A promising large-eddy simulation (LES) approach is monotonically integrated LES (MILES) which involves solving the Navier-Stokes equations using high-resolution monotone algorithms. In MILES, the subgrid scale (SGS) flow physics is provided by intrinsic, nonlinear, high-frequency filters built into the discretization and implicit SGS models. Mathematical and physical aspects of implicit SGS modeling using nonlinear flux-limiters are addressed using a formalism based on the modified LES equations approach. Detailed properties of the implicit subgrid model are related to the flux limiter, which in turn depends on the specifics of the numerical scheme; we illustrate how the latter properties can directly affect their potential in the MILES framework. Major unresolved issues relevant to LES of complex practical turbulent flows are discussed in this context, including some aspects of boundary condition modeling and overall computational model validation.

Issue Section:
Technical Papers
Keywords:
flow simulation, turbulence, Navier-Stokes equations, computational fluid dynamics
Topics:
Flow (Dynamics), Turbulence, Modeling
1.
Sagaut
,
P.
, 2001, Large Eddy Simulation for Incompressible Flows, Springer-Verlag, Heidelberg.
2.
Lesieur
,
M.
, and
Metais
,
O.
,
1996
, “
New Trends in Large Eddy Simulations of Turbulence
,”
Annu. Rev. Fluid Mech.
,
28
, p.
45
45
.
3.
Fureby
,
C.
,
Tabor
,
G.
,
Weller
,
H.
, and
Gosman
,
D.
,
1997
, “
A Comparative Study of Sub Grid Scale Models in Homogeneous Isotropic Turbulence
,”
Phys. Fluids
,
9
, p.
1416
1416
.
4.
Metais
,
O.
, and
Lesieur
,
M.
,
1992
, “
Spectral Large Eddy Simulation of Isotropic and Stably Stratified Turbulence
,”
J. Fluid Mech.
,
239
, p.
157
157
.
5.
McComb, W. D., 1994, The Physics of Fluid Turbulence, Clarendon Press, Oxford.
6.
Kuo
,
A. Y.
, and
Corrsin
,
S.
,
1971
, “
Experiment on the Geometry of the Fine-Structure Regions in Fully Developed Turbulent Fluid
,”
J. Fluid Mech.
,
56
, p.
447
447
.
7.
Sigga
,
E. D.
, and
Patterson
,
G. S.
,
1988
, “
Intermittency Effects in a Numerical Simulation of Stationary Three Dimensional Turbulence
,”
J. Fluid Mech.
,
86
, p.
567
567
.
8.
Jimenez
,
J.
,
Wray
,
A.
,
Saffman
,
P.
, and
Rogallo
,
R.
,
1993
, “
The Structure of Intense Vorticity in Isotropic Turbulence
,”
J. Fluid Mech.
,
255
, p.
65
65
.
9.
Vincent
,
A.
, and
Meneguzzi
,
M.
,
1994
, “
The Spatial Structure and Statistical Properties of Homogeneous Turbulence
,”
J. Fluid Mech.
,
225
, p.
1
1
.
10.
Kerr
,
R. M.
,
1985
, “
Higher Order Derivative Correlation and the Alignment of Small Scale Structures in Numerical Turbulence
,”
J. Fluid Mech.
,
153
, p.
31
31
.
11.
Ashurst
,
W. T.
,
Kerstein
,
A. R.
,
Kerr
,
R. M.
, and
Gibson
,
C. H.
,
1987
, “
Alignment of Vorticity of Scalar Gradients With Strain Rate in Simulated Navier Stokes Turbulence
,”
Phys. Fluids
,
30
, p.
2343
2343
.
12.
Misra
,
A.
, and
Pullin
,
D. I.
,
1997
, “
A Vortex Based Subgrid Stress Model for Large Eddy Simulation
,”
Phys. Fluids
,
9
, p.
2443
2443
.
13.
Bagget, J. S., Jime´nez, J., and Kravchenko, A. G., 1997, “Resolution Requirements in Large Eddy Simulations of Shear Flows,” Ann. Res. Briefs, CTR, NASA Ames/Stanford University, p. 55.
14.
Jimenez, J., 1998, private communication; see also AIAA 98-2891.
15.
