Mathematical and Physical Constraints on Large-Eddy Simulations |
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Authors: | C Fureby G Tabor |
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Institution: | (1) Department of Mechanical Engineering, Imperial College, Exhibition Road, London SW7 2BX, England, US |
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Abstract: | We examine the mathematical constraints on the filtering operation in large-eddy simulation (LES), and the physical constraints
on the formulation of subgrid scale (SGS) models. The mathematical constraints on filtering arise from the assumption of commutativity
between the filtering operation and the differential operators: this breaks down for finite domains and for non-uniform filter
kernels. The physical constraints on the modelling are twofold; invariance principles require any model to be invariant under
a group of transformations: the most stringent of these being the principle of frame indifference. In addition, realizability
requires that the SGS model should have the same mathematical properties as the term it replaces, which leads to further constraints
on the modelling. Finally, we investigate the effects of commutation and realizability for two simulated cases: forced homogeneous
isotropic turbulence in a box and fully developed channel flow. In particular, we look for correlations between the commutation
errors and the non-realizable regions, and the large-scale resolved flow structures in the simulations.
Received: 17 June 1996 and accepted 3 April 1997 |
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Keywords: | PACS: |
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