Abstract
Subgrid-scale models for large-eddy simulation that are based on exact series expansions for filtered products are considered. In particular, if the first two terms are retained, the result is a diffusive subgrid term with a tensor diffusivity. This tensor is proportional to the rate-of-strain tensor of the large-scale velocity field. This leads to negative diffusion in the stretching directions. Implications of this result are considered for the filtered scalar advection-diffusion equation and for the momentum equation for incompressible fluid flow. When coupled with a dynamic Smagorinsky term to form a mixed model, very encouraging results are shown for turbulent, isotropic decay and for turbulent channel flow. In addition, it is shown that the model, mixed or not, transforms appropriately when differing frames of reference are considered. Modifications to the model are suggested for the case in which the unfiltered field(s) has discontinuities.
On leave: University of Cambridge, Isaac Newton Institute for mathematical Sciences, 20 Clarkson Road, Cambridge CB3 0EH, United Kingdom
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References
Bardina, J., Ferziger, J. H. & Reynolds, W. C.:1983 ‘Improved turbulence models based on large eddy simulation of homogeneous incompressible turbulence’, Report TF-19, Thermosciences Div., Dept. of Mech. Eng., Stanford University
Borue, V. & Orszag,S. A.:1998 ‘Local energy flux and subgrid-scale statistics in three-dimensional turbulence’ J. Fluid Mech. 366: 1–31
Bedford, K. W. & Yeo, W. K.: 1993 ‘Conjunctive filtering procedures in surface water flow and transport’, in Large Eddy Simulation of Complex Engineering and Geophysical Flows, Ed. B. Galperin & S. A. Orszag, Cambridge University Press, 513–537
Carati, D., Winckelmans, G. S. & Jeanmart, H.:1998 ‘On the reversibility in modelling the filtered-scale stress tensor for large-eddy simulation’, submitted to J. Fluid Mech., Dec.
Clark, R. A., Ferziger, J. H. & Reynolds, W. C.:1979 ‘Evaluation of subgrid-scale turbulence models using an accurately simulated turbulent flow’, J. Fluid Mech. 91(1): 1–16
Domaradzki, J. A. & Saiki, E. M.:1997 ‘A subgrid-scale model based on the estimation of unresolved scales of turbulence’, Phys. Fluids 9: 2148–2164
Domaradzki, J. A. & Loh K.-C.:1998 ‘The subgrid-scale estimation model in the physical space representation’, submitted to Phys. Fluids, Sept.
Fureby, C.:1996 ‘On subgrid scale modeling in large eddy simulations of compressible flow’, Phys. Fluids 8: 1301–11
Germano, M., Piomelli, U., Moin, P. & Cabot, W.:1991 ‘A dynamic subgrid-scale eddy-viscosity model’, Phys. Fluids A 3(7): 1760–65
Ghosal, S., Lund, T. S. Moin, P.:1992 ‘A local dynamic model for large-eddy simulation’, Annu. Res. Briefs, Center for Turbulence Research (Stanford University and NASA Ames), 3–25
Ghosal, S., Lund, T. S.,a Moin, P. & Akselvoll, K.:1995 ‘A dynamic localization model for large-eddy simulation of turbulent flows’, J. Fluid Mech. 286: 229–255
Geurts, B.:1997 ‘Inverse modeling for large-eddy simulation’, Phys. Fluids 9: 3585–3587
Leonard, A.:1974 ‘Energy cascade in large-eddy simulations of turbulent fluid flows’, Adv. Geophys. 18: 237
Leonard, A.:1997 ‘Large-eddy simulation of chaotic convection and beyond’, 35th Aerospaces Sciences Meeting & Exhibit, Jan. 6–10, 1997, Reno, NV, AIAA Paper 97–0204 (8 pages).
Liu, S., Meneveau, C. & Katz, J.:1994 ‘On the properties of similarity subgrid-scale models as deduced from measurements in a turbulent jet’, J. Fluid Mech. 275: 83–119
Moeleker, P. & Leonard, A.:1999 ‘Lagrangian methods for the tensor diffusivity subgrid model’, to be submitted
Mansour, N. N., Moser, R. D. & Kim, J.:1996, J.:1996 ‘Reynolds number effects in low Reynolds number turbulent channel’, in preparation, see AGARD-AR-345, April 1998.
Shah, K. B. & Ferziger, J. H.:1995 ‘A new non-eddy viscosity subgrid-scale model and its application to channel flow’, Summer Program Center for Turbulence Research (Stanford University and NASA Ames)
Smagorinsky, J.:1963 ‘General circulation experiments with the primitive equations’, Mon. Weather Rev. 91: 99–164
Stolz, S. & Adams, N. A.:1999 ‘An approximate deconvolution procedure for large-eddy simulation’, Phys. Fluids to appear
Vreman, B., Geurts, B. & Kuerten, H.:1996 ‘Large-eddy simulation of the temporal mixing layer using the mixed Clark model’, Theoret. Comput. Fluid Dynamics 8: 309–324
Vreman, B., Geurts, B. & Kuerten, H.:1997 ‘Large-eddy simulation of the turbulent mixing layer’, J. Fluid Mech. 339: 357–390
Winckelmans, G. S., Wray, A. A. & Vasilyev, O. V.:1998 ‘Testing of a new mixed model for LES: the Leonard model supplemented by a dynamic Smagorinsky term’, Proc. Summer Program, Center for Turbulence Research (Stanford University and NASA Ames), 367–388
Winckelmans, G. S., Wray, A. A., Vasilyev, O. V. & Jeanmart, H.:1999 `Large-eddy simulations using a mixed model with explicit filtering: the tensor-diffusivity model supplemented by a dynamic Smagorinsky term’, to be submitted.
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Leonard, A., Winckelmans, G.S. (1999). A Tensor-Diffusivity Subgrid Model for Large-Eddy Simulation. In: Voke, P.R., Sandham, N.D., Kleiser, L. (eds) Direct and Large-Eddy Simulation III. ERCOFTAC Series, vol 7. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9285-7_13
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DOI: https://doi.org/10.1007/978-94-015-9285-7_13
Publisher Name: Springer, Dordrecht
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