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A physics-inspired alternative to spatial filtering for large-eddy simulations of turbulent flows

Published online by Cambridge University Press:  18 January 2022

Perry L. Johnson Open the ORCID record for Perry L. Johnson [Opens in a new window]
Perry L. Johnson*
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA, USA
*
†Email address for correspondence: perry.johnson@uci.edu
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Abstract

Large-eddy simulations (LES) are widely used for computing high Reynolds number turbulent flows. Spatial filtering theory for LES is not without its shortcomings, including how to define filtering for wall-bounded flows, commutation errors for non-uniform filters and extensibility to flows with additional complexity, such as multiphase flows. In this paper, the theory for LES is reimagined using a coarsening procedure that imitates nature. This physics-inspired coarsening approach is equivalent to Gaussian filtering for single-phase wall-free flows but opens up new insights for both physical understanding and modelling even in that simple case. For example, an alternative to the Germano identity is introduced and used to define a dynamic procedure without the need for a test filter. Non-uniform resolution can be represented in this framework without commutation errors, and the divergence-free condition is retained for incompressible flows. Potential extensions of the theory to more complex physics such as multiphase flows are briefly discussed.

JFM classification

Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulence simulation

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Type
JFM Papers
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Journal of Fluid Mechanics , Volume 934 , 10 March 2022 , A30
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© The Author(s), 2022. Published by Cambridge University Press

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References

REFERENCES

Bae, H.J. & Lozano-Duran, A. 2017 Towards exact subgrid-scale models for explicitly filtered large-eddy simulation of wall-bounded flows. Ann. Res. Br. 2017, 207–214.Google ScholarPubMed
Bae, H.J. & Lozano-Duran, A. 2018 DNS-aided explicitly filtered les of channel flow. Ann. Res. Br. 2018, 197–207.Google ScholarPubMed
Bae, H.J. & Lozano-Duran, A. 2021 Effect of wall boundary conditions on a wall-modeled large-eddy simulation in a finite-difference framework. Fluids 6 (3), 112.CrossRefGoogle Scholar
Balachandar, S. & Eaton, J.K. 2010 Turbulent dispersed multiphase flow. Annu. Rev. Fluid Mech. 42 (1), 111–133.CrossRefGoogle Scholar
Balachandar, S., Liu, K. & Lakhote, M. 2019 Self-induced velocity correction for improved drag estimation in Euler–Lagrange point-particle simulations. J. Comput. Phys. 376, 160–185.CrossRefGoogle Scholar
Ballouz, J.G. & Ouellette, N.T. 2018 Tensor geometry in the turbulent cascade. J. Fluid Mech. 835, 1048–1064.CrossRefGoogle Scholar
Bardina, J., Ferziger, J. & Reynolds, W. 1980 Improved subgrid-scale models for large-eddy simulation. In AIAA 13th Fluid & Plasma Dynamics Conference AIAA Paper 80-1357.CrossRefGoogle Scholar
