We employ renormalized viscosity to perform large eddy simulations (LESs) of decaying homogeneous and isotropic turbulence in a cubical domain. We perform a direct numerical simulation (DNS) on 5123 and 2563 grids and LES on 323, 643, and 1283 grids with the same initial conditions in the resolved scales for a flow with Taylor Reynolds number Reλ = 210. We observe good agreement between LES and DNS results for the temporal evolution of turbulence kinetic energy Eu(t), kinetic energy spectrum Eu(k), and kinetic energy flux Πu(k). Also, the large-scale structures of the flow in LES are similar to those in DNS. These results establish the suitability of our renormalized viscosity scheme for LES.
REFERENCES
1.
C.
Meneveau
and J.
Katz
, “Scale-invariance and turbulence models for large-eddy simulation
,” Annu. Rev. Fluid Mech.
32
(1
), 1
–32
(2000
).2.
M.
Lesieur
and O.
Metais
, “New trends in large-eddy simulations of turbulence
,” Annu. Rev. Fluid. Mech.
28
(1
), 45
–82
(1996
).3.
P.
Sagaut
, Large Eddy Simulation for Incompressible Flows: An Introduction
(Springer-Varlag
, Berlin
, 2006
).4.
A. N.
Kolmogorov
, “Dissipation of energy in locally isotropic turbulence
,” Dokl. Acad. Nauk SSSR
32
(1
), 16
–18
(1941
).5.
A. N.
Kolmogorov
, “The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers
,” Dokl. Acad. Nauk SSSR
30
(4
), 301
–305
(1941
).6.
M. K.
Verma
, A.
Kumar
, P.
Kumar
, S.
Barman
, A. G.
Chatterjee
, R.
Samtaney
, and R. A.
Stepanov
, “Energy spectra and fluxes in dissipation range of turbulent and laminar flows
,” Fluid Dyn.
53
(6
), 862
–873
(2018
).7.
R. H.
Kraichnan
, “Eddy viscosity in two and three dimensions
,” J. Atmos. Sci.
33
, 1521
–1536
(1976
).8.
J.
Smagorinsky
, “General circulation experiments with the primitive equations: I. The basic experiment
,” Mon. Weather Rev.
91
(3
), 99
–164
(1963
).9.
J. W.
Deardorff
, “A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers
,” J. Fluid Mech.
41
, 453
–480
(1970
).10.
M.
Germano
, U.
Piomelli
, P.
Moin
, and W. H.
Cabot
, “A dynamic subgrid-scale eddy viscosity model
,” Phys. Fluids A
3
(7
), 1760
–1765
(1991
).11.
D. K.
Lilly
, “A proposed modification of the Germano subgrid-scale closure method
,” Phys. Fluids A
4
, 633
–635
(1992
).12.
M.
Abkar
and F.
Porté-Agel
, “Influence of atmospheric stability on wind-turbine wakes: A large-eddy simulation study
,” Phys. Fluids
27
(3
), 035104
(2015
).13.
J. R.
Chasnov
, “Simulation of the Kolmogorov inertial subrange using an improved subgrid model
,” Phys. Fluids A
3
(1
), 188
–200
(1991
).14.
G.
Dantinne
, H.
Jeanmart
, G. S.
Winckelmans
, V.
Legat
, and D.
Carati
, “Hyperviscosity and vorticity-based models for subgrid scale modeling
,” Appl. Sci. Res.
59
(4
), 409
–420
(1997
).15.
J.-P.
Chollet
and M.
Lesieur
, “Parameterization of small scales of three-dimensional isotropic turbulence utilizing spectral closures
,” J. Atmos. Sci.
38
(12
), 2747
–2757
(1981
).16.
O.
Métais
and M.
Lesieur
, “Spectral large-eddy simulation of isotropic and stably stratified turbulence
,” J. Fluid Mech.
239
, 157
–194
(1992
).17.
F.
Sarghini
, U.
Piomelli
, and E.
Balaras
, “Scale-similar models for large-eddy simulations
,” Phys. Fluids
11
(6
), 1596
–1607
(1999
).18.
U.
Piomelli
, W. H.
Cabot
, P.
Moin
, and S.
Lee
, “Subgrid-scale backscatter in turbulent and transitional flows
,” Phys. Fluids A
3
(7
), 1766
–1771
(1991
).19.
S.
Prinz
, T.
Boeck
, and J.
Schumacher
, “Large eddy simulation of hydrodynamic and magnetohydrodynamic channel flows with a collocated finite-volume scheme and improved subgrid-scale modeling
,” Eur. J. Mech. - B/Fluids
72
, 189
–198
(2018
).20.
A.
Cimarelli
and E.
De Angelis
, “The physics of energy transfer toward improved subgrid-scale models
,” Phys. Fluids
26
(5
), 055103
(2014
).21.
D.
Dupuy
, A.
Toutant
, and F.
Bataille
, “A posteriori tests of subgrid-scale models in an isothermal turbulent channel flow
,” Phys. Fluids
31
(4
), 045105
(2019
).22.
S.
Heinz
, “The large eddy simulation capability of Reynolds-averaged Navier-Stokes equations: Analytical results
,” Phys. Fluids
31
(2
), 021702
(2019
).23.
S.
Menon
, P. K.
Yeung
, and W. W.
Kim
, “Effect of subgrid models on the computed interscale energy transfer in isotropic turbulence
,” Comput. Fluids
25
(2
), 165
–180
(1996
).24.
P.
Perlekar
, D.
Mitra
, and R.
Pandit
, “Manifestations of drag reduction by polymer additives in decaying, homogeneous, isotropic turbulence
,” Phys. Rev. Lett.
