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3 - Filtering Approaches and Coarse Graining

from Part I - Paradigms and Tools

Published online by Cambridge University Press:  31 January 2025

By
Massimo Germano
Edited by
Fernando F. Grinstein ,
Filipe S. Pereira  and
Massimo Germano
Fernando F. Grinstein
Affiliation:
Los Alamos National Laboratory
Filipe S. Pereira
Affiliation:
Los Alamos National Laboratory
Massimo Germano
Affiliation:
Duke University, North Carolina
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Summary

The filtering approach is a simple deterministic way to formalize analytically coarse-grained representations of a given turbulent flow. By their own nature, turbulence and coarse graining (CG) are multiscaled, and in this chapter, we discuss the specific question of the relations between turbulence, coarse graining, and filtering in a unified operational form, with particular interest to multiscale properties and aspects. Reynolds averaged Navier–Stokes (RANS) averaging, explicit convolutional large eddy simulation (LES) filtering formulations (Leonard, 1975), implicit LES and scale resolving simulations (SRS) approaches (Grinstein et al., 2010; Grinstein, 2016; Pereira et al., 2021), functional and structural LES modeling procedures (Sagaut, 2006) and hybrid RANS/LES methods (Fr¨ohlich and von Terzi, 2008), are revisited and discussed from the point of view of a multiscale operational filtering approach (OFA) (Germano, 1992) based on the multiscale properties of the generalized central moments (GCM). Some recent results are presented both as regards analysis, modeling, and post-processing of turbulent flows, and finally, some conclusions and some personal recalls are provided.

Type
Chapter
Information
Coarse Graining Turbulence
Modeling and Data-Driven Approaches and their Applications
 , pp. 91 - 126
Publisher: Cambridge University Press
Print publication year: 2025

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References

Abbà, A., and Germano, M. 2012. A Mixed RANS/LES Model Applied to the Channel Flow. Pages 217–222 in Progress in Turbulence V, Talamelli, A., Oberlack, M., and Peinke, J. (eds). Springer.Google Scholar
Abbà, A., and Valdettaro, L. 2023. Tensorial Turbulent Viscosity Model for LES: Properties and Applications. Pages 9–20 in From Kinetic Theory to Turbulence Modeling – The Legacy of Carlo Cercignani, Barbante, P., Belgiorno, F. D., Lorenzani, S., and Valdettaro, L. (eds). Springer.Google Scholar
Abbà, A., Cimarelli, A., Klein, M., Ferrero, A., Grinstein, F. F., Larocca, F., Saenz, J. A., Scovazzi, G., and Germano, M. 2021. The Filtering Approach as a Tool for Modeling and Analyzing Turbulence. Pages 67–77 in Progress in Turbulence IX, Örlü, R., Talamelli, A., Peinke, J., and Oberlack, M. (eds). Proceedings in Physics, vol. 267. Springer.Google Scholar
Aubry, N. 1991. On the Hidden Beauty of the Proper Orthogonal Decomposition. Theoretical and Computational Fluid Dynamics, 2, 339–352.CrossRefGoogle Scholar
Boussinesq, J. 1877. Essai sur la théorie des eaux courantes. Memoires presentes par divers savants a l’Académie des sciences, 26, 1–680.Google Scholar
Bull, R., and Jameson, A. 2016. Explicit Filtering and Exact Reconstruction of the Sub-Filter Stresses in Large Eddy Simulation. Journal of Computational Physics, 306, 117–136.CrossRefGoogle Scholar
Celik, I., Cehreli, Z. N., and Yavuz, I. 2005. Index of Resolution Quality for Large Eddy Simulations. Journal of Fluids Engineering, 127, 949–958.CrossRefGoogle Scholar
