We revisit coarse-grained simulation strategies for turbulent material mixing applications involving shock-driven turbulence in the context of the Radiation Adaptive Grid Eulerian (xRAGE) hydrodynamics and Besnard–Harlow–Rauenzahn (BHR) Reynolds-averaged Navier–Stokes codes, using newly available Low-Mach-Corrected (LMC) xRAGE hydrodynamics. Impact assessments are based on comparisons with a relevant shock-tube experiment for which turbulent mixing and velocity data are available. xRAGE Implicit Large-Eddy Simulation (ILES) and a recently proposed xRAGE-BHR bridging paradigm are tested. Bridging models turbulent stresses dynamically, based on decomposing the full stress into modeled and resolved components, using a differential filter as a secondary filtering operation to define the resolved part, and additionally requiring the resolved stress to approach the full stress with grid resolution refinement to ensure realizability of the bridging-based large-eddy simulation. Much improved scale-resolving with LMC-xRAGE ILES and with dynamic LMC-xRAGE/BHR bridging enables higher simulated mixing and turbulence levels on coarser grids. For the tested planar shock-tube case, the more-accurate models can achieve the same level of accuracy with less resolution than required with the highest-fidelity turbulence simulation models typically used at scale with default xRAGE hydrodynamics; two-levels of grid-coarsening savings can be thus achieved for the mixing prediction in these comparisons: one associated with the more-accurate LMC xRAGE hydrodynamics and an additional one from using the dynamic xRAGE-BHR bridging.
References
1.
Y.
Zhou
, “Rayleigh-Taylor and Richtmyer-Meshkov instability induced flow, turbulence, and mixing. I
,” Phys. Rep.
720–722
, 1
–136
(2017
).2.
Y.
Zhou
, “Rayleigh-Taylor and Richtmyer-Meshkov instability induced flow, turbulence, and mixing. II
,” Phys. Rep.
723–725
, 1
–160
(2017
).3.
J. R.
Ristorcelli
, A. A.
Gowardhan
, and F. F.
Grinstein
, “Two classes of Richtmyer-Meshkov instabilities; a detailed statistical look
,” Phys. Fluids
25
, 044106
(2013
).4.
F. F.
Grinstein
, Coarse Grained Simulation and Turbulent Mixing
(Cambridge
, 2016
).5.
Y.
Zhou
, F. F.
Grinstein
, A. J.
Wachtor
, and B. M.
Haines
, “Estimating the effective Reynolds number in implicit large-eddy simulation
,” Phys. Rev. E
89
, 013303
(2014
).6.
F. F.
Grinstein
, L. G.
Margolin
, and W. J.
Rider
, Implicit Large Eddy Simulation: Computing Turbulent Flow Dynamics
, 2nd printing (Cambridge UP
, New York
, 2010
).7.
S.
Ghosal
, “An analysis of numerical errors in large-eddy simulations of turbulence
,” J. Comput. Phys.
125
, 187
–206
(1996
).8.
J. D.
Schwarzkopf
, D.
Livescu
, R. A.
Gore
, R. M.
Rauenzahn
, and J. R.
Ristorcelli
, “Application of a second-moment closure model to mixing processes involving multi-component miscible fluids
,” J. Turbul.
12
(49
), N49
(2011
).9.
K.
Sinha
, K.
Mahesh
, and G. V.
Candler
, “Modeling shock unsteadiness in shock/turbulence interaction
,” Phys. Fluids
15
(8
), 2290
–2297
(2003
).10.
W. K.
George
and L.
Davidson
, “Role of initial conditions in establishing asymptotic flow behavior
,” AIAA J.
42
, 438
–446
(2004
).11.
J.
Frolich
and D. A.
von Terzi
, “Hybrid LES/RANS methods for the simulation of turbulent flows
,” Prog. Aerosp. Sci.
44
, 349
–377
(2008
).12.
P. R.
Spalart
, “Detached-eddy simulation
,” Annu. Rev. Fluid Mech.
41
, 181
–202
(2009
).13.
C. G.
Speziale
, “A combined large-eddy simulation and time-dependent RANS capability for high-speed compressible flows
,” J. Sci. Comput.
13
, 253
–274
(1998
).14.