Bassenne, M., Esmaily, M., Livescu, D., Moin, P. & Urzay, J. 2019 A dynamic spectrally enriched subgrid-scale model for preferential concentration in particle-laden turbulence. Intl J. Multiphase Flow 116, 270–280.CrossRefGoogle Scholar
Beck, A., Flad, D. & Munz, C.-D. 2019 Deep neural networks for data-driven LES closure models. J. Comput. Phys. 398, 108910.CrossRefGoogle Scholar
Bode, M., Gauding, M., Lian, Z., Denker, D., Davidovic, M., Kleinheinz, K., Jitsev, J. & Pitsch, H. 2021 Using physics-informed enhanced super-resolution generative adversarial networks for subfilter modeling in turbulent reactive flows. Proc. Combust. Inst. 38 (2), 2617–2625.CrossRefGoogle Scholar
Borue, V. & Orszag, S.A. 1998 Local energy flux and subgrid-scale statistics in three-dimensional turbulence. J. Fluid Mech. 366, 1–31.CrossRefGoogle Scholar
Bose, S.T. & Moin, P. 2014 A dynamic slip boundary condition for wall-modeled large-eddy simulation. Phys. Fluids 26 (1), 015104.CrossRefGoogle Scholar
Bose, S.T. & Park, G.I. 2018 Wall-modeled large-eddy simulation for complex turbulent flows. Annu. Rev. Fluid Mech. 50 (1), 535–561.CrossRefGoogle ScholarPubMed
Bou-Zeid, E., Meneveau, C. & Parlange, M. 2005 A scale-dependent Lagrangian dynamic model for large eddy simulation of complex turbulent flows. Phys. Fluids 17 (2), 025105.CrossRefGoogle Scholar
Bull, J.R. & Jameson, A. 2016 Explicit filtering and exact reconstruction of the sub-filter stresses in large eddy simulation. J. Comput. Phys. 306, 117–136.CrossRefGoogle Scholar
Capecelatro, J. & Desjardins, O. 2013 An Euler–Lagrange strategy for simulating particle-laden flows. J. Comput. Phys. 238, 1–31.CrossRefGoogle Scholar
Chen, X., Lu, J. & Tryggvason, G. 2021 Interface retaining coarsening of multiphase flows. Phys. Fluids 33 (7), 073316.CrossRefGoogle Scholar
Cheng, Y., Giometto, M., Kauffmann, P., Lin, L., Cao, C., Zupnick, C., Li, H., Li, Q., Abernathey, R. & Gentine, P. 2019 Deep learning for subgrid-scale turbulence modeling in large-eddy simulations of the atmospheric boundary layer. arXiv:1910.12125.Google Scholar
Clark, R.A., Ferziger, J.H. & Reynolds, W.C. 1979 Evaluation of subgrid-scale models using an accurately simulated turbulent flow. J. Fluid Mech. 91 (1), 1–16.CrossRefGoogle Scholar
Deardorff, J.W. 1970 A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers. J. Fluid Mech. 41 (2), 453–480.CrossRefGoogle Scholar
Domaradzki, J.A. & Loh, K.-C. 1999 The subgrid-scale estimation model in the physical space representation. Phys. Fluids 11 (8), 2330–2342.CrossRefGoogle Scholar
Donzis, D.A. & Sreenivasan, K.R. 2010 The bottleneck effect and the Kolmogorov constant in isotropic turbulence. J. Fluid Mech. 657, 171–188.CrossRefGoogle Scholar
Drivas, T.D. & Nguyen, H.Q. 2018 Onsager's conjecture and anomalous dissipation on domains with boundary. SIAM J. Math. Anal. 50 (5), 4785–4811.CrossRefGoogle Scholar
Duraisamy, K. 2021 Perspectives on machine learning-augmented Reynolds-averaged and large eddy simulation models of turbulence. Phys. Rev. Fluids 6, 050504.CrossRefGoogle Scholar
Falkovich, G. 1994 Bottleneck phenomenon in developed turbulence. Phys. Fluids 6 (4), 1411–1414.CrossRefGoogle Scholar
Fox, R.O. 2003 Computational Models for Turbulent Reacting Flows. Cambridge University Press.CrossRefGoogle Scholar
