Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-29T01:00:31.513Z Has data issue: false hasContentIssue false
  • English
  • Français

A grid-independent length scale for large-eddy simulations

Published online by Cambridge University Press:  05 February 2015

Ugo Piomelli ,
Amirreza Rouhi  and
Bernard J. Geurts
Ugo Piomelli*
Affiliation:
Department of Mechanical and Materials Engineering, Queen’s University, Kingston, Ontario K7L 3N6, Canada
Amirreza Rouhi
Affiliation:
Department of Mechanical and Materials Engineering, Queen’s University, Kingston, Ontario K7L 3N6, Canada
Bernard J. Geurts
Affiliation:
Department of Applied Mathematics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands Faculty of Applied Physics, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We propose a new length scale as a basis for the modelling of subfilter motions in large-eddy simulations (LES) of turbulent flow. Rather than associating the model length scale with the computational grid, we put forward an approximation of the integral length scale to achieve a non-uniform flow coarsening through spatial filtering that reflects the local, instantaneous turbulence activity. Through the introduction of this grid-independent, solution-specific length scale it becomes possible to separate the problem of representing small-scale turbulent motions in a coarsened flow model from that of achieving an accurate numerical resolution of the primary flow scales. The formulation supports the notion of grid-independent LES, in which a prespecified reliability measure is used. We investigate a length-scale definition based on the resolved turbulent kinetic energy (TKE) and its dissipation. The proposed approach, which we call integral length-scale approximation (ILSA) model, is illustrated for turbulent channel flow at high Reynolds numbers and for homogeneous isotropic turbulence (HIT). We employ computational optimization of the model parameter based on various measures of subfilter activity, using the successive inverse polynomial interpolation (SIPI) and establish the efficiency of this route to subfilter modelling.