97
(26
), 264501
(2006
).25.
P.
Perlekar
, D.
Mitra
, and R.
Pandit
, “Direct numerical simulations of statistically steady, homogeneous, isotropic fluid turbulence with polymer additives
,” Phys. Rev. E
82
(6
), 066313
(2010
).26.
J. A.
Domaradzki
and E. M.
Saiki
, “A subgrid-scale model based on the estimation of unresolved scales of turbulence
,” Phys. Fluids
9
(7
), 2148
–2164
(1997
).27.
A.
Misra
and D. I.
Pullin
, “A vortex-based subgrid stress model for large-eddy simulation
,” Phys. Fluids
9
(8
), 2443
–2454
(1997
).28.
W.
Cheng
, D. I.
Pullin
, and R.
Samtaney
, “Large-eddy simulation of separation and reattachment of a flat plate turbulent boundary layer
,” J. Fluid Mech.
785
, 78
–108
(2015
).29.
B.
Kosović
, D. I.
Pullin
, and R.
Samtaney
, “Subgrid-scale modeling for large-eddy simulations of compressible turbulence
,” Phys. Fluids
14
(4
), 1511
–1522
(2002
).30.
V.
Yakhot
and S. A.
Orszag
, “Renormalization group analysis of turbulence. I. Basic theory
,” J. Sci. Comput.
1
(1
), 3
–51
(1986
).31.
32.
W. D.
McComb
, Homogeneous, Isotropic Turbulence: Phenomenology, Renormalization and Statistical Closures
(Oxford University Press
, 2014
).33.
Y.
Zhou
, G.
Vahala
, and M.
Hossain
, “Renormalization-group theory for the eddy viscosity in subgrid modeling
,” Phys. Rev. A
37
(7
), 2590
–2598
(1988
).34.
Y.
Zhou
, “Renormalization group theory for fluid and plasma turbulence
,” Phys. Rep.
488
(1
), 1
–49
(2010
).35.
A.
Berera
, M.
Salewski
, and W. D.
McComb
, “Eulerian field-theoretic closure formalisms for fluid turbulence
,” Phys. Rev. E
87
(1
), 013007
(2013
).36.
W. D.
McComb
and A. G.
Watt
, “Two-field theory of incompressible-fluid turbulence
,” Phys. Rev. A
46
(8
), 4797
–4812
(1992
).37.
M. K.
Verma
, “Statistical theory of magnetohydrodynamic turbulence: Recent results
,” Phys. Rep.
401
(5
), 229
–380
(2004
).38.
G. L.
Eyink
and H.
Aluie
, “Localness of energy cascade in hydrodynamic turbulence. I. Smooth coarse graining
,” Phys. Fluids
21
, 115107
(2009
).39.
D.
Carati
and L.
Brenig
, “Renormalization-group method for anisotropic turbulent transport
,” Phys. Rev. A
40
(9
), 5193
(1989
).40.
M. K.
Verma
and S.
Kumar
, “Large-eddy simulations of fluid and magnetohydrodynamic turbulence using renormalized parameters
,” Pramana
63
(3
), 553
–561
(2004
).41.
W. D.
McComb
, Renormalization Methods: A Guide for Beginners
(Oxford University Press
, Oxford
, 2004
).42.
M. K.
Verma
, “Introduction to statistical theory of fluid turbulence
,” e-print arXiv:nlin/0510069 (2005
).43.
G.
Dar
, M. K.
Verma
, and V.
Eswaran
, “Energy transfer in two-dimensional magnetohydrodynamic turbulence: Formalism and numerical results
,” Physica D
157
(3
), 207
–225
(2001
).44.
M. K.
Verma
, A. G.
Chatterjee
, R. K.
Yadav
, S.
Paul
, M.
Chandra
, and R.
Samtaney
, “Benchmarking and scaling studies of pseudospectral code Tarang for turbulence simulations
,” Pramana
81
(4
), 617
–629
(2013
).45.
A. G.
Chatterjee
, M. K.
Verma
, A.
Kumar
, R.
Samtaney
, B.
Hadri
, and R.
Khurram
, “Scaling of a Fast Fourier Transform and a pseudo-spectral fluid solver up to 196608 cores
,” J. Parallel Distrib. Comput.
113
, 77
–91
(2018
).46.
C.
Canuto
, M.
Yousuff Hussaini
, A.
Quarteroni
, and T. A.
Zang
, Spectral Methods in Fluid Dynamics
(Springer-Verlag
, Berlin Heidelberg
, 1988
).47.
G.
Falkovich
, “Bottleneck phenomenon in developed turbulence
,” Phys. Fluids
6
(4
), 1411
–1414
(1994
).48.
M. K.
Verma
and D. A.
Donzis
, “Energy transfer and bottleneck effect in turbulence
,” J. Phys. A: Math. Theor.
40
(16
), 4401
–4412
(2007
).49.
M.
Linkmann
, M.
Buzzicotti
, and L.
Biferale
, “Multi-scale properties of large eddy simulations: Correlations between resolved-scale velocity-field increments and subgrid-scale quantities
,” J. Turbul.
19
(6
), 493
–527
(2018
).50.
A.
Yakhot
, S. A.
Orszag
, V.
Yakhot
, and M.
Israeli
, “Renormalization group formulation of large-eddy simulations
,” J. Sci. Comput.
4
(2
), 139
–158
(1989
).51.
U.
Frisch
, Turbulence: The Legacy of A. N. Kolmogorov
(Cambridge University Press
, Cambridge
, 1995
).© 2019 Author(s).
2019
Author(s)
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