Recent progress in understanding the theoretical basis and effectiveness of implicit large eddy simulation (ILES) is reviewed in both incompressible and compressible flow regimes. We use a modified equation analysis to show that the leading-order truncation error terms introduced by certain hybrid high resolution methods provide implicit subgrid scale (SGS) models similar in form to those of conventional mixed SGS models. Major properties of the implicit SGS model are related to the choice of high-order and low-order scheme components, the choice of a flux limiter, which determines how these schemes are blended locally depending on the flow, and the designed balance of the dissipation and dispersion contributions to the numerical solution. Comparative tests of ILES and classical LES in the Taylor–Green vortex case show robustness in capturing established theoretical findings for transition and turbulence decay.

1.
Sagaut
,
P.
, 2005,
Large Eddy Simulation for Incompressible Flows
,
3rd ed.
,
Springer
,
New York
.
2.
Ghosal
,
S.
, 1996, “
An Analysis of Numerical Errors in Large-Eddy Simulations of Turbulence
,”
J. Comput. Phys.
0021-9991,
125
, pp.
187
206
.
3.
Grinstein
,
F. F.
, and
Fureby
,
C.
, 2004, “
From Canonical to Complex Flows: Recent Progress on Monotonically Integrated LES
,”
Comput. Sci. Eng.
1521-9615,
6
, pp.
37
49
.
4.
Margolin
,
L. G.
,
Rider
,
W. G.
, and
Grinstein
,
F. F.
, 2006, “
Modeling Turbulent Flow With Implicit LES
,”
J. Turbul.
1468-5248,
7
, pp.
1
27
.
5.
Implicit Large Eddy Simulation: Computing Turbulent Fluid Dynamics
,
F. F.
Grinstein
,
L. G.
Margolin
, and
W. J.
Rider
, eds.,
Cambridge University Press
,
Cambridge, England
.
6.
Harten
,
A.
, 1983, “
High Resolution Schemes for Hyperbolic Conservation Laws
,”
J. Comput. Phys.
0021-9991,
49
, pp.
357
393
.
7.
P. J.
Boris
, 1990, “
On Large Eddy Simulation Using Subgrid Turbulence Models
,” in
Whither Turbulence? Turbulence at the Crossroads
,
J. L.
Lumley
, ed.,
Springer
,
New York
, p.
344
.
8.
Boris
,
J. P.
,
Grinstein
,
F. F.
,
Oran
,
E. S.
, and
Kolbe
,
R. L.
, 1992, “
New Insights Into Large Eddy Simulation
,”
Fluid Dyn. Res.
0169-5983,
10
, pp.
199
228
.
9.
Fureby
,
C.
, and
Grinstein
,
F. F.
, 1999, “
Monotonically Integrated Large Eddy Simulation of Free Shear Flows
,”
AIAA J.
0001-1452,
37
, pp.
544
556
.
10.
Margolin
,
L. G.
, and
Rider
,
W. J.
, 2002, “
A Rationale for Implicit Turbulence Modeling
,”
Int. J. Numer. Methods Fluids
0271-2091,
39
, pp.
821
841
.
11.
Brachet
,
M. E.
,
Meiron
,
D. I.
,
Orszag
,
S. A.
,
Nickel
,
B. G.
,
Morg
,
R. H.
, and
Frisch
,
U. J.
, 1983, “
Small-Scale Structure of the Taylor-Green Vortex
,”
J. Fluid Mech.
0022-1120,
130
, pp.
411
452
.
12.
Drikakis
,
D.
,
Fureby
,
C.
,
Grinstein
,
F. F.
, and
Youngs
,
D.
2007, “
Simulation of Transition and Turbulence Decay in the Taylor-Green Vortex
,”
J. Turbul.
1468-5248
8
(
020
), pp.
1
12
.
13.
Hirt
,
C. W.
, 1968, “
Heuristic Stability Theory for Finite Difference Equations
,”
J. Comput. Phys.
0021-9991,
2
, pp.
339
355
.
14.
Fureby
,
C.
, and
Grinstein
,
F. F.
, 2002, “
Large Eddy Simulation of High Reynolds-Number Free and Wall Bounded Flows
,”
J. Comput. Phys.
0021-9991,
181
, pp.
68
97
.
15.
Gurtin
,
M. E.
, 1981,
An Introduction to Continuum Mechanics
,
Academic
,
Orlando
.
16.
Kellogg
,
O. D.
, 1929,
Foundations of Potential Theory
,
Springer
,
New York
.
17.