JFM classification

Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulence simulation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 766 , 10 March 2015 , pp. 499 - 527
Check for updates
Copyright
© 2015 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bardina, J., Ferziger, J. H. & Rogallo, R. S.1980 Improved subgrid scale models for large eddy simulation. AIAA Paper 80-1357.Google Scholar
Bose, S. T., Moin, P. & You, D. 2010 Grid-independent large-eddy simulation using explicit filtering. Phys. Fluids 22, 105103.CrossRefGoogle Scholar
Chorin, A. J. 1968 Numerical solution of Navier–Stokes equations. Math. Comput. 22 (104), 745–762.Google Scholar
Dean, R. B. 1978 Reynolds number dependence of skin friction and other bulk flow variables in two-dimensional rectangular duct flow. Trans. ASME J. Fluids Eng. 100, 215–223.CrossRefGoogle Scholar
Dubief, Y. & Delcayre, F. 2000 On coherent vortex identification in turbulence. J. Turbul. 1, 011-1-22.Google Scholar
Germano, M. 1992 Turbulence: the filtering approach. J. Fluid Mech. 238, 325–336.Google Scholar
Germano, M., Piomelli, U., Moin, P. & Cabot, W. H. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3, 1760–1765.CrossRefGoogle Scholar
Geurts, B. J. 1999 Balancing errors in LES. In Direct and Large-Eddy Simulation III: Proceedings of the Isaac Newton Institute Symposium/ERCOFTAC Workshop, Cambridge, UK, 12–14 May 1999 (ed. Voke, P. R., Sandham, N. D. & Kleiser, L.), pp. 1–12. Kluwer.Google Scholar
Geurts, B. J. 2003 Elements of Direct and Large-Eddy Simulation. Edwards.Google Scholar
Geurts, B. J. & Fröhlich, J. 2002 A framework for predicting accuracy limitations in large-eddy simulation. Phys. Fluids 14 (6), L41–L44.CrossRefGoogle Scholar
Geurts, B. J. & Holm, D. D. 2006a Commutator errors in large-eddy simulation. J. Phys. A: Math. Gen. 39, 2213–2229.Google Scholar
Geurts, B. J. & Holm, D. D. 2006b Leray and LANS- ${\it\alpha}$ modelling of turbulent mixing. J. Turbul. 7, 10-1-44.Google Scholar
Geurts, B. J., Kuczaj, A. K. & Titi, E. S. 2008 Regularization modeling for large-eddy simulation of homogeneous isotropic decaying turbulence. J. Phys. A: Math. Theor. 41 (34), 344008.CrossRefGoogle Scholar
Geurts, B. J. & Meyers, J. 2006 Successive inverse polynomial interpolation to optimize Smagorinsky’s model for large-eddy simulation of homogeneous turbulence. Phys. Fluids 18, 118102.Google Scholar
Geurts, B. J., Vreman, B., Kuerten, H. & Van Buuren, R. 1997 Noncommuting filters and dynamic modelling for LES of turbulent compressible flow in 3d shear layers. In Direct and Large-Eddy Simulation II: Proceedings of the ERCOFTAC Workshop held in Grenoble, France, 16–19 September, 1996 (ed. Chollet, J.-P., Voke, P. R. & Kleiser, L.), pp. 47–56. Kluwer.Google Scholar
Ghosal, S. 1996 An analysis of numerical errors in large-eddy simulations of turbulence. J. Comput. Phys. 125, 187–206.Google Scholar
Ghosal, S., Lund, T. S., Moin, P. & Akselvoll, K. 1995 A dynamic localization model for large-eddy simulation of turbulent flows. J. Fluid Mech. 286, 229–255.Google Scholar
Ghosal, S. & Moin, P. 1995 The basic equations for the large-eddy simulation of turbulent flows in complex geometries. J. Comput. Phys. 118, 24–37.Google Scholar
Girimaji, S. S. 2006 Partially averaged Navier–Stokes method for turbulence: a Reynolds-averaged Navier–Stokes to direct numerical simulation bridging method. Trans. ASME J. Appl. Mech. 73, 413–421.Google Scholar
Girimaji, S. S., Jeong, E. & Srinivas, R. 2006 Partially averaged Navier–Stokes method for turbulence: fixed point analysis and comparison with unsteady partially averaged Navier–Stokes. Trans. ASME J. Appl. Mech. 63 (3), 422–429.Google Scholar
Gullbrand, J. 2002 Grid-independent large-eddy simulation in turbulent channel flow using three-dimensional explicit filtering. In Center for Turbulence Research Annual Research Briefs 2002, pp. 167–179. Stanford University.Google Scholar
Hanjalić, K. & Launder, B. E. 1972 A Reynolds stress model of turbulence and its application to thin shear flows. J. Fluid Mech. 52 (4), 609–638.Google Scholar
Hoyas, S. & Jiménez, J. 2006 Scaling of the velocity fluctuations in turbulent channels up to $\mathit{Re}_{{\it\tau}}=2003$ . Phys. Fluids 18, 011702.CrossRefGoogle Scholar
Hunt, J. C. R., Wray, A. A. & Moin, P. 1988 Eddies, streams, and convergence zones in turbulent flows. In Studying Turbulence Using Numerical Simulation Databases, 2. Proceedings of the 1988 Summer Program, pp. 193–208. Stanford University.Google Scholar
Keating, A. & Piomelli, U. 2006 A dynamic stochastic forcing method as a wall-layer model for large-eddy simulation. J. Turbul. 7, 12-1-24.Google Scholar
Keating, A., Piomelli, U., Balaras, E. & Kaltenbach, H.-J. 2004a A priori and a posteriori tests of inflow conditions for large-eddy simulation. Phys. Fluids 16 (12), 4696–4712.Google Scholar
Keating, A., Piomelli, U., Bremhorst, K. & Nešić, S. 2004b Large-eddy simulation of heat transfer downstream of a backward-facing step. J. Turbul. 5, 20-1-27.CrossRefGoogle Scholar
Kim, J. & Moin, P. 1985 Application of a fractional step method to incompressible Navier–Stokes equations. J. Comput. Phys. 59, 308–323.Google Scholar
Leonard, A. 1975 Energy cascade in large-eddy simulations of turbulent fluid flows. Adv. Geophys. 18A, 237–248.Google Scholar
