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Ninth International Symposium on Turbulence and Shear Flow Phenomena
June 30 - July 3, 2015, University of Melbourne, Australia

DOI: 10.1615/TSFP9

STOCHASTIC FLUID DYNAMIC MODEL AND DIMENSIONAL REDUCTION

pages 649-654
DOI: 10.1615/TSFP9.1090
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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 stochastic representation of the Reynolds transport theorem and Navier-Stokes equations can be derived, based on physical conservation laws. This physically relevant stochastic 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, inhomogeneous 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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