Boris
,
J. P.
, and
Book
,
D. L.
, 1973, “
Flux-Corrected Transport I. SHASTA, A Fluid Transport Algorithm That Works
,”
J. Comput. Phys.
0021-9991,
11
, pp.
38
69
.
18.
Sweby
,
P. K.
, 1985, “
Flux Limiters
,” in
Numerical Methods for the Euler Equations of Fluid Dynamics
,
F.
Angrand
,
A.
Dervieux
,
J. A.
Desideri
, and
R.
Glowinski
, eds.,
Siam
,
Philadelphia
, pp.
48
65
.
19.
Drikakis
,
D.
, and
Rider
,
W.
, 2004,
High-Resolution Methods for Incompressible and Low-Speed Flows
,
Springer
,
New York
.
20.
Kuzmin
,
D.
,
Lohner
,
R.
, and
Turek
,
S.
, 2005,
High-Resolution Schemes for Convection Dominated Flows: 30Years of FCT
,
Springer
,
New York
.
21.
Drikakis
,
D.
,
Hahn
,
M.
,
Grinstein
,
F. F.
,
DeVore
,
C. R.
,
Fureby
,
C.
,
Liefvendahl
,
M.
, and
Youngs
,
D. L.
, 2007, “
Limiting Algorithms
,” in
Implicit Large Eddy Simulation: Computing Turbulent Fluid Dynamics
,
F. F.
Grinstein
,
L. G.
Margolin
, and
W. J.
Rider
, eds.,
Cambridge University Press
,
Cambridge, England
.
22.
Van der Bos
,
F.
, and
Geurts
,
B. J.
, 2006, “
Computational Turbulent Stress Closure for Large-Eddy Simulation of Compressible Flow
,”
J. Turbul.
1468-5248,
7
(
9
), pp.
1
16
.
23.
Brenner
,
H.
, 2005, “
Kinematics of Volume Transport
,”
Physica A
0378-4371,
349
, pp.
11
59
.
24.
Clark
,
R. A.
,
Ferziger
,
J. H.
, and
Reynolds
,
W. C.
, 1979, “
Evaluation of Sub-Grid Scale Models Using an Accurately Simulated Turbulent Flow
,”
J. Fluid Mech.
0022-1120,
118
, pp.
1
16
.
25.
Aldama
,
A. A.
, 1993, “
Leonard and Cross-Term Approximations in the Anisotropically Filtered Equations of Motion
,” in
Large Eddy Simulation of Complex Engineering and Geophysical Flows
,
B.
Galperin
and
S. A.
Orszag
, eds.,
Cambridge University Press
,
New York
.
26.
Shao
,
L.
,
Sarkar
,
S.
, and
Pantano
,
C.
, 1999, “
On the Relationship Between the Mean Flow and Subgrid Stresses in Large Eddy Simulation of Turbulent Shear Flows
,”
Phys. Fluids
1070-6631,
11
, pp.
1229
1248
.
27.
Borue
,
V.
, and
Orszag
,
S. A.
, 1998, “
Local Energy Flux and Subgrid-Scale Statistics in Three Dimensional Turbulence
,
J. Fluid Mech.
0022-1120,
366
, pp.
1
31
.
28.
van Leer
,
B.
, 1977, “
Towards the Ultimate Conservative Difference Scheme IV. A New Approach to Numerical Convection
,”
J. Comput. Phys.
0021-9991,
23
, pp.
276
299
.
29.
Margolin
,
L.
, 2005, private communication.
30.
Schlichting
,
H.
, 1979,
Boundary Layer Theory
,
McGraw-Hill
,
New York
, p.
585
.
31.
Baker
,
G. A.
, 1975,
Essentials of Padé Approximants
,
Academic
,
New York
.
32.
Frisch
,
U.
, 1995,
Turbulence
,
Cambridge University Press
,
Cambridge, England
, p.
57
.
33.
Porter
,
D. H.
,
Pouquet
,
A.
, and
Woodward
,
P. R.
, 1994, “
Kolmogorov-Like Spectra in Decaying Three-Dimensional Supersonic Flows
,”
Phys. Fluids
1070-6631,
6
, pp.
2133
2142
.
34.
Domaradzki
,
J. A.
,
Xiao
,
Z.
, and
Smolarkiewicz
,
P. K.
, 2003, “
Effective Eddy Viscosities in Implicit Modeling of Turbulent Flows
,”
Phys. Fluids
1070-6631,
15
, pp.
3890
3893
.
35.
Garnier
,
E.
,
Mossi
,
M.
,
Sagaut
,
P.
,
Comte
,
P.
, and
Deville
,
M.
, 1999, “
On the Use of Shock-Capturing Schemes for Large Eddy Simulation
,”
J. Comput. Phys.
0021-9991,
153
, pp.