Leonard, A. & Winckelmans, G. S. 1999 A tensor-diffusivity subgrid model for large-eddy simulations. In Direct and Large-Eddy Simulation III: Proceedings of the Isaac Newton Institute Symposium/ERCOFTAC Workshop, Cambridge, UK, 12–14 May 1999 (ed. Voke, P. R., Sandham, N. D. & Kleiser, L.), pp. 147–162. Kluwer.Google Scholar
Lilly, D. K.1967 The representation of small scale turbulence in numerical simulation experiments. In Proceedings of the IBM Scientific Computing Symposium on Environmental Sciences, pp. 195–210.Google Scholar
Lilly, D. K. 1992 A proposed modification of the Germano subgrid-scale closure method. Phys. Fluids A 4, 633–635.Google Scholar
Lund, T. S. 2003 The use of explicit filters in large-eddy simulations. Comput. Math. Appl. 46, 603–616.Google Scholar
Mason, P. J. & Callen, N. S. 1986 On the magnitude of the subgrid-scale eddy coefficient in large-eddy simulations of turbulent channel flow. J. Fluid Mech. 162, 439–462.CrossRefGoogle Scholar
McMillan, O. J. & Ferziger, J. H. 1979 Direct testing of subgrid-scale models. AIAA J. 17, 1340–1346.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.Google Scholar
Menter, F. R. & Egorov, Y.2005 A scale-adaptive simulation model using two-equation models. AIAA Paper 2005–1095.CrossRefGoogle Scholar
Menter, F. R. & Egorov, Y. 2010 The scale-adaptive simulation method for unsteady turbulent flow predictions. Part 1: theory and model description. Flow Turbul. Combust. 85 (1), 113–138.Google Scholar
Meyers, J., Geurts, B. J. & Baelmans, M. 2003 Database analysis of errors in large-eddy simulation. Phys. Fluids 15 (9), 2740–2755.Google Scholar
Meyers, J., Geurts, B. J. & Baelmans, M. 2005 Optimality of the dynamic procedure for large-eddy simulations. Phys. Fluids 17, 045108.Google Scholar
Morinishi, Y., Lund, T. S., Vasilyev, O. V. & Moin, P. 1998 Fully conservative higher order finite difference schemes for incompressible flows. J. Comput. Phys. 143, 90–124.Google Scholar
Piomelli, U. 1993 High Reynolds number calculations using the dynamic subgrid-scale stress model. Phys. Fluids A 5 (6), 1484–1490.Google Scholar
Piomelli, U. & Geurts, B. J.2010 A grid-independent length scale for large-eddy simulations of wall-bounded flows. In Proceedings of 8th International Symposium Engineering Turbulence Modelling and Measurements – ETMM8 (ed. M. A. Leschziner, P. Bontoux, B. J. Geurts, B. E. Launder & C. Tropea), pp. 226–231.Google Scholar
Piomelli, U. & Geurts, B. J. 2011 A physical length scale for LES of turbulent flow. In Direct and Large-Eddy Simulations VIII (ed. Kuerten, H., Geurts, B. J., Armenio, V. & Fröhlich, J.), pp. 15–20. Springer.CrossRefGoogle 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 J. Phys. 6 (35), 1–24.Google Scholar
Rosales, C. & Meneveau, C. 2005 Linear forcing in numerical simulations of isotropic turbulence: physical space implementations and convergence properties. Phys. Fluids 17, 095106.Google Scholar
Rotta, J. C. 1970 über eine methode zur berechnung turbulenter scherströmungsfelder. Z. Angew. Math. Mech. 50, 204–205.Google Scholar
Saffman, P. G. 1970 A model for inhomogeneous turbulent flows. Proc. R. Soc. Lond. A 317, 417–433.Google Scholar
Singh, S., You, D. & Bose, S. T. 2012 Large-eddy simulation of turbulent channel flow using explicit filtering and dynamic mixed models. Phys. Fluids 24, 085105.CrossRefGoogle Scholar
Smagorinsky, J. 1963 General circulation experiments with the primitive equations. I. The basic experiment. Mon. Weath. Rev. 91, 99–164.Google Scholar
Spalart, P. R., Jou, W. H., Strelets, M. Kh. & Allmaras, S. R. 1997 Comments on the feasibility of LES for wings, and on a hybrid RANS/LES approach. In Advances in DNS/LES (ed. Liu, C. & Liu, Z.), pp. 137–148. Greyden.Google Scholar
Speziale, C. G. 1991 Analytical methods for the development of Reynolds-stress closures in turbulence. Annu. Rev. Fluid Mech. 23, 107–157.Google Scholar
Sullivan, P. P., McWilliams, J. C. & Moeng, C. H. 1996 A grid-nesting method for large-eddy simulation of planetary boundary-layer flows. Boundary-Layer Meteorol. 80, 167–202.CrossRefGoogle Scholar
van der Bos, F. & Geurts, B. J. 2005a Commutator errors in the filtering approach to large-eddy simulation. Phys. Fluids 17, 035108.Google Scholar
van der Bos, F. & Geurts, B. J. 2005b Lagrangian dynamics of commutator errors in large-eddy simulation. Phys. Fluids 17, 075101.Google Scholar
Vanella, M., Piomelli, U. & Balaras, E. 2008 Effect of grid discontinuities in large-eddy simulation statistics and flow fields. J. Turbul. 9, N32-1-23.Google Scholar
Vreman, A. W., Geurts, B. J. & Kuerten, J. G. M. 1996 Comparison of numerical schemes in large-eddy simulation of the temporal mixing layer. Int. J. Numer. Methods Fluids 22, 297–311.Google Scholar
Vreman, B., Geurts, B. J. & Kuerten, H. 1994 Discretization error dominance over subgrid terms in large eddy simulation of compressible shear layers in 2d. Commun. Modern Methods Eng. 10 (10), 785–790.Google Scholar
Wilcox, D. C. 1974 Comparison of two-equation turbulence models for boundary layers with pressure gradient. AIAA J. 31 (8), 1414–1421.Google Scholar
Wilcox, D. C. 1993 Turbulence Modeling for CFD. DCW Industries.Google Scholar
Yoshizawa, A. 1982 A statistically-derived subgrid model for the large-eddy simulation of turbulence. Phys. Fluids 25 (9), 1532–1538.Google Scholar
Yoshizawa, A. 1986 Statistical theory for compressible turbulent shear flows, with the application to subgrid modeling. Phys. Fluids 29 (7), 2152–2164.Google Scholar