Extended discrete element method: Difference between revisions

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{{Short description|Granular material interaction simulation technique}}

[[File:Internal temperature distribution in a particle.png|thumb|An internal temperature distribution for a spherical particle versus radius and time under a time-varying [[heat flux]].]]

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| authorlink2=D. J. Tildesley

| title=Computer Simulation of Liquids

| publisher=ClaredonClarendon Press Oxford

| year=1990}}</ref>) by additional properties such as the [[thermodynamic]] state, [[Stress (mechanicalmechanics)|stress]]/[[Deformation (mechanics)|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.

==History==

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| year=1959

| volume=31

| pagesissue=4592

| pages=459–466

| doi=10.1063/1.1730376}}</ref> and early 1960s by Rahman<ref>{{cite journal

| doi=10.1063/1.1730376

| doibibcode=101959JChPh.1063/1.173037631..459A}}</ref> and early 1960s by Rahman<ref>{{cite journal

| first1=A.

| last1=Rahman

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| year=1964

| volume=136

| issue=2A

}}</ref> 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.

| doi=10.1103/physrev.136.a405

| pages=A405–A411

|bibcode = 1964PhRv..136..405R }}</ref> 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 (physics)|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.,<ref>{{cite journal

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| year=1993

| volume=77

| doi=10.1016/0032-5910(93)85010-7

| pages=79–87

}}</ref> Hoomans,<ref>{{cite journal

| first1=B. P. B.

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| year=1996

| volume=51

| doi=10.1016/0009-2509(95)00271-5

| pages=99–118

| citeseerx=10.1.1.470.6532

| s2cid=17460834

}}</ref> Xu 1997<ref>{{cite journal

| first1=B. H.

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| year=1997

| volume=52

| pagesissue=278516

| pages=2785–2809

| doi=10.1016/s0009-2509(97)00081-x

}}</ref> and Xu 1998.<ref>{{cite journal

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| year=1998

| volume=53

| issue=14

| pages=2646–2647

| doi=10.1016/s0009-2509(98)00086-4

}}</ref> Due to a discrete description of the solid phase, [[constitutive equation|constitutive]] relations are omitted, and therefore, leads to a better understanding of the fundamentals. This was also concluded by Zhu 2007 et al.<ref>{{cite journal

| first1=H. P.

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| year=2007

| volume=62

| issue=13

| pages=3378–3396

| doi=10.1016/j.ces.2006.12.089

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| year=2008

| volume=63

| issue=23

| pages=5728–5770

| doi=10.1016/j.ces.2008.08.006

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| year=2003

| volume=78

| issue=2–3

| pages=111–121

| doi=10.1002/jctb.788

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| year=2004

| volume=43

| issue=26

| pages=8378–8390

| doi=10.1021/ie049387v

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| year=2007

| volume=62

| issue=1–2

| pages=28–44

| doi=10.1016/j.ces.2006.08.014

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| year=2009

| volume=87

| issue=2

| pages=318–328

| doi=10.1002/cjce.20143

| citeseerx=10.1.1.335.4108

}}</ref>

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| year=1999

| volume=116

| issue=1–2

| pages=297–301

| doi=10.1016/s0010-2180(98)00048-0

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| year=2002

| volume=131

| issue=1–2

| pages=132–146

| doi=10.1016/s0010-2180(02)00393-0

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| year=2009

| volume=193

| issue=3

| pages=266–273

| doi=10.1016/j.powtec.2009.03.011

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| year=2010

| volume=50

| issue=2

| pages=207–214

| doi=10.2355/isijinternational.50.207

| doi-access=free

}}</ref> Numerical simulation of fluid injection into a gaseous environment nowadays is adopted by a large number of CFD-codes codes such as Star-CD of [[CDSimcenter STAR-adapcoCCM+]], [[Ansys]] and [[AVL (Engineering Firm)|AVL]]-Fire. Droplets of a spray are treated by a zero-dimensional approach to account for heat and mass transfer to the fluid phase.

==Methodology==

[[File:Staggered methodology for software coupling.png|thumb|Staggered methodology for discrete/continuous applications.]]

NumerousMany challengesengineering in engineeringproblems exist and evolve, that include a continuous and discrete phase simultaneouslyphases, and therefore,those problems cannot be solvedsimulated accurately by continuous or discrete approaches, only. Therefore, XDEM provides a platform, that couples discrete and continuous phasessolution for asome largeof number ofthose engineering applications.

Although research and development of numerical methods in each domains of discrete and continuous solvers is still progressing, respective software tools haveare reached a high degree of maturityavailable. In order to couple discrete and continuous approaches, two major conceptsapproaches are available:

*'''Monolithic conceptapproach''': The equations describing multi-physics phenomena are solved simultaneously by a single solver producing a complete solution.