H. F.
Fasel
, D. A.
von Terzi
, and R. D.
Sandberg
, “A methodology for simulating compressible turbulent flows
,” J. Appl. Mech.
73
, 405
–412
(2006
).15.
C. G.
Speziale
, “Turbulence modeling for time-dependent RANS and VLES: A review
,” AIAA J.
36
(2
), 173
–184
(1998
).16.
M. Y.
Hussaini
, S.
Thangam
, S. L.
Woodruff
, and Y.
Zhou
, “Development of a continuous model for simulation of turbulent flows
,” J. Appl. Mech.
73
, 441
(2006
).17.
L. J.
Peltier
and F. J.
Zajaczkowski
, “Maintenance of the near-wall cycle of turbulence for hybrid RANS/LES of fully-developed channel flow
,” in DNS/LES Progress and Challenges, Proceedings of the 3rd AFOSR International Conference on DNS/LES
(Kluwer Academic
, 2001
), Paper No. ADP013707.18.
S. S.
Girimaji
, “Partially-averaged Navier-Stokes model for turbulence: A Reynolds-averaged Navier-Stokes to direct numerical simulation bridging method
,” J. Appl. Mech.
73
, 413
–421
(2006
).19.
M.
Germano
, “Readers' forum, comment on turbulence modeling for time-dependent RANS and VLES: A review
,” AIAA J.
36
(9
), 1766
–1767
(1998
).20.
F. F.
Grinstein
, J. A.
Saenz
, R. M.
Rauenzahn
, M.
Germano
, and D. M.
Israel
, “Dynamic bridging modeling for coarse grained simulations of shock driven turbulent mixing
,” Comput. Fluids
199
, 104430
(2020
).21.
C. W.
Hirt
, “Computer studies of time-dependent turbulent flows
,” Phys. Fluids
12
, II
–219
(1969
).22.
L. G.
Margolin
and W. J.
Rider
, “Numerical regularization: The numerical analysis of implicit subgrid models
,” in Implicit Large Eddy Simulation: Computing Turbulent Fluid Dynamics
, edited by F. F.
Grinstein
, L. G.
Margolin
, and W. J.
Rider
, 2nd printing (Cambridge
: Cambridge University Press
, 2010
), Chap. 5.23.
F. F.
Grinstein
and C.
Fureby
, “On flux-limiting-based implicit large eddy simulation
,” J. Fluids Eng
129
, 1483
–1492
(2007
).24.
R.
von Kaenel
, N. A.
Adams
, L.
Kleiser
, and J. B.
Vos
, “The approximate deconvolution model for large-eddy simulation of compressible flows with finite volume schemes
,” J. Fluids Eng.
124
(4
), 829
(2002
).25.
S. T.
Bose
, P.
Moin
, and D.
You
, “Grid-independent large-eddy simulation using explicit filtering
,” Phys. Fluids
22
, 105103
(2010
).26.
P. E.
Dimotakis
, “T he mixing transition in turbulent flows
,” J. Fluid Mech.
409
, 69
–98
(2000
).27.
Y.
Zhou
, “Unification and extension of the concepts of similarity criteria and mixing transition for studying astrophysics using high energy density laboratory experiments or numerical simulations
,” Phys. Plasmas
14
, 082701
(2007
).28.
A. J.
Wachtor
, F. F.
Grinstein
, C. R.
Devore
, J. R.
Ristorcelli
, and L. G.
Margolin
, “Implicit large-eddy simulations of passive scalar mixing in statistically stationary isotropic turbulence
,” Phys. Fluids
25
, 025101
(2013
).29.
J.
Jimenez
, A. A.
Wray
, P. G.
Saffman
, and R. S.
Rogallo
, “The structure of intense vorticity in isotropic turbulence
,” J. Fluid Mech.
255
, 65
–90
(1993
).30.
M. R.
Overholt
and S. B.
Pope
, “Direct numerical simulation of a passive scalar with imposed mean gradient in isotropic turbulence
,” Phys. Fluids
8
, 3128
–3148
(1996
).31.
D. I.
Pullin
, “A vortex-based model for the subgrid flux of a passive scalar
,” Phys. Fluids
12
, 2311
(2000
).32.
T.
Gotoh
and T.
