Discrete element method: Difference between revisions

Revision as of 15:36, 20 September 2022

Revision as of 04:24, 23 October 2022

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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 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, 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 }}</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 }}</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 and should be considered carefully before attempting to use a continuum approach.

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==Applications==

The fundamental assumption of the method is that the material consists of separate, discrete particles. These particles may have different shapes and properties that influence inter-particle contact.<ref name="Wilke2022">{{Cite journal | last1 = Wilke | first1 = Daniel N. | doi = 10.1016/j.powtec.2022.117362 | title = Traction chain networks: Insights beyond force chain networks for non-spherical particle systems | journal = Powder Technology | volume = 402 | pages = 117362 | year = 2022 | arxiv = 2106.03771 | s2cid = 235359147 }}</ref> Some examples are:

* liquids and solutions, for instance of sugar or proteins;

* bulk materials in storage silos, like cereal;

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* Mining

* Mineral processing

* Pharmaceutical industry<ref>{{Cite journal|last1=Behjani|first1=Mohammadreza Alizadeh|last2=Motlagh|first2=Yousef Ghaffari|last3=Bayly|first3=Andrew|last4=Hassanpour|first4=Ali|date=2019-11-07|title=Assessment of blending performance of pharmaceutical powder mixtures in a continuous mixer using Discrete Element Method (DEM)|url=http://www.sciencedirect.com/science/article/pii/S0032591019309313|journal=Powder Technology|volume=366|pages=73–81|doi=10.1016/j.powtec.2019.10.102|s2cid=209718900 |issn=0032-5910|archive-url=http://eprints.whiterose.ac.uk/157493/|archive-date=21 Feb 2020}}</ref>

* [[Powder metallurgy]]

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==Combined finite-discrete element method==

Following the work by Munjiza and Owen, the combined finite-discrete element method has been further developed to various irregular and deformable particles in many applications including pharmaceutical tableting,<ref>{{Cite journal |last1=Lewis |first1=R. W. |last2=Gethin |first2=D. T. |last3=Yang |first3=X. S. |last4=Rowe |first4=R. C. |title=A combined finite-discrete element method for simulating pharmaceutical powder tableting |doi=10.1002/nme.1287 |journal=International Journal for Numerical Methods in Engineering |volume=62 |issue=7 |pages=853 |year=2005|bibcode = 2005IJNME..62..853L |arxiv=0706.4406 |s2cid=122962022 }}</ref> packaging and flow simulations,<ref>{{Cite journal |last1=Gethin |first1=D. T. |last2=Yang |first2=X. S. |last3=Lewis |first3=R. W. |doi=10.1016/j.cma.2005.10.025 |title=A two dimensional combined discrete and finite element scheme for simulating the flow and compaction of systems comprising irregular particulates |journal=Computer Methods in Applied Mechanics and Engineering |volume=195 |issue=41–43 |pages=5552 |year=2006 |bibcode = 2006CMAME.195.5552G }}</ref> and impact analysis.<ref>{{Cite journal |last1=Chen |first1=Y. |last2=May |first2=I. M. |doi=10.1680/stbu.2009.162.1.45 |title=Reinforced concrete members under drop-weight impacts |journal=Proceedings of the ICE - Structures and Buildings |volume=162 |pages=45–56 |year=2009 }}</ref>

==Advantages and limitations==

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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,<ref>{{Cite journal |last1=Xu |first1=J. |last2=Qi |first2=H. |last3=Fang |first3=X.|last4=Lu |first4=L.|last5=Ge |first5=W. |last6=Wang |first6=X.|last7=Xu |first7=M. |last8=Chen |first8=F. |last9=He |first9=X. |last10=Li |first10=J.|doi=10.1016/j.partic.2011.01.003 |title=Quasi-real-time simulation of rotating drum using discrete element method with parallel GPU computing |journal=Particuology |volume=9 |issue=4 |pages=446–450 |year=2011 |s2cid=93467044 }}</ref><ref>{{Cite journal |last1=Govender |first1=N. |last2=Wilke |first2=D. N. |last3=Kok |first3=S.|doi=10.1016/j.softx.2016.04.004 |title=Blaze-DEMGPU: Modular high performance DEM framework for the GPU architecture |journal=SoftwareX |volume=5 |pages=62–66 |year=2016 |bibcode=2016SoftX...5...62G |doi-access=free }}</ref> 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 ==