Freund, A. & Ferrante, A. 2021 Large-eddy simulation of droplet-laden decaying isotropic turbulence using artificial neural networks. Intl J. Multiphase Flow 142, 103704.CrossRefGoogle Scholar
Frohlich, J. & von Terzi, D. 2008 Hybrid LES/RANS methods for the simulation of turbulent flows. Prog. Aerospace Sci. 44 (5), 349–377.CrossRefGoogle Scholar
Gamahara, M. & Hattori, Y. 2017 Searching for turbulence models by artificial neural network. Phys. Rev. Fluids 2, 054604.CrossRefGoogle Scholar
Germano, M. 1986 a Differential filters for the large eddy numerical simulation of turbulent flows. Phys. Fluids 29 (6), 1755–1757.CrossRefGoogle Scholar
Germano, M. 1986 b Differential filters of elliptic type. Phys. Fluids 29 (6), 1757–1758.CrossRefGoogle Scholar
Germano, M. 1992 Turbulence: the filtering approach. J. Fluid Mech. 238, 325–336.CrossRefGoogle Scholar
Germano, M., Piomelli, U., Moin, P. & Cabot, W.H. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A: Fluid Dyn. 3 (7), 1760–1765.CrossRefGoogle Scholar
Ghate, A.S. & Lele, S.K. 2017 Subfilter-scale enrichment of planetary boundary layer large eddy simulation using discrete Fourier–Gabor modes. J. Fluid Mech. 819, 494–539.CrossRefGoogle Scholar
Ghate, A.S. & Lele, S.K. 2020 Gabor mode enrichment in large eddy simulations of turbulent flow. J. Fluid Mech. 903, A13.CrossRefGoogle Scholar
Ghosal, S. & Moin, P. 1995 The basic equations for the large eddy simulation of turbulent flows in complex geometry. J. Comput. Phys. 118 (1), 24–37.CrossRefGoogle Scholar
Haering, S.W., Lee, M. & Moser, R.D. 2019 Resolution-induced anisotropy in large-eddy simulations. Phys. Rev. Fluids 4, 114605.CrossRefGoogle Scholar
Herrmann, M. 2013 A sub-grid surface dynamics model for sub-filter surface tension induced interface dynamics. Comput. Fluids 87, 92–101.CrossRefGoogle Scholar
Herrmann, M., Kedelty, D. & Ziegenhein, T. 2018 A dual-scale subgrid closure for les of phase interfaces in turbulent flows. In Proceedings of the Summer Program, Center for Turbulence Research, Stanford University, pp. 45–54.Google Scholar
Hinze, J.O. 1955 Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes. AIChE J. 1 (3), 289–295.CrossRefGoogle Scholar
Horwitz, J.A.K. & Mani, A. 2016 Accurate calculation of stokes drag for point–particle tracking in two-way coupled flows. J. Comput. Phys. 318, 85–109.CrossRefGoogle Scholar
Horwitz, J.A.K. & Mani, A. 2018 Correction scheme for point-particle models applied to a nonlinear drag law in simulations of particle–fluid interaction. Intl J. Multiphase Flow 101, 74–84.CrossRefGoogle Scholar
Ishihara, T., Kaneda, Y., Yokokawa, M., Itakura, K. & Uno, A. 2007 Small-scale statistics in high-resolution direct numerical simulation of turbulence: Reynolds number dependence of one-point velocity gradient statistics. J. Fluid Mech. 592, 335–366.CrossRefGoogle Scholar
Johnson, P.L. 2020 Energy transfer from large to small scales in turbulence by multi-scale nonlinear strain and vorticity interactions. Phys. Rev. Lett. 124, 104501.CrossRefGoogle Scholar
Johnson, P.L. 2021 a On the role of vorticity stretching and strain self-amplification in the turbulence energy cascade. J. Fluid Mech. 922, A3.CrossRefGoogle Scholar
Johnson, P.L. 2021 b The squeezes, stretches, and whirls of turbulence. Phys. Today 74 (4), 46–51.CrossRefGoogle Scholar