Celik, I., Klein, M., Freitag, M., and Janicka, J. 2006. Assessment Measures for URANS/DES/LES: an Overview with Applications. Journal of Turbulence, 7, N48.CrossRefGoogle Scholar
Chang, N., Yuan, Z., and Wang, J. 2022. The Effect of Sub-Filter Scale Dynamics in Large Eddy Simulation of Turbulence. Physics of Fluids, 34, 095104.CrossRefGoogle Scholar
Cimarelli, A., Abbà, A., and Germano, M. 2019. General Formalism for a Reduced Description and Modelling of Momentum and Energy Transfer in Turbulence. Journal of Fluid Mechanics, 866, 865–896.CrossRefGoogle Scholar
Errante, M., Klein, M., Ferrero, A., Larocca, F., Scovazzi, G., and Germano, M. 2023. Mixed Averaging Procedures. Flow Turbulence and Combustion. Vol. 112, pag. 1001–1008, (2024).Google Scholar
Eyink, G. L. 2007–2008. Course Notes for Turbulence Theory. www.ams.jhu.edu/~eyink/Turbulence/notes.html.Google Scholar
Ferrero, A., Larocca, F., Scovazzi, G., and Germano, M. 2021. A Numerical Study of the Spanwise Turbulence Past a Cylinder Flow. Pages 91–96 in Progress in Turbulence IX, Örlü, R., Talamelli, A., Peinke, J., and Oberlack, M. (eds). Springer Proceedings in Physics, vol. 267.Google Scholar
Fröhlich, J., and von Terzi, D. 2008. Hybrid LES/RANS Methods for the Simulation of Turbulent Flows. Progress in Aerospace Sciences, 44(5), 349–377.CrossRefGoogle Scholar
Fuchs, L. 1996. An Exact SGS model for LES. Pages 23–26 in Advances in Turbulence VI, vol. 36, Gavrilakis, S., Machiels, L., and Monkewitz, P. A. (eds). Springer.Google Scholar
Galanti, B., and Tsinober, A. 2004. Is Turbulence Ergodic? Physics Letters, A330, 173–180.Google Scholar
Germano, M. 1986a. A Proposal for a Redefinition of the Turbulent Stress in the Filtered Navier–Stokes Equations. Physics of Fluids, 29, 2323–2324.Google Scholar
Germano, M. 1986b. Differential Filters for the Large Eddy Numerical Simulation of Turbulent Flows. Physics of Fluids, 29, 1755–1757.Google Scholar
Germano, M. 1986c. Differential Filters of Elliptic Type. Physics of Fluids, 29, 1757–1758.Google Scholar
Germano, M. 1990. Averaging Invariance of the Turbulent Equations and Similar Subgrid Modeling. Center for Turbulence Research Report, 116.Google Scholar
Germano, M. 1992. Turbulence: the Filtering Approach. Journal of Fluid Mechanics, 238, 325–336.CrossRefGoogle Scholar
Germano, M. 1996. A Statistical Formulation of the Dynamic Model. Physics of Fluids, 8, 565–570.CrossRefGoogle Scholar
Germano, M. 1998. Comment on “Turbulence Modeling for Time-Dependent RANS and VLES: A Review”. AIAA Journal, 36(9), 1766.CrossRefGoogle Scholar
Germano, M. 2000. Fundamentals of Large Eddy Simulation. Pages 81–130 in Advanced Turbulent Flows Computations, Peyret, R. and Krause, E. (eds). Springer.Google Scholar
Germano, M. 2004. Properties of the Hybrid RANS/ LES filter. Theoretical and Computational Fluid Dynamics, 17, 225–231.CrossRefGoogle Scholar
Germano, M. 2007. A Direct Relation between the Filtered Subgrid Stress and the Second Order Structure Function. Physics of Fluids, 19, 038102/2.CrossRefGoogle Scholar
Germano, M. 2014. On the Hybrid RANS-LES of Compressible flows. Pages 253–263 in Progress in Hybrid RANS-LES Modelling, Lamballais, E., Friedrich, R., Geurts, B. J., and Métais, O. (eds). Springer.Google Scholar
Germano, M. 2015. The Similarity Subgrid Stresses Associated to the Approximate Van Cittert Deconvolutions. Physics of Fluids, 27, 035111.CrossRefGoogle Scholar
Germano, M. 2023. Turbulence without Fluctuations. Pages 129–139 in From Kinetic Theory to Turbulence Modeling – The Legacy of Carlo Cercignani, Barbante, L. P., Belgiorno, F. D., Lorenzani, S., and Valdettaro, L. (eds). Springer.Google Scholar