Watanabe
, “Scalar flux in a uniform mean scalar gradient in homogeneous isotropic steady turbulence
,” Phys. D
241
, 141
–148
(2012
).33.
P. K.
Yeung
, S.
Xu
, and K. R.
Sreenivasan
, “Schmidt number effects on turbulent transport with uniform mean scalar gradient
,” Phys. Fluids
14
, 4178
–4191
(2002
).34.
J. R.
Ristorcelli
, “Passive scalar mixing: Analytic study of time scale ratio, variance, and mix rate
,” Phys. Fluids
18
, 075101
(2006
).35.
A.
Misra
and D. I.
Pullin
, “A vortex-based subgrid stress model for large-eddy simulation
,” Phys. Fluids
9
, 2443
(1997
).36.
J. C.
Vassilicos
, “Dissipation in turbulent flows
,” Annu. Rev. Fluid Mech.
47
, 95
–114
(2015
).37.
F. F.
Grinstein
, “Coarse grained simulation of convectively driven turbulent mixing transition and turbulence decay
,” Physica D
407
, 132419
(2020
).38.
M.
Gittings
, R.
Weaver
, M.
Clover
, T.
Betlach
, N.
Byrne
, R.
Coker
, E.
Dendy
, R.
Hueckstaedt
, K.
New
, W. R.
Oakes
, D.
Ranta
, and R.
Stefan
, “The RAGE radiation hydrodynamic code
,” Comput. Sci. Discovery
1
, 015005
(2008
).39.
P.
Colella
, “Glimm's method for gas dynamics
,” SIAM J. Sci. Stat. Comput.
3
, 76
–110
(1982
).40.
B.
Van Leer
, “Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method
,” J. Comput. Phys.
135
, 229
–248
(1997
).41.
J. C.
Dolence
and T.
Masser
, “A new directionally unsplit option for hydrodynamics in the Eulerian AMR code xRAGE
,” International Conference on Numerical Methods for Multi-Material Fluid Flows (MultiMat)
, Santa Fe, NM, 18–22 September 2017
.42.
A.
Mignone
, “High-order conservative reconstruction schemes for finite volume methods in cylindrical and spherical coordinates
,” J. Comput. Phys.
270
, 784
(2014
).43.
C.-W.
Shu
and S.
Osher
, “Efficient implementation of essentially non-oscillatory shock capturing schemes
,” J. Comput. Phys.
77
, 439
(1988
).44.
B.
Thornber
, A.
Mosedale
, D.
Drikakis
, D.
Youngs
, and R. J. R.
Williams
, “An improved reconstruction method for compressible flows with low Mach number features
,” J. Comput. Phys.
227
, 4873
–4894
(2008
).45.
A.
Harten
, P. D.
Lax
, and B.
van Leer
, “On upstream differencing and Godunov-type schemes for hyperbolic conservation laws
,” SIAM Rev.
25
, 35
–61
(1983
).46.
E. F.
Toro
, M.
Spruce
, and W.
Speares
, “Restoration of the contact surface in the HLL-Riemann solver
,” Shock Waves
4
, 25
–34
(1994
).47.
H.
Guillard
and A.
Murrone
, “On the behaviour of upwind schemes in the low Mach number limit: II. Godunov type schemes
,” Comput. Fluids
33
, 655
–675
(2004
).48.
D.
Youngs
and R. J. R.
Williams
, “Turbulent mixing in spherical implosions
,” Int. J. Numer. Meth. Fluids
56
, 1597
–1603
(2008
).49.
D.
Besnard
, F. H.
Harlow
, R. M.
Rauenzahn
, and C.
Zemach
, “Turbulence transport equations for variable-density turbulence and their relationship to two-field models
,” Report No. LA-UR-12303, Los Alamos National Laboratory, 1992
.50.
B. M.
Haines
, F. F.
Grinstein
, and J. D.
Schwarzkopf
, “Reynolds-averaged Navier-Stokes initialization and benchmarking in shock-driven turbulent mixing
,” J. Turbul.
14
(2
), 46
–70
(2013
).51.
J. D.
Schwarzkopf
, D.
Livescu
, J. R.
Baltzer
, R. A.
Gore
, and J. R.