Kim, H., Kim, J., Won, S. & Lee, C. 2021 Unsupervised deep learning for super-resolution reconstruction of turbulence. J. Fluid Mech. 910, A29.CrossRefGoogle Scholar
Kim, W.-W. & Menon, S. 1996 A new dynamic one-equation subgrid-scale model for large eddy simulations. AIAA Paper 1995-356.CrossRefGoogle Scholar
Kim, D. & Moin, P. 2020 Subgrid-scale capillary breakup model for liquid jet atomization. Combust. Sci. Technol. 192 (7), 1334–1357.CrossRefGoogle Scholar
Kolmogorov, A.N. 1941 The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk SSSR 30, 299–303.Google Scholar
Kumar, S., Quan, H. & Eyink, G.L. 2021 Onsager approach to wall bounded turbulence. In 74th Annual Meeting of the American Physical Society Division of Fluid Dynamics, vol. 66, issue 17, M04.00008. American Physical Society.Google Scholar
Labourasse, E., Lacanette, D., Toutant, A., Lubin, P., Vincent, S., Lebaigue, O., Caltagirone, J.P. & Sagaut, P. 2007 Towards large eddy simulation of isothermal two-phase flows: governing equations and a priori tests. Intl J. Multiphase Flow 33 (1), 1–39.CrossRefGoogle Scholar
Lakehal, D. 2018 Status and future developments of large-eddy simulation of turbulent multi-fluid flows (LEIS and LESS). Intl J. Multiphase Flow 104, 322–337.CrossRefGoogle Scholar
Langford, J.A. & Moser, R.D. 1999 Optimal LES formulations for isotropic turbulence. J. Fluid Mech. 398, 321–346.CrossRefGoogle Scholar
Langford, J.A. & Moser, R.D. 2001 Breakdown of continuity in large-eddy simulation. Phys. Fluids 13 (5), 1524–1527.CrossRefGoogle Scholar
Larsson, J., Kawai, S., Bodart, J. & Bermejo-Moreno, I. 2016 Large eddy simulation with modeled wall-stress: recent progress and future directions. Mech. Engng Rev. 3 (1), 15–00418.Google Scholar
Leonard, A. 1975 Energy cascade in large-eddy simulations of turbulent fluid flows. In Turbulent Diffusion in Environmental Pollution (ed. F.N. Frenkiel & R.E. Munn), Advances in Geophysics, vol. 18, pp. 237–248. Elsevier.CrossRefGoogle Scholar
Leonard, A. 2016 Large-Eddy Simulation of the Navier–Stokes Equations: Deconvolution, Particle Methods, and Super-Resolution, pp. 1–16. World Scientific.Google Scholar
Lilly, D.K. 1992 A proposed modification of the germano subgrid-scale closure method. Phys. Fluids 4 (3), 633–635.CrossRefGoogle Scholar
Liu, B., Tang, J., Huang, H. & Lu, X.-Y. 2020 Deep learning methods for super-resolution reconstruction of turbulent flows. Phys. Fluids 32 (2), 025105.CrossRefGoogle Scholar
Lund, T.S. & Rogers, M.M. 1994 An improved measure of strain state probability in turbulent flows an improved measure of strain state probability in turbulent flows. Phys. Fluids 6, 1838–1847.CrossRefGoogle Scholar
Maulik, R. & San, O. 2017 A neural network approach for the blind deconvolution of turbulent flows. J. Fluid Mech. 831, 151–181.CrossRefGoogle Scholar
Maxey, M.R. & Riley, J.J. 1983 Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 26 (4), 883–889.CrossRefGoogle Scholar
McCaslin, J.O. & Desjardins, O. 2014 Theoretical and computational modeling of turbulence / interface interactions. In Center for Turbulence Research Proceedings of the Summer Program 2014, pp. 79–88.Google Scholar
Meneveau, C., Lund, T.S. & Cabot, W.H. 1996 A lagrangian dynamic subgrid-scale model of turbulence. J. Fluid Mech. 319, 353–385.CrossRefGoogle Scholar