*'''Partitioned or staggered conceptapproach''': The equations describing multi-physics phenomena are solved sequentially by appropriately tailored and distinct solvers with passing the results of one analysis as a load to the nextother.

The former conceptapproach requires a solver that includes a combination ofhandles all physical problems involved, and therefore, it requires a largelarger implementation effort. However, there exist scenarios for which it is difficult to arrange the coefficients of combined [[differential equations]] in one [[Matrix (mathematics)|matrix]]. A partitioned concept as a coupling between a number of solvers representing individual domains of physics offers distinctive advantages over a monolithic concept.

The latter, partitioned, approach couples a number of solvers representing individual domains of physics offers advantages over a monolithic concept. It encompasses a larger degree of flexibility because it can use many solvers. Furthermore, it allows a more modular software development. However, partitioned simulations require stable and accurate coupling algorithms.

It inherently encompasses a large degree of flexibility by coupling an almost arbitrary number of solvers.

Within the staggered concept of XDEM, continuous fields are described by the solution the respective continuous (conservation) equations. Properties of individual particles such as temperature are also resolved by solving respective conservation equations that yieldsyield both a spatial and temporal internal distribution of relevant variables. MayorMajor conservation principles with their equations and variables to be solved for and that are employed to an individual particle within XDEM are listed in the following table.

Furthermore, a more modular software development is retained that allows by far more specific solver techniques adequate to the

problems addressed. However, partitioned simulations impose stable and accurate coupling algorithms that convince by their pervasive character.

Within the staggered concept of XDEM, continuous fields are described by the solution the respective continuous (conservation) equations. Properties of individual particles such as temperature are also resolved by solving respective conservation equations that yields both a spatial and temporal internal distribution of relevant variables. Mayor conservation principles with their equations and variables to be solved for and that are employed to an individual particle within XDEM are listed in the

following table.

{| border="2" cellspacing="0" align="right" width="400" cellpadding="3" rules="all" style="border-collapse:collapse; empty-cells:show; margin: 1em 0em 1em 1em; border: solid 1px #aaaaaa;"

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| volume=97

| pages=1–16

| doi=10.1016/0010-2180(94)90112-0

}}</ref> while the importance of a transient behaviour is stressed by Lee et al.<ref>{{cite journal

| first1=J. C.

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| year=1996

| volume=105

| issue=4

| pages=591–599

| doi=10.1016/0010-2180(96)00221-0

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| year=1996

| volume=51

| doi=10.1016/0009-2509(95)00271-5

| pages=99–118

| citeseerx=10.1.1.470.6532

| s2cid=17460834

}}</ref> however, Chu and Yu<ref>{{cite journal

| first1=K. W.

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| year=2008

| volume=179

| issue=3

| pages=104–114

| doi=10.1016/j.powtec.2007.06.017

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| year=2011

| volume=90

| issue=4

| pages=1584–1590

| doi=10.1016/j.fuel.2010.10.017

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| year=2009

| volume=22

| issue=11

| pages=893–909

| doi=10.1016/j.mineng.2009.04.008

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| year=1976

| volume=15

| issue=2

| pages=141–147

| doi=10.1016/0032-5910(76)80042-3

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| year=2004

| volume=43

| issue=26

| pages=8378–8390

| doi=10.1021/ie049387v

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| year=2008

| volume=6

| issue=6

| pages=549–556

| doi=10.1016/j.partic.2008.07.011

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| year=2002

| volume=57

| issue=13

| pages=2395–2410

| doi=10.1016/s0009-2509(02)00140-9

}}</ref> describe discrete particle-continuum fluid modelling of gas-solid fluidised beds. Further applications of XDEM include thermal conversion of biomass on a backward and forward acting grate. Heat transfer in athermal/reacting [[packedparticulate bed]] reactorsystems was also solved and investigated, foras hotcomprehensively airreviewed streamingby upwardPeng throughet theal.<ref packedname="Peng">{{cite bedjournal to|last1=Peng heat|first1=Z. the|last2=Doroodchi particles,|first2=E. which|last3=Moghtaderi dependent|first3=B. on|date=2020 |title=Heat transfer modelling in Discrete Element Method (DEM)-based simulations of thermal processes: positionTheory and sizemodel experiencedevelopment different|journal=Progress heatin transferEnergy ratesand Combustion Science |volume=79,100847 |page=100847 |doi=10.1016/j.pecs.2020.100847|s2cid=218967044 }}</ref> The [[deformation (engineering)|deformation]] of a conveyor belt due to impacting [[granular material]] that is discharged over a chute represents an application in the field of [[Stress (mechanicalmechanics)|stress]]/[[Deformation (mechanics)|strain]] analysis.

{|

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[[Category:Numerical differential equations]]

[[Category:PartialComputational differential equationsphysics]]

[[Category:Continuum mechanics]]