Ristorcelli
, “A two-length scale turbulence model for single-phase multi-fluid mixing
,” Flow Turbul. Combust.
96
, 1
–43
(2016
).52.
M.
Germano
, “Differential filters for the large eddy numerical simulation of turbulent flows
,” Phys. Fluids
29
(6
), 1755
–1757
(1986
).53.
J. R.
Bull
, M. D.
Piggot
, and C. C.
Pain
, “A finite element LES methodology for anisotropic inhomogeneous meshes
,” in THMT-12. Proceedings of the Seventh International Symposium on Turbulence, Heat and Mass Transfer (
2012
), pp. 1516
–1527
.54.
M.
Germano
, “A statistical formulation of the dynamic model
,” Phys. Fluids
8
(2
), 565
–570
(1996
).55.
D. K.
Walters
, S.
Bhushan
, M. F.
Alam
, and D. S.
Thompson
, “Investigation of a dynamic hybrid RANS/LES modeling methodology for finite-volume CFD simulations
,” Flow, Turbul. Combust.
91
(3
), 643
–667
(2013
).56.
S.
Bhushan
and D. K.
Walters
, “A dynamic hybrid Reynolds-averaged Navier-Stokes large eddy simulation modeling framework
,” Phys. Fluids
24
(1
), 015103
(2012
).57.
J.
Smagorinsky
, “General circulation experiments with the primitive equations
,” Mon. Weather Rev.
91
(3
), 99
–164
(1963
).58.
F. F.
Grinstein
, “Initial conditions and modeling for simulations of shock driven turbulent material mixing
,” Comput. Fluids
151
, 58
–72
(2017
).59.
F.
Poggi
, M.-H.
Thorembey
, and G.
Rodriguez
, “Velocity measurements in turbulent gaseous mixtures induced by Richtmyer-Meshkov instability
,” Phys. Fluids
10
, 2698
(1998
).60.
C.
Mugler
and S.
Gauthier
, “Two-dimensional Navier–Stokes simulations of gaseous mixtures induced by Richtmyer–Meshkov instability
,” Phys. Fluids
12
, 1783
(2000
).61.
C. W.
Barnes
, S. H.
Batha
, A. M.
Dunne
, G. R.
Magelssen
, S.
Rothman
, R. D.
Day
, N. E.
Elliott
, D. A.
Haynes
, R. L.
Holmes
, J. M.
Scott
, D. L.
Tubbs
, D. L.
Youngs
, T. R.
Boehly
, and P.
Jaanimagi
, “Observation of mix in a compressible plasma in a convergent cylindrical geometry
,” Phys. Plasmas
9
, 4431
(2002
).62.
O.
Grégoire
, D.
Souffland
, and S.
Gauthier
, “A second-order turbulence model for gaseous mixtures induced by Richtmyer-Meshkov instability
,” J. Turbul.
6
, N29
(2005
).63.
A.
Banerjee
, R. A.
Gore
, and M. J.
Andrews
, “Development and validation of a turbulent-mix model for variable-density and compressible flows
,” Phys. Rev. E
82
, 046309
(2010
).64.
D. J.
Hill
, C.
Pantano
, and D. I.
Pullin
, “Large-eddy simulation and multiscale modeling of a Ritchmyer-Meshkov instability with reshock
,” J. Fluid Mech.
557
, 29
–61
(2006
).65.
F. F.
Grinstein
, A. A.
Gowardhan
, and A. J.
Wachtor
, “Simulations of Richtmyer-Meshkov instabilities in planar shock-tube experiments
,” Phys. Fluids
23
, 034106
(2011
).66.
F. F.
Grinstein
, F. J. A.
Saenz
, J. C.
Dolence
, T. O.
Masser
, R. M.
Rauenzahn
, and M. M.
Francois
, “Effects of operator splitting and low Mach-number correction in turbulent mixing transition simulations
,” Comput. Math. Appl.
78
, 437
–458
(2019
).67.
F. S.
Pereira
, L.
Eça
, G.
Vaz
, and S. S.
Girimaji
, “Challenges in Scale-Resolving Simulations of turbulent wake flows with coherent structures
,” J. Comput. Phys.
363
, 98
–115
(2018
).© 2021 Author(s).
2021
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