Milano, M. & Koumoutsakos, P. 2002 Neural network modeling for near wall turbulent flow. J. Comput. Phys. 182 (1), 1–26.CrossRefGoogle Scholar
Mockett, C., Fuchs, M. & Thiele, F. 2012 Progress in DES for wall-modelled LES of complex internal flows. Comput. Fluids 65, 44–55.CrossRefGoogle Scholar
Moin, P., Squires, K., Cabot, W. & Lee, S. 1991 A dynamic subgrid-scale model for compressible turbulence and scalar transport. Phys. Fluids 3 (11), 2746–2757.CrossRefGoogle Scholar
Monin, A.S. & Yaglom, A.M. 1975 Statistical Fluid Mechanics: Mechanics of Turbulence, vol. II. Dover Publications.Google Scholar
Moreau, A., Teytaud, O. & Bertoglio, J.P. 2006 Optimal estimation for large-eddy simulation of turbulence and application to the analysis of subgrid models. Phys. Fluids 18 (10), 105101.CrossRefGoogle Scholar
Moser, R.D., Haering, S.W. & Yalla, G.R. 2021 Statistical properties of subgrid-scale turbulence models. Annu. Rev. Fluid Mech. 53 (1), 255–286.CrossRefGoogle Scholar
Park, J. & Choi, H. 2021 Toward neural-network-based large eddy simulation: application to turbulent channel flow. J. Fluid Mech. 914, A16.CrossRefGoogle Scholar
Patterson, G.S. & Orszag, S.A. 1971 Spectral calculations of isotropic turbulence: efficient removal of aliasing interactions. Phys. Fluids 14 (11), 2538–2541.CrossRefGoogle Scholar
Piomelli, U. & Balaras, E. 2002 Wall-layer models for large-eddy simluations. Annu. Rev. Fluid Mech. 34 (1), 349–374.CrossRefGoogle Scholar
Pope, S.B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Pope, S.B. 2010 Self-conditioned fields for large-eddy simulations of turbulent flows. J. Fluid Mech. 652, 139–169.CrossRefGoogle Scholar
Portwood, G.D., Nadiga, B.T., Saenz, J.A. & Livescu, D. 2021 Interpreting neural network models of residual scalar flux. J. Fluid Mech. 907, A23.CrossRefGoogle Scholar
Prakash, A., Jansen, K.E. & Evans, J.A. 2021 Invariant data-driven subgrid stress modeling in the strain-rate eigenframe for large eddy simulation. arXiv:2106.13410.Google Scholar
Rozema, W., Bae, H.J., Moin, P. & Verstappen, R. 2015 Minimum-dissipation models for large-eddy simulation. Phys. Fluids 27 (8), 085107.CrossRefGoogle Scholar
Sagaut, P. 2006 Large Eddy Simulation for Incompressible Flows: An Introduction. Springer.Google Scholar
Sagaut, P. & Germano, M. 2005 On the filtering paradigm for LES of flows with discontinuities. J. Turbul. 6 (23), 1–9.CrossRefGoogle Scholar
Sarghini, F., de Felice, G. & Santini, S. 2003 Neural networks based subgrid scale modeling in large eddy simulations. Comput. Fluids 32 (1), 97–108.CrossRefGoogle Scholar
Scotti, A. & Meneveau, C. 1999 A fractal model for large eddy simulation of turbulent flow. Phys. D 127 (3-4), 198–232.CrossRefGoogle Scholar
Scotti, A., Meneveau, C. & Lilly, D.K. 1993 Generalized Smagorinsky model for anisotropic grids. Phys. Fluids A 5, 2306–2308.CrossRefGoogle Scholar
Sirignano, J., MacArt, J.F. & Freund, J.B. 2020 DPM: A deep learning PDE augmentation method with application to large-eddy simulation. J. Comput. Phys. 423, 109811.CrossRefGoogle Scholar
Spalart, P.R. 2009 Detached-eddy simulation. Annu. Rev. Fluid Mech. 41 (1), 181–202.CrossRefGoogle Scholar
