Stochastic Fluid Dynamic Model and Dimensional Reduction

Valentin Resseguier 1, 2 Etienne Mémin 1 Bertrand Chapron 2
1 FLUMINANCE - Fluid Flow Analysis, Description and Control from Image Sequences
IRSTEA - Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture, Inria Rennes – Bretagne Atlantique
Abstract : This paper uses a new decomposition of the fluid velocity in terms of a large-scale continuous component with respect to time and a small-scale non continuous random component. Within this general framework, a stochas-tic representation of the Reynolds transport theorem and Navier-Stokes equations can be derived, based on physical conservation laws. This physically relevant stochas-tic model is applied in the context of the POD-Galerkin method. In both the stochastic Navier-Stokes equation and its reduced model, a possibly time-dependent, inhomoge-neous and anisotropic diffusive subgrid tensor appears naturally and generalizes classical subgrid models. We proposed two ways of estimating its parametrization in the context of POD-Galerkin. This method has shown to be able to successfully reconstruct energetic Chronos for a wake flow at Reynolds 3900, whereas standard POD-Galerkin diverged systematically.
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International Symposium on Turbulence and Shear Flow Phenomena (TSFP-9), Jun 2015, Melbourne, Australia. International Symposium on Turbulence and Shear Flow Phenomena (TSFP-9), 〈http://tsfp9.org〉
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Valentin Resseguier, Etienne Mémin, Bertrand Chapron. Stochastic Fluid Dynamic Model and Dimensional Reduction. International Symposium on Turbulence and Shear Flow Phenomena (TSFP-9), Jun 2015, Melbourne, Australia. International Symposium on Turbulence and Shear Flow Phenomena (TSFP-9), 〈http://tsfp9.org〉. 〈hal-01238301〉

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