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A Comparative Study of LES Models Under Location Uncertainty

Pranav Chandramouli 1 Dominique Heitz 1, 2 Etienne Mémin 1 Sylvain Laizet 3
1 FLUMINANCE - Fluid Flow Analysis, Description and Control from Image Sequences
IRMAR - Institut de Recherche Mathématique de Rennes, IRSTEA - Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture, Inria Rennes – Bretagne Atlantique
Abstract : The models under location uncertainty recently introduced by Mémin [16] provide a new outlook on LES modelling for turbulence studies. These models are derived from the stochastic conservation equations using stochastic calculus. These stochastic conservation equations are similar to the filtered Navier- Stokes equation wherein we observe a sub-grid scale dissipation term. However, in the stochastic version, an extra term appears, termed as "velocity bias", which can be treated as a biasing/modification of the large scale advection by the small scales. This velocity bias, introduced first in stochastic models by MacInnes and Bracco [14] albeit artificially, appears here automatically through a decorrelation assumption of the small scales at the resolved scale. All sub-grid contributions for the stochastic models are defined by the small scale velocity auto-correlation (a = $σσT$ ) which can be modelled through a Smagorinsky equivalency or by a local variance calculation. In this study, we have worked towards verifying the applicability and accuracy of these models in two well-studied cases namely that of flow over a circular cylinder at Re ∼ 3900 and smooth channel flow at Reτ ∼ 395. Both these flows have been extensively studied in literature and provide well-established data sets for model comparison. In addition, these flows display numerous important characteristics of turbulence flows that needs to be captured efficiently by the model. This combined with the flow associated numerical complexities makes these the ideal flow for model study. A comparison of the models indicates a statistical improvement in the models under location uncertainty compared with classical deterministic models for both flows.
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Pranav Chandramouli, Dominique Heitz, Etienne Mémin, Sylvain Laizet. A Comparative Study of LES Models Under Location Uncertainty. Congrès Français de Mécanique, Aug 2017, Lille, France. ⟨hal-01584736⟩

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