Boris
,
J. P.
, and
Book
,
D. L.
,
1973
, “
Flux Corrected Transport I, SHASTA, a Fluid Transport Algorithm That Works
,”
J. Comput. Phys.
,
11
, p.
38
38
.
16.
Colella
,
P.
, and
Woodward
,
P.
,
1984
, “
The Piecewise Parabolic Method (PPM) for Gas Dynamic Simulations
,”
J. Comput. Phys.
,
54
, p.
174
174
.
17.
Sytine
,
I. V.
,
Porter
,
D. H.
,
Woodward
,
P. R.
, and
Hodson
,
S. W.
,
2000
, “
Convergence Tests for the Piecewise Parabolic Method and Navier-Stokes Solutions for Homogeneous Compressible Turbulence
,”
J. Comput. Phys.
,
158
, p.
225
225
.
18.
Garnier
,
E.
,
Mossi
,
M.
,
Sagaut
,
P.
,
Comte
,
P.
, and
Deville
,
M.
,
2000
, “
On the Use of Shock-Capturing Schemes for Large Eddy Simulation
,”
J. Comput. Phys.
,
153
, p.
273
273
.
19.
Okong’o
,
N.
,
Knight
,
D. D.
, and
Zhou
,
G.
,
2000
, “
Large Eddy Simulations Using an Unstructured Grid Compressible Navier-Stokes Algorithm
,”
Int. J. Comput. Fluid Dyn.
,
13
, p.
303
303
.
20.
Margolin
,
L. G.
,
Smolarkiewicz
,
P. K.
, and
Sorbjan
,
Z.
,
1999
, “
Large-Eddy Simulation of Convective Boundary Layers Using Non-Oscillatory Differencing
,”
Physica D
,
133
, p.
390
390
.
21.
Karamanos
,
G.-S.
, and
Karniadakis
,
G. E.
,
2000
, “
A Spectral Vanishing Viscosity Method for Large-Eddy Simulations
,”
J. Comput. Phys.
,
163
, p.
22
22
.
22.
Boris
,
J. P.
,
Grinstein
,
F. F.
,
Oran
,
E. S.
, and
Kolbe
,
R. J.
,
1992
, “
New Insights Into Large Eddy Simulation
,”
Fluid Dyn. Res.
,
10
, p.
199
199
.
23.
Fureby
,
C.
, and
Grinstein
,
F. F.
,
1999
, “
Monotonically Integrated Large Eddy Simulation of Free Shear Flows
,”
AIAA J.
,
37
, p.
544
544
.
24.
Fureby
,
C.
, and
Grinstein
,
F. F.
,
2002
, “
Large Eddy Simulation of High Reynolds Number Free and Wall Bounded Flows
,”
J. Comput. Phys.
,
181
, p.
68
68
.
25.
Ferziger, J. H., and Leslie, D. C., 1979, “Large Eddy Simulation—A Predictive Approach to Turbulent Flow Computation,” AIAA paper 79-1441.
26.
Fureby
,
C.
, and
Tabor
,
G.
, 1997, “Mathematical and Physical Constraints on Large Eddy Simulations,” J. Theoretical Fluid Dyn., 9, p. 85.
27.
Speziale
,
C. G.
,
1985
, “
Galilean Invariance of Sub Grid Scale Stress Models in Large Eddy Simulations of Turbulence
,”
J. Fluid Mech.
,
156
, p.
55
55
.
28.
Vreman
,
B.
,
Geurts
,
B.
, and
Kuerten
,
H.
,
1994
, “
Realizability Conditions for the Turbulent Stress Tensor in Large Eddy Simulation
,”
J. Fluid Mech.
,
278
, p.
351
351
.
29.
Ghosal
,
S.
, and
Moin
,
P.
,
1995
, “
The Basic Equations for the Large Eddy Simulation of Turbulent Flows in Complex Geometry
,”
J. Comput. Phys.
,
118
, p.
24
24
.
30.
Lesieur
,
M.
, and
Metais
,
O.
,
1996
, “
New Trends in Large Eddy Simulations of Turbulence
,”
Annu. Rev. Fluid Mech.
,
28
, p.
45
45
.
31.