Germano, M., and Sagaut, P. 2006. Formal Properties of the Additive RANS/DNS Filter. Pages 127–134 in Direct and Large-Eddy Simulation V, Lamballais, E., Friedrich, R., Geurts, B. J., and Métais, O. (eds). Springer.Google Scholar
Germano, M., Piomelli, U., Moin, P., and Cabot, W. H. 1990. A Dynamic Subgrid-Scale Eddy Viscosity Model. Proceedings of the 1990 Summer Program, 5–17.Google Scholar
Germano, M., Piomelli, U., Moin, P., and Cabot, W. H. 1991. A Dynamic Subgrid-Scale Eddy Viscosity Model. Physics of Fluids, A3, 1760–1765.Google Scholar
Germano, M., Abbà, A., Cimarelli, A., Ferrero, A., Grinstein, F. F., Klein, M., Larocca, F., Saenz, J. A., and Scovazzi, G. 2021. The Filtering Approach as a Tool for Modeling and Analyzing Turbulence. Pages 67–77 in Progress in Turbulence IX, Örlü, R., Talamelli, A., Peinke, J., and Oberlack, M. (eds). Springer Proceedings in Physics, vol. 267.Google Scholar
Ghosal, S., Lund, T., Moin, P., and Akselvoll, K. 1995. A Dynamic Localization Model for Large-Eddy Simulation of Turbulent Flows. Journal of Fluid Mechanics, 286, 229–255.CrossRefGoogle Scholar
Girimaji, S. S. 2006. Partially Averaged Navier–Stokes Model for Turbulence: A Reynolds-Averaged Navier–Stokes to Direct Numerical Simulation Bridging Method. Journal of Applied Mechanics, 73, 413–421.Google Scholar
Grinstein, F. F. 2016. Coarse Grained Simulation and Turbulent Mixing. Cambridge University Press.CrossRefGoogle Scholar
Grinstein, F. F., Margolin, L. G., and Rider, W. J. 2010. Implicit Large Eddy Simulation: Computing Turbulent Flow Dynamics. 2nd ed. Cambridge University Press.Google Scholar
Grinstein, F. F., Saenz, J. A., Rauenzahn, R. M., Germano, M., and Israel, D. M. 2020. Dynamic Bridging Modeling for Coarse Grained Simulations of Shock Driven Turbulent Mixing. Computers and Fluids, 199, 104430.CrossRefGoogle Scholar
Grinstein, F. F., Pereira, F. S., and Rider W., J. 2023. Numerical Approximations Formulated as LES Models. Pages 393–434 in Numerical Methods in Turbulence Simulation, Moser, R. D. (ed). Academic Press.Google Scholar
GS, S., and Candler, G. V. 2018. Subgrid-Scale Effects in Compressible Variable-Density Decaying Turbulence. Journal of Fluid Mechanics, 846, 428–459.Google Scholar
Guermond, J. L., Oden, J. T., and Prudhomme, S. 2004. Mathematical Perspectives on Large Eddy Simulation Models for Turbulent Flows. Journal of Mathematical Fluid Mechanics, 6, 194–248.CrossRefGoogle Scholar
Hamba, F. 2011. Analysis of Filtered Navier–Stokes Equation for Hybrid RANS/LES Simulation. Physics of Fluids, 23, 015108/13.CrossRefGoogle Scholar
Härtel, C., Kleiser, L., Unger, F., and Friedrich, R. 1994. Subgrid Scale Energy Transfer in the Near Wall Region of Turbulent Flows. Physics of Fluids, 6, 3130–3143.CrossRefGoogle Scholar
Harten, A. 1996. Multiresolution Representation of Data: A General Framework. SIAM Journal on Numerical Analysis, 33(3), 1205–1256.CrossRefGoogle Scholar
Kampé de Fériet, J. 1957a. La Notion de Moyenne Dans la Thèorie de la Turbulence. Rendiconti del Seminario Matematico e Fisico di Milano, 27, 167–207.Google Scholar
Kampé de Fériet, J. 1957b. Problèmes Mathématiques de la Théorie de la Turbulence Homogène. Pages 1–104 in Corso Sulla Teoria Della Turbolenza, Varenna 1–10 Settembre 1957, Torino, Italy, Levrotto e Bella, (ed) Re-edited by Springer, (2011).Google Scholar
Kampé de Fériet, J., and Betchov, R. 1951. Theoretical and Experimental Averages of Turbulent Functions. Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen, 53, 389–398.Google Scholar