273
311
.
36.
Margolin
,
L. G.
, and
Rider
,
W. J.
, 2007, “
Numerical Regularization: The Numerical Analysis of Implicit Subgrid Models
,” in
Implicit Large Eddy Simulation: Computing Turbulent Fluid Dynamics
,
F. F.
Grinstein
,
L. G.
Margolin
, and
W. J.
Rider
, eds.,
Cambridge University Press
,
Cambridge, England
.
37.
Shu
,
C.-W.
,
Don
,
W.-S.
,
Gottlieb
,
D.
,
Schilling
,
O.
, and
Jameson
,
L.
2005, “
Numerical Convergence Sudy of Nearly Incompressible, Inviscid Taylor-Green Vortex Flow
,”
J. Sci. Comput.
0885-7474,
24
, pp.
1
27
.
38.
Morf
,
R. H.
,
Orszag
,
S. A.
, and
Frisch
,
U.
, 1980, “
Spontaneous Singularity in Three-Dimensional, Inviscid, Incompressible Flow
,”
Phys. Rev. Lett.
0031-9007,
44
, pp.
572
575
.
39.
Brachet
,
M. E.
, 1991, “
Direct Numerical Simulation of Three-Dimensional Turbulence in the Taylor-Green Vortex
,”
Fluid Dyn. Res.
0169-5983,
8
, pp.
1
8
.
40.
DeVore
,
C. R.
, 1998, “
An Improved Limiter for Multidimensional Flux-Corrected Transport
,” NRL, Report No. NRL-MR-6440-98-8330.
41.
Zoltak
,
J.
, and
Drikakis
,
D.
, 1998, “
Hybrid Upwind Methods for the Simulation of Unsteady Shock-Wave Diffraction Over a Cylinder
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
162
, pp.
165
185
.
42.
Bagabir
,
A.
, and
Drikakis
,
D.
, 2004, “
Numerical Experiments Using High-Resolution Schemes for Unsteady, Inviscid, Compressible Flows
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
193
, pp.
4675
4705
.
43.
Eberle
,
A.
, 1987, “
Characteristic Flux Averaging Approach to the Solution of Euler’s Equations
,”
VKI Lecture Series
, Computational Fluid Dynamics Report No. 1987-04.
44.
Youngs
,
D. L.
, 1991, “
Three-Dimensional Numerical Simulation of Turbulent Mixing by Rayleigh-Taylor Instability
,”
Phys. Fluids A
0899-8213,
3
, pp.
1312
1320
.
45.
Germano
,
M.
,
Piomelli
,
U.
,
Moin
,
P.
, and
Cabot
,
W. H.
, 1994, “
A Dynamic Sub Grid Scale Eddy Viscosity Model
,”
Phys. Fluids A
0899-8213,
3
, pp.
1760
1765
.
46.
Schumann
,
U.
, 1975, “
Subgrid Scale Model for Finite Difference Simulation of Turbulent Flows in Plane Channels and Annuli
,”
J. Comput. Phys.
0021-9991,
18
, pp.
376
404
.
47.
Bardina
,
J.
,
Ferziger
,
J. H.
, and
Reynolds
,
W. C.
, 1980, “
Improved Subgrid Scale Models for Large Eddy Simulations
,” AIAA Paper No. 80-1357.
48.
Jeong
,
J.
, and
Hussain
,
F.
, 1995, “
On the Identification of a Vortex
,”
J. Fluid Mech.
0022-1120,
285
, pp.
69
94
.
49.
Jimenez
,
J.
,
Wray
,
A.
,
Saffman
,
P.
, and
Rogallo
,
R.
, 1993, “
The Structure of Intense Vorticity in Isotropic Turbulence
,”
J. Fluid Mech.
0022-1120,
255
, pp.
65
90
.
50.
Lesieur
,
M.
, and
Ossia
,
S.
, 2000, “
3D Isotropic at Very High Reynolds Numbers: EDQNM Study
,”
J. Turbul.
1468-5248,
1
(
007
), pp.
1
25
.
51.
Skrbek
,
L.
, and
Stalp
,
S. R.
, 2000, “
On the Decay of Homogeneous Isotropic Turbulence
,”
Phys. Fluids
1070-6631,
12
, pp.
1997
2019
.
52.
Margolin
,
L. G.
, and
Rider
,
W. J.
, 2005, “
The Design and Construction of Implicit Subgrid Scale Models
,”
Int. J. Numer. Methods Fluids
0271-2091,
47
, pp.
1173
1179
.
You do not currently have access to this content.