Stoffer, R., van Leeuwen, C.M., Podareanu, D., Codreanu, V., Veerman, M.A., Janssens, M., Hartogensis, O.K. & van Heerwaarden, C.C. 2021 Development of a large-eddy simulation subgrid model based on artificial neural networks: a case study of turbulent channel flow. Geosci. Model Develop. 14 (6), 3769–3788.CrossRefGoogle Scholar
Stolz, S. & Adams, N.A. 1999 An approximate deconvolution procedure for large-eddy simulation. Phys. Fluids 11 (7), 1699–1701.CrossRefGoogle Scholar
Tennekes, H. & Lumley, J.L. 1972 A First Course in Turbulence. MIT Press.CrossRefGoogle Scholar
Toutant, A., Chandesris, M., Jamet, D. & Lebaigue, O. 2009 Jump conditions for filtered quantities at an under-resolved discontinuous interface. Part 1: theoretical development. Intl J. Multiphase Flow 35 (12), 1100–1118.CrossRefGoogle Scholar
Tryggvason, G. & Lu, J. 2020 Direct numerical simulations of multiphase flows: opportunities and challenges. AIP Conf. Proc. 2293 (1), 030002.CrossRefGoogle Scholar
Verstappen, R. 2011 When does eddy viscosity damp subfilter scales sufficiently? J. Sci. Comput. 49 (1), 94–110.CrossRefGoogle Scholar
Vollant, A., Balarac, G. & Corre, C. 2017 Subgrid-scale scalar flux modelling based on optimal estimation theory and machine-learning procedures. J. Turbul. 18 (9), 854–878.CrossRefGoogle Scholar
Vreman, A.W. 2004 An eddy-viscosity subgrid-scale model for turbulent shear flow: algebraic theory and applications. Phys. Fluids 16 (10), 3670–3681.CrossRefGoogle Scholar
Vreman, B., Geurts, B. & Kuerten, H. 1994 On the formulation of the dynamic mixed subgrid-scale model. Phys. Fluids 6 (12), 4057–4059.CrossRefGoogle Scholar
Wang, Z., Luo, K., Li, D., Tan, J. & Fan, J. 2018 Investigations of data-driven closure for subgrid-scale stress in large-eddy simulation. Phys. Fluids 30 (12), 125101.CrossRefGoogle Scholar
Wang, Y., Yuan, Z., Xie, C. & Wang, J. 2021 Artificial neural network-based spatial gradient models for large-eddy simulation of turbulence. AIP Adv. 11 (5), 055216.CrossRefGoogle Scholar
Wang, Q., Zhao, X. & Ihme, M. 2019 A regularized deconvolution model for sub-grid dispersion in large eddy simulation of turbulent spray flames. Combust. Flame 207, 89–100.CrossRefGoogle Scholar
Xie, C., Wang, J. & Weinan, E. 2020 a Modeling subgrid-scale forces by spatial artificial neural networks in large eddy simulation of turbulence. Phys. Rev. Fluids 5, 054606.CrossRefGoogle Scholar
Xie, C., Yuan, Z. & Wang, J. 2020 b Artificial neural network-based nonlinear algebraic models for large eddy simulation of turbulence. Phys. Fluids 32 (11), 115101.CrossRefGoogle Scholar
Yalla, G.R., Oliver, T.A., Haering, S.W., Engquist, B. & Moser, R.D. 2021 Effects of resolution inhomogeneity in large-eddy simulation. Phys. Rev. Fluids 6, 074604.CrossRefGoogle Scholar
Yang, X.I.A., Zafar, S., Wang, J.-X. & Xiao, H. 2019 Predictive large-eddy-simulation wall modeling via physics-informed neural networks. Phys. Rev. Fluids 4, 034602.CrossRefGoogle Scholar
Yuan, Z., Xie, C. & Wang, J. 2020 Deconvolutional artificial neural network models for large eddy simulation of turbulence. Phys. Fluids 32 (11), 115106.CrossRefGoogle Scholar
Zhou, Z., He, G., Wang, S. & Jin, G. 2019 Subgrid-scale model for large-eddy simulation of isotropic turbulent flows using an artificial neural network. Comput. Fluids 195, 104319.CrossRefGoogle Scholar