85" /> showed that DEM could be viewed as a generalized finite element method, allowing deformation and fracturing of particles. Its application to [[geomechanics]] problems is described in the book ''Numerical Methods in Rock Mechanics''.{{sfn|Williams|Pande|Beer|1990}} The 1st, 2nd and 3rd International Conferences on Discrete Element Methods have been a common point for researchers to publish advances in the method and its applications. Journal articles reviewing the state of the art have been published by Williams and O'Connnor,<ref>{{cite journal |last1=Williams |first1=J. R. |last2=O'Connor |first2=R. |title=Discrete element simulation and the contact problem |journal=Archives of Computational Methods in Engineering |date=December 1999 |volume=6 |issue=4 |pages=279–304 |doi=10.1007/BF02818917|citeseerx=10.1.1.49.9391 |s2cid=16642399 }}</ref> [[Nenad Bicanic|Bicanic]], and [[Antonio Bobet|Bobet]] et al. (see below). A comprehensive treatment of the combined Finite Element-Discrete Element Method is contained in the book ''The Combined Finite-Discrete Element Method''.<ref name="Munjiza 2004">{{cite book |last1=Munjiza |first1=Ante |title=The Combined Finite-Discrete Element Method |date=2004 |publisher=Wiley |___location=Chichester |isbn=978-0-470-84199-0}}</ref>

[[File:Cundall DEM.gif|thumb|upright=1|Discrete-element simulation with particles arranged after a photo of [[Peter A. Cundall]]. As proposed in Cundall and Strack (1979), grains interact with linear-elastic forces and Coulomb friction. Grain kinematics evolve through time by temporal integration of their force and torque balance. The collective behavior is self-organizing with discrete shear zones and angles of repose, as characteristic to cohesionless granular materials.]]

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Disadvantages

* The maximum number of particles, and duration of a virtual simulation is limited by computational power. Typical flows contain billions of particles, but contemporary DEM simulations on large cluster computing resources have only recently been able to approach this scale for sufficiently long time (simulated time, not actual program execution time).

* DEM is computationally demanding, which is the reason why it has not been so readily and widely adopted as continuum approaches in [[computational engineering]] sciences and industry. However, the actual program execution times can be reduced significantly when graphical processing units (GPUs) are utilized to conduct DEM simulations, due to the large number of computing cores on typical GPUs. In addition GPUs tend to be significantly more energy efficient than conventional computing clusters when conducting DEM simulations i.e. a DEM simulation solved on GPUs requires less energy than when it is solved on a conventional computing cluster.<ref>{{Cite journal|last1=He|first1=Yi|last2=Bayly|first2=Andrew E.|last3=Hassanpour|first3=Ali|last4=Muller|first4=Frans|last5=Wu|first5=Ke|last6=Yang|first6=Dongmin|date=2018-10-01|title=A GPU-based coupled SPH-DEM method for particle-fluid flow with free surfaces|journal=Powder Technology|volume=338|pages=548–562|doi=10.1016/j.powtec.2018.07.043|issn=0032-5910|doi-access=free}}</ref>

== See also ==