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Realizability conditions for the turbulent stress tensor in large-eddy simulation

Published online by Cambridge University Press:  26 April 2006

Bert Vreman ,
Bernard Geurts  and
Hans Kuerten
Bert Vreman
Affiliation:
Department of Applied Mathematics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
Bernard Geurts
Affiliation:
Department of Applied Mathematics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
Hans Kuerten
Affiliation:
Department of Applied Mathematics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
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Abstract

The turbulent stress tensor in large-eddy simulation is examined from a theoretical point of view. Realizability conditions for the components of this tensor are derived, which hold if and only if the filter function is positive. The spectral cut-off, one of the filters frequently used in large-eddy simulation, is not positive. Consequently, the turbulent stress tensor based on spectrally filtered fields does not satisfy the realizability conditions, which leads to negative values of the generalized turbulent kinetic energy k. Positive filters, e. g. Gaussian or top-hat, always give rise to a positive k. For this reason, subgrid models which require positive values for k should be used in conjunction with e. g. the Gaussian or top-hat filter rather than with the spectral cutoff filter. If the turbulent stress tensor satisfies the realizability conditions, it is natural to require that the subgrid model for this tensor also satisfies these conditions. With respect to this point of view several subgrid models are discussed. For eddy-viscosity models a lower bound for the generalized turbulent kinetic energy follows as a necessary condition. This result provides an inequality for the model constants appearing in a ‘Smagorinsky-type’ subgrid model for compressible flows.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 278 , 10 November 1994 , pp. 351 - 362
Copyright
© 1994 Cambridge University Press

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