Sullivan
,
P. P.
,
McWilliams
,
J. C.
, and
Moeng
,
C. H.
,
1994
, “
A Subgrid Scale Model for Large Eddy Simulation of Planetary Boundary-Layer Flows
,”
Bound. Layer Meth.
,
71
, p.
247
247
.
32.
Fureby, C., 2001, “Towards Large Eddy Simulation of Complex Flows,” Direct and Large Eddy Simulation IV, R. Friedrich and W. Rodi, eds., Kluwer, Dordrecht, The Netherlands.
33.
Lund, T. S., and Novikov, E. A., 1994, “Parameterization of Subgrid-Scale Stress by the Velocity Gradient Tensor,” Annual Res. Briefs, Center for Turbulence Research, p. 185.
34.
Deardorff
,
J. W.
,
1973
, “
The Use of Subgrid Transport Equations in a Three-Dimensional Model of Atmospherical Turbulence
,”
ASME J. Fluids Eng.
,
95
, p.
429
429
.
35.
Bardina, J., Ferziger, J. H., and Reynolds, W. C., 1980, “Improved Subgrid Scale Models for Large Eddy Simulations,” AIAA Paper No. 80-1357.
36.
Liu
,
S.
,
Meneveau
,
C.
, and
Katz
,
J.
,
1994
, “
On the Properties of Similarity Subgridscale Models as Deduced From Measurements in a Turbulent Jet
,”
J. Fluid Mech.
,
275
, p.
83
83
.
37.
Hirsch, C., 1999, Numerical Computation of Internal and External Flows, John Wiley and Sons, New York.
38.
Fureby
,
C.
,
Tabor
,
G.
,
Weller
,
H.
, and
Gosman
,
D.
,
1997
, “
A Comparative Study of Sub Grid Scale Models in Homogeneous Isotropic Turbulence
,”
Phys. Fluids
,
9
, p.
1416
1416
.
39.
Godunov
,
S. K.
,
1959
, “
A Difference Method for Numerical Calculation of Discontinuous Solutions of the Equations of Hydrodynamics
,”
Mat. Sb.
,
47
, p.
271
271
.
40.
LeVeque, R. J., 1992, Numerical Methods for Conservation Laws, 2nd Ed., Birkhu¨ser Verlag, Berlin.
41.
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
,
11
, p.
1229
1229
.
42.
Borue
,
V.
, and
Orszag
,
S. A.
,
1998
, “
Local Energy Flux and Subgrid-Scale Statistics in Three Dimensional Turbulence
,”
J. Fluid Mech.
,
366
, p.
1
1
.
43.
Margolin
,
L. G.
, and
Rider
,
W. J.
,
2002
, “
A Rationale for Implicit Turbulence Modeling
,”
Intl. J. Numer. Meth. Fluids
,
39
, p.
821
821
.
44.
Harten
,
A.
,
1984
, “
On a Class of High Resolution Total Variation Stable Finite Difference Schemes
,”
SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal.
,
21
, p.
1
1
.
45.
Sweby
,
P. K.
,
1984
, “
High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws
,”
SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal.
,
21
, p.
995
995
.
46.
Roe, P. L., 1985, Some Contributions to the Modelling of Discontinuous Flows (Lectures in Applied Mathematics), Springer-Verlag, Heidelberg, 22, p. 163.
47.
Jasak
,
H.
,
Weller
,
H. G.
, and
Gosman
,
A. D.
,
1999
, “
High Resolution NVD Differencing Scheme for Arbitrarily Unstructured Meshes
,”
Int. J. Numer. Methods Fluids
,
31
, p.
431
431
.
48.
Sandham, N. D., and Howard, R. J. A., 1995, “Statistics Databases From Direct Numerical Simulation of Fully-Developed Turbulent Channel Flow,” private communication, QMW-EP-1106, Queen Mary and Westfield College, Department of Engineering, London.
49.
Grinstein
,
F. F.
et al.,
1996
, “
Streamwise and Spanwise Vortex Interaction in an Axisymmetric Jet. A Computational and Experimental Study
,”
Phys. Fluids
,
8
, p.
1515
1515
.
50.
Grinstein
,
F. F.
,
2001
, “
Vortex Dynamics and Entrainment in Regular Free Jets
,”
J. Fluid Mech.
,
437
, p.
