Editing Large eddy simulation (section)

{{Short description|Mathematical model for turbulence}}
[[Image:LES Turbulent Velocity Field.png|300px|right|thumb|Large eddy simulation of a [[turbulent]] gas velocity field.]]
'''Large eddy simulation''' ('''LES''') is a mathematical model for [[turbulence]] used in [[computational fluid dynamics]]. It was initially proposed in 1963 by [[Joseph Smagorinsky]] to simulate atmospheric air currents,<ref name="Smagorinsky_1963">{{Cite journal
| last=Smagorinsky
| first=Joseph
| title=General Circulation Experiments with the Primitive Equations
| journal=Monthly Weather Review
|date=March 1963
| volume=91
| issue=3
| pages=99–164|bibcode = 1963MWRv...91...99S |doi = 10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2 | doi-access=free
}}</ref> and first explored by Deardorff (1970).<ref name="Deardorff_1970">{{Cite journal
|last=Deardorff
|first=James
|title=A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers
|journal=[[Journal of Fluid Mechanics]]
|year=1970
|volume=41
|issue=2
|pages=453–480|bibcode = 1970JFM....41..453D |doi = 10.1017/S0022112070000691 |s2cid=121884175
}}</ref>  LES is currently applied in a wide variety of engineering applications, including [[combustion]],<ref name="Pitsch_2006">{{Cite journal
|last=Pitsch
|first=Heinz
|title=Large-Eddy Simulation of Turbulent Combustion
|journal=Annual Review of Fluid Mechanics
|year=2006
|volume=38
|issue=1
|pages=453–482|bibcode = 2006AnRFM..38..453P |doi = 10.1146/annurev.fluid.38.050304.092133 |s2cid=5487815
|url=http://caltechconf.library.caltech.edu/145/1/Abstract1.pdf
}}</ref> acoustics,<ref name="Wagner_2007">{{cite book
|last1=Wagner
|first1=Claus
|last2=Hüttl
|first2=Thomas
|last3=Sagaut
|first3=Pierre
|title=Large-Eddy Simulation for Acoustics
|publisher=Cambridge University Press
|year=2007
|isbn=978-0-521-87144-0
}}</ref> and simulations of the atmospheric boundary layer.<ref name="Sullivan_1994">{{cite journal
|last1=Sullivan
|first1=Peter P.
|last2=McWilliams
|first2=James C.
|last3=Moeng
|first3=Chin-Hoh
|title=A subgrid-scale model for large-eddy simulation of planetary boundary-layer flows
|journal=Boundary-Layer Meteorology
|year=1994
|volume=71
|number=3
|issn=0006-8314
|pages=247–276
|doi=10.1007/BF00713741 |bibcode = 1994BoLMe..71..247S |citeseerx=10.1.1.463.6006
|s2cid=53051046
}}</ref>

The simulation of turbulent flows by numerically solving the [[Navier–Stokes equations]] requires resolving a very wide range of time and length scales, all of which affect the flow field.  Such a resolution can be achieved with [[direct numerical simulation]] (DNS), but DNS is computationally expensive, and its cost prohibits simulation of  practical engineering systems with complex geometry or flow configurations, such as turbulent jets, pumps, vehicles, and landing gear.

The principal idea behind LES is to reduce the computational cost by ignoring the smallest length scales, which are the most computationally expensive to resolve, via [[Filter (signal processing)|low-pass filtering]] of the Navier–Stokes equations. Such a low-pass filtering, which can be viewed as a time- and spatial-averaging, effectively removes small-scale information from the numerical solution.  This information is not irrelevant, however, and its effect on the flow field must be modelled, a task which is an active area of research for problems in which small-scales can play an important role, such as near-wall flows,<ref name="piomelli-02">{{cite journal|author1=Piomelli, Ugo |author2=Elias Balaras |title= Wall-layer models for large-eddy simulations.|journal=Annual Review of Fluid Mechanics|year=2002|volume=34|issue=34 |pages=349–374 |doi=10.1146/annurev.fluid.34.082901.144919|bibcode=2002AnRFM..34..349P}}</ref><ref name="spalart-09">{{cite journal|last=Spalart |first=Philippe R. |title= Detached-eddy simulation |journal=Annual Review of Fluid Mechanics |year=2009 |volume=41 |issue=1 |doi=10.1146/annurev.fluid.010908.165130 |pages=181–202 |bibcode=2009AnRFM..41..181S }}</ref> reacting flows,<ref name="Pitsch_2006" /> and multiphase flows.<ref name="fox-12">{{cite journal|last=Fox, R. O.|year=2012|title=Large-eddy-simulation tools for multiphase flows.|journal=Annual Review of Fluid Mechanics|volume=44|issue=1|pages=47–76|bibcode=2012AnRFM..44...47F|doi=10.1146/annurev-fluid-120710-101118}}</ref>