Klein, M., and Germano, M. 2018. Decomposition of the Reynolds Stress from Filtered Data. Physical Review Fluids, 3, 114606.CrossRefGoogle Scholar
Klein, M., and Germano, M. 2021. Analysis and Modelling of the Commutation Error. Fluids, 6(15).Google Scholar
Kuerten, J. G. M., Geurts, B. J., Vreman, A. W., and M., Germano. 1999. Dynamic Inverse Modeling and its Testing in Large Eddy Simulations of the Mixing Layer. Physics of Fluids, 11, 3778–3785.CrossRefGoogle Scholar
Lee, J. 1995. Chaos and Direct Numerical Simulation in Turbulence. Theoretical and Computational Fluid Dynamics, 7, 363–395.CrossRefGoogle Scholar
Leonard, A. 1975. Energy Cascade in Large-Eddy Simulations of Turbulent Fluid Flows. Advances in Geophysics, 18A, 237–248.Google Scholar
Lilly, D. K. 1992. A Proposed Modification of the Germano Subgrid Scale Closure Method. Physics of Fluids, A4, 633–635.Google Scholar
Lilly, D. K. 1966. On the Application of the Eddy Viscosity Concept in the Inertial Sub-Range of Turbulence. NCAR Manuscript, 123, Boulder, Colorado, USA.Google Scholar
Meneveau, C. 2012. Germano Identity-Based Subgrid-Scale Modeling: A Brief Survey of Variations on a Fertile Theme. Physics of Fluids, 24, 121301.CrossRefGoogle Scholar
Moin, P., and Kim, J. 1982. Numerical Investigation of Turbulent Channel Flow. Journal of Fluid Mechanics, 118, 341–377.CrossRefGoogle Scholar
Moser, R. D., Haering, S. W., and Yalla, G. R. 2021. Statistical Properties of Subgrid-Scale Turbulence Models. Annual Review of Fluid Mechanics, 53, 255–286.Google Scholar
Najafiyazdi, M., Mongeau, L., and S., Nadarajah. 2023. Large Eddy Simulation on Unstructured Grids Using Explicit Differential Filtering: A Case Study of Taylor–Green Vortex. Journal of Computational Physics, 476, 111833.CrossRefGoogle Scholar
Nini, M., Abbà, A., Germano, M., and Restelli, M. 2016. Analysis of a Hybrid RANS/LES Model Using RANS Reconstruction. Pages 83–86 in Progress in Turbulence VI, Peinke, J., Kampers, G., Oberlack, M., Wac lawczyk, M., and Talamelli, A. (eds). Springer.Google Scholar
Oberlack, M. 1997. Invariant Modelling in Large-Eddy Simulation of Turbulence. Pages 3–22 in Annual Research Briefs. Center for Turbulence Research, Moin, P. (ed).Google Scholar
Otte, M. 2005. Mathematics, Sign and Activity. Pages 9–22 in Activity and Science – Grounding Mathematics, Hoffman, M. H. G., Lenhard, J. and Seeger, F. (eds). Springer.Google Scholar
Papoulis, A. 1965. Probability, Random Variables and Stochastic Processes. International Student Edition ed. Kogakusha, McGraw-Hill, LTD.Google Scholar
Pereira, F. S., Eça, L., Vaz, G., and Girimaji, S. S. 2021. Toward Predictive RANS and SRS Computations of Turbulent External Flows of Practical Interest. Archives of Computational Methods in Engineering, 28, 3953–4029.CrossRefGoogle Scholar
Pereira, F. S., Grinstein, F. F., Israel, D. M., and Eça, L. 2022. Verification and Validation: The Path to Predictive Scale-Resolving Simulations of Turbulence. ASME Journal of Verification, Validation, and Uncertainty Quantification, 7(2), 021003.Google Scholar
Pope, S. B. 2000. Turbulent Flows. Cambridge University Press.Google Scholar
Pope, S. B. 2004. Ten Questions Concerning the Large-Eddy Simulation of Turbulent Flows. New Journal of Physics, 6, 35.CrossRefGoogle Scholar
Rajamani, B., and Kim, J. 2010. A Hybrid-Filter Approach to Turbulence Simulation. Flow, Turbulence and Combustion, 85, 421–441.CrossRefGoogle Scholar