69
69
.
51.
Grinstein, F. F., 1998, “Vortex Dynamics and Aeroacoustics of Low Aspect Ratio Rectangular Jets,” Proc. AFOSR Conference on Turbulence and Internal Flows, Annapolis, MD, Aug. 18–20, AFOSR, Washsington, DC, p. 131.
52.
Grinstein
,
F. F.
, and
DeVore
,
C. R.
,
2002
, “
On Global Instabilities in Countercurrent Jets
,”
Phys. Fluids
,
14
, p.
1095
1095
.
53.
Hussain
,
F.
, and
Husain
,
H. S.
,
1989
, “
Elliptic Jets. Part I. Characteristics of Unexcited and Excited Jets
,”
J. Fluid Mech.
,
208
, p.
257
257
.
54.
Tam, C., 1998, “LES for Aeroacoustics,” AIAA Paper 98-2805.
55.
Brown
,
G.
, and
Roshko
,
A.
,
1974
, “
On Density Effects and Large Structure in Turbulent Mixing Layers
,”
J. Fluid Mech.
,
64
, p.
775
775
.
56.
Mitchell
,
B. E.
,
Lele
,
S. K.
, and
Moin
,
P.
,
1999
, “
Direct Computation of the Sound Generated by Vortex Pairing in an Axisymmetric Jet
,”
J. Fluid Mech.
,
383
, p.
113
113
.
57.
Grinstein
,
F. F.
,
Oran
,
E. S.
, and
Boris
,
J. P.
,
1991
, “
Pressure Field, Feedback and Global Instabilities of Subsonic Spatially Developing Mixing Layers
,”
Phys. Fluids A
,
A3
, p.
2401
2401
.
58.
Bridges
,
J.
, and
Hussain
,
F.
,
1992
, “
Direct Evaluation of Aeroacoustic Theory in a Jet
,”
J. Fluid Mech.
,
240
, p.
469
469
.
59.
Tam
,
C. K. W.
, and
Webb
,
J. C.
,
1993
, “
Dispersion Related Preserving Finite Difference Schemes for Computational Aeroacoustics
,”
J. Comput. Phys.
,
107
, p.
1262
1262
.
60.
Germano
,
M.
,
Piomelli
,
U.
,
Moin
,
P.
, and
Cabot
,
W. H.
,
1994
, “
A Dynamic Sub Grid Scale Eddy Viscosity Model
,”
Phys. Fluids A
,
A3
, p.
1760
1760
.
61.
Voke
,
P.
, 1996, “Subgrid-Scale Modeling at Low Mesh Reynolds Number,” J. Theoret. Fluid Dyn., 8, p. 131.
62.
Sagaut
,
P.
,
1996
, “
Numerical Simulations of Separated Flows With Subgrid Models
,”
Rech. Aerosp.
,
1
, p.
51
51
.
63.
Gro¨tzbach, G., 1987, “Direct Numerical and large Eddy Simulation of Turbulent Channel Flows,” Encyclopedia of Fluid Mechanics, N. P. Cheremisinoff, ed., 34, Gulf Publishing, Houston, p. 1337.
64.
Piomelli
,
U.
,
Ferziger
,
J.
, and
Moin
,
P.
,
1981
, “
New Approximate Boundary Conditions for Large Eddy Simulations of Wall Bounded Flows
,”
Phys. Fluids
,
1
, p.
1061
1061
.
65.
Cabot
,
W.
, and
Moin
,
P.
,
2000
, “
Approximate Wall Boundary Conditions in the Large Eddy Simulation of High Reynolds Number Flows
,”
Flow, Turbul. Combust.
,
63
, p.
269
269
.
66.
Menon, S., 2001, private communication.
67.
Fureby, C., Persson, L., and Svanstedt, N., 2002, “On Homogenization Based Methods for Large Eddy Simulation,” AIAA Paper No 02-7462; J. Fluids Engineering, in press.
68.
Antonia
,
R. A.
,
Teitel
,
M.
,
Kim
,
J.
, and
Browne
,
L. W. B.
,
1992
, “
Low-Reynolds-Number Effects in a Fully Developed Turbulent Channel Flow
,”
J. Fluid Mech.
,
236
, p.
579
579
.
