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A grid-independent length scale for large-eddy simulations

  • Ugo Piomelli (a1), Amirreza Rouhi (a1) and Bernard J. Geurts (a2) (a3)


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.


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Bardina, J., Ferziger, J. H. & Rogallo, R. S.1980 Improved subgrid scale models for large eddy simulation. AIAA Paper 80-1357.
Bose, S. T., Moin, P. & You, D. 2010 Grid-independent large-eddy simulation using explicit filtering. Phys. Fluids 22, 105103.
Chorin, A. J. 1968 Numerical solution of Navier–Stokes equations. Math. Comput. 22 (104), 745762.
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, 215223.
Dubief, Y. & Delcayre, F. 2000 On coherent vortex identification in turbulence. J. Turbul. 1, 011-1-22.
Germano, M. 1992 Turbulence: the filtering approach. J. Fluid Mech. 238, 325336.
Germano, M., Piomelli, U., Moin, P. & Cabot, W. H. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3, 17601765.
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. 112. Kluwer.
Geurts, B. J. 2003 Elements of Direct and Large-Eddy Simulation. Edwards.
Geurts, B. J. & Fröhlich, J. 2002 A framework for predicting accuracy limitations in large-eddy simulation. Phys. Fluids 14 (6), L41L44.
Geurts, B. J. & Holm, D. D. 2006a Commutator errors in large-eddy simulation. J. Phys. A: Math. Gen. 39, 22132229.
Geurts, B. J. & Holm, D. D. 2006b Leray and LANS- ${\it\alpha}$ modelling of turbulent mixing. J. Turbul. 7, 10-1-44.
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.
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.
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. 4756. Kluwer.
Ghosal, S. 1996 An analysis of numerical errors in large-eddy simulations of turbulence. J. Comput. Phys. 125, 187206.
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, 229255.
Ghosal, S. & Moin, P. 1995 The basic equations for the large-eddy simulation of turbulent flows in complex geometries. J. Comput. Phys. 118, 2437.
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, 413421.
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), 422429.
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. 167179. Stanford University.
Hanjalić, K. & Launder, B. E. 1972 A Reynolds stress model of turbulence and its application to thin shear flows. J. Fluid Mech. 52 (4), 609638.
Hoyas, S. & Jiménez, J. 2006 Scaling of the velocity fluctuations in turbulent channels up to $\mathit{Re}_{{\it\tau}}=2003$ . Phys. Fluids 18, 011702.
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. 193208. Stanford University.
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.
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), 46964712.
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.
Kim, J. & Moin, P. 1985 Application of a fractional step method to incompressible Navier–Stokes equations. J. Comput. Phys. 59, 308323.
Leonard, A. 1975 Energy cascade in large-eddy simulations of turbulent fluid flows. Adv. Geophys. 18A, 237248.
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. 147162. Kluwer.
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.
Lilly, D. K. 1992 A proposed modification of the Germano subgrid-scale closure method. Phys. Fluids A 4, 633635.
Lund, T. S. 2003 The use of explicit filters in large-eddy simulations. Comput. Math. Appl. 46, 603616.
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, 439462.
McMillan, O. J. & Ferziger, J. H. 1979 Direct testing of subgrid-scale models. AIAA J. 17, 13401346.
Meneveau, C., Lund, T. S. & Cabot, W. H. 1996 A Lagrangian dynamic subgrid-scale model of turbulence. J. Fluid Mech. 319, 353385.
Menter, F. R. & Egorov, Y.2005 A scale-adaptive simulation model using two-equation models. AIAA Paper 2005–1095.
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), 113138.
Meyers, J., Geurts, B. J. & Baelmans, M. 2003 Database analysis of errors in large-eddy simulation. Phys. Fluids 15 (9), 27402755.
Meyers, J., Geurts, B. J. & Baelmans, M. 2005 Optimality of the dynamic procedure for large-eddy simulations. Phys. Fluids 17, 045108.
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, 90124.
Piomelli, U. 1993 High Reynolds number calculations using the dynamic subgrid-scale stress model. Phys. Fluids A 5 (6), 14841490.
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.
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. 1520. Springer.
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.
Pope, S. B. 2004 Ten questions concerning the large-eddy simulation of turbulent flows. New J. Phys. 6 (35), 124.
Rosales, C. & Meneveau, C. 2005 Linear forcing in numerical simulations of isotropic turbulence: physical space implementations and convergence properties. Phys. Fluids 17, 095106.
Rotta, J. C. 1970 über eine methode zur berechnung turbulenter scherströmungsfelder. Z. Angew. Math. Mech. 50, 204205.
Saffman, P. G. 1970 A model for inhomogeneous turbulent flows. Proc. R. Soc. Lond. A 317, 417433.
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.
Smagorinsky, J. 1963 General circulation experiments with the primitive equations. I. The basic experiment. Mon. Weath. Rev. 91, 99164.
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. 137148. Greyden.
Speziale, C. G. 1991 Analytical methods for the development of Reynolds-stress closures in turbulence. Annu. Rev. Fluid Mech. 23, 107157.
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, 167202.
van der Bos, F. & Geurts, B. J. 2005a Commutator errors in the filtering approach to large-eddy simulation. Phys. Fluids 17, 035108.
van der Bos, F. & Geurts, B. J. 2005b Lagrangian dynamics of commutator errors in large-eddy simulation. Phys. Fluids 17, 075101.
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.
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, 297311.
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), 785790.
Wilcox, D. C. 1974 Comparison of two-equation turbulence models for boundary layers with pressure gradient. AIAA J. 31 (8), 14141421.
Wilcox, D. C. 1993 Turbulence Modeling for CFD. DCW Industries.
Yoshizawa, A. 1982 A statistically-derived subgrid model for the large-eddy simulation of turbulence. Phys. Fluids 25 (9), 15321538.
Yoshizawa, A. 1986 Statistical theory for compressible turbulent shear flows, with the application to subgrid modeling. Phys. Fluids 29 (7), 21522164.
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A grid-independent length scale for large-eddy simulations

  • Ugo Piomelli (a1), Amirreza Rouhi (a1) and Bernard J. Geurts (a2) (a3)


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