Reynolds, O. 1895. On the Dynamical Theory of Incompressible Viscous Fluids and the Determination of the Criterion. Philosophical Transactions of the Royal Society of London, A186, 123–164.Google Scholar
Richardson, L. F. 1927. The Deferred Approach to the Limit. Philosophical Transactions of the Royal Society of London Series, A226, 229–361.Google Scholar
Roache, P. J. 1997. Quantification of Uncertainty in Computational Fluid Dynamics. Annual Reviews of Fluid Mechanics, 29, 123–160.CrossRefGoogle Scholar
Sagaut, P. (2006). Large Eddy Simulation for Incompressible Flows. Springer, New York, USA, 3rd edition.Google Scholar
Multiscale and Multiresolution Approaches in Turbulence. Imperial College Press.Google Scholar
Sagaut, P., and Deck, S. 2009. Large Eddy Simulations for Aerodynamics: Status and Perspectives. Philosophical Transactions of the Royal Society of London, A367, 2849–2860.Google Scholar
San, O., Staples, A. E., and Iliescu, T. 2013. Approximate Deconvolution Large Eddy Simulation of a Stratified Two-Layer Quasigeostrophic Ocean Model. Ocean Modeling, 3, 1–20.Google Scholar
Sánchez-Rocha, M., and Menon, S. 2009. The Compressible Hybrid RANS/LES Formulation Using an Additive Operator. Journal of Computational Physics, 228, 2037–2062.CrossRefGoogle Scholar
Schiestel, R., and Dejoan, A. 2005. Towards a New Partially Integrated Transport Model for Coarse Grid and Unsteady Turbulent Flow Simulations. Theoretical and Computational Fluid Dynamics, 18, 443–468.CrossRefGoogle Scholar
Schumann, U. 1975. Subgrid Scale Model for Finite Difference Simulations of Turbulent Flows in Plane Channels and Annuli. Journal of Computational Physics, 18, 376–404.CrossRefGoogle Scholar
Scotti, A., and Piomelli, U. 2001. Numerical Simulation of Pulsating Turbulent Channel Flow. Physics of Fluids, 13, 1367–1384.CrossRefGoogle Scholar
Smagorinsky, J. 1963. General Circulation Experiments with the Primitive Equations. I The Basic Experiment. Monthly Weather Reviews, 91, 99–164.Google Scholar
Spalart, P. R., Jou, W. H., Strelets, M., and Allmaras, S. R. 1997. Comments on the Feasibility of LES for Wings, and on a Hybrid RANS/LES Approach. In: Advances in DNS/LES, Liu C., Liu Z. (eds). Greyden Press.Google Scholar
Speziale, C. G. 1985. Galilean Invariance of Subgrid-Scale Stress Models in the Large Eddy Simulation of Turbulence. Journal of Fluid Mechanics, 156, 55–62.CrossRefGoogle Scholar
Speziale, C. G. 1998. Turbulence Modeling for Time-Dependent RANS and VLES: A Review. AIAA Journal, 36(2), 173–184.CrossRefGoogle Scholar
Stolz, S., and Adams, N. A. 1999. An Approximate Deconvolution Procedure for Large Eddy Simulation. Physics of Fluids, 11, 1699–1701.CrossRefGoogle Scholar
Taneda, S. 1956. Experimental Investigation of the Wake behind a Sphere at Low Reynolds Numbers. Journal of the Physical Society of Japan, 11, 1104–1108.Google Scholar
Tennekes, H., and Lumley, J. L. 1972. A First Course in Turbulence. MIT Press.CrossRefGoogle Scholar
Tsinober, A. 2014. The Essence of Turbulence as a Physical Phenomenon. 1st ed. Springer.CrossRefGoogle Scholar
van Dyke, M. 1982. An Album of Fluid Motion. The Parabolic Press.CrossRefGoogle Scholar
Warming, R. F., and Hyett, B. J. 1974. The Modified Equation Approach and the Stability and Accuracy Analysis of Finite-Difference Methods. Journal of the Physical Society, 14, 159–179.Google Scholar
Werlé, M. 1982. Transition et décollement: visualisations en tunnel hydrodynamique de l’ONERA. https://publis.onera.fr/DOC169704_s1.pdf.Google Scholar

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