69.
Wei
,
T.
, and
Willmarth
,
W. W.
,
1989
, “
Reynolds Number Effects on the Structure of a Turbulent Channel Flow
,”
J. Fluid Mech.
,
204
, p.
57
57
.
70.
Dean
,
R. B.
,
1978
, “
Reynolds Number Dependence of Skin Friction and Other Bulk Flow Variables in Two-Dimensional Rectangular Duct Flow
,”
ASME J. Fluids Eng.
,
100
, p.
215
215
.
71.
Smith, C. R., and Walker, J. D. A., 1995, “Turbulent Wall-Layer Vortices,” Fluid Vortices, S. Green ed., Kluwer, Dordrecht, The Netherlands.
72.
Blackwelder
,
R. F.
,
1979
, “
Boundary Layer Transition
,”
Phys. Fluids
,
22
, p.
583
583
.
73.
Jeong
,
J.
,
Hussain
,
F.
,
Shoppa
,
W.
, and
Kim
,
J.
,
1997
, “
Coherent Structures Near the Wall in a Turbulent Channel Flow
,”
J. Fluid Mech.
,
332
, p.
185
185
.
74.
Moin
,
P.
, and
Kim
,
J.
,
1982
, “
Large Eddy Simulation of Turbulent Channel Flow
,”
J. Fluid Mech.
,
118
, p.
341
341
.
75.
Comte-Bellot, G., 1965, “Ecoulment Turbulent Entre Deaux Parois Paralleles,” Publications Scientifiques et Techniques du Ministere de l’Air No. 419.
76.
Author please insert Ref. 76
77.
Colonius
,
T.
,
Lele
,
S. K.
, and
Moin
,
P.
,
1993
, “
Boundary Conditions for Direct Computations of Aerodynamic Sound
,”
AIAA J.
,
31
, p.
1574
1574
.
78.
Poinsot
,
T. J.
, and
Lele
,
S. K.
,
1994
, “
Boundary Conditions for Direct Simulations of Compressible Viscous Flows
,”
J. Comput. Phys.
,
101
, p.
104
104
.
79.
Grinstein
,
F. F.
,
1994
, “
Open Boundary Conditions in the Simulation of Subsonic Turbulent Shear Flows
,”
J. Comput. Phys.
,
115
, p.
43
43
.
80.
Turkel
,
E.
,
1998
, “
Special Issue on Absorbing Boundary Conditions
,”
Appl. Numer. Math.
,
27
, p.
327
327
.
81.
Kong
,
H.
,
Choi
,
H.
, and
Lee
,
J. S.
,
2000
, “
Direct Numerical Simulation of Turbulent Thermal Boundary Layers
,”
Phys. Fluids
,
12
, p.
2555
2555
.
82.
Strikwerda
,
J. C.
,
1977
, “
Initial Value Boundary Value Problems for Incompletely Parabolic Systems
,”
Commun. Pure Appl. Math.
,
30
, p.
797
797
.
83.
Thompson
,
K.
,
1987
, “
Time Dependent Boundary Conditions for Hyperbolic Systems
,”
J. Comput. Phys.
,
68
, p.
1
1
.
84.
Thompson
,
K.
,
1990
, “
Time Dependent Boundary Conditions for Hyperbolic Systems, II
,”
J. Comput. Phys.
,
89
, p.
439
439
.
85.
Pitz
,
R. W.
, and
Daily
,
J. W.
,
1983
, “
Experimental Study of Combustion in a Turbulent Free Shear Layer Formed at a Rearward Facing Step
,”
AIAA J.
,
21
, p.
1565
1565
.
86.
Pitz, R. W., and Daily, J. W., 1981, “Experimental Study of Combustion: The Turbulent Structure of a Reacting Shear Layer Formed at a Rearward Facing Step,” NASA Contractor Report 165427.
87.
Fureby
,
C.
,
1999
, “
Large Eddy Simulation of Rearward Facing Step Flow
,”
AIAA J.
,
37
, p.
1401
1401
.
88.
Eaton, J. K., and Johnston, J. P., 1980, “Turbulent Flow Reattachment: An Experimental Study of the Flow and Structure Behind a Backward Facing Step,” Stanford University, Report No. MD-39.
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