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Journal Articles ESAIM: Mathematical Modelling and Numerical Analysis Year : 2010

Stochastic Lagrangian Method for Downscaling Problems in Computational Fluid Dynamics

Abstract

This work aims at introducing modelization, theoretical and numerical studies related to a new downscaling technique applied to Computational Fluid Dynamics. Our method consists in building a local model, forced by large scale information computed thanks to a classical numerical weather predictor. The local model, compatible with the Navier-Stokes equations, is used for the small scale computation (downscaling) of the considered fluid. It is inspired by S.B. Pope's works on turbulence, and consists in a so-called Langevin system of stochastic differential equations. We introduce this model and exhibit its links with classical RANS models. Well-posedness, as well as mean-field interacting particle approximations and boundary condition issues are addressed. We present the numerical discretization of the stochastic downscaling method and investigate the accuracy of the proposed algorithm on simplified situations.
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Dates and versions

inria-00410932 , version 1 (25-08-2009)
inria-00410932 , version 2 (09-03-2010)
inria-00410932 , version 3 (09-03-2010)
inria-00410932 , version 4 (31-01-2014)

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Cite

Frédéric Bernardin, Mireille Bossy, Claire Chauvin, Jean-Francois Jabir, Antoine Rousseau. Stochastic Lagrangian Method for Downscaling Problems in Computational Fluid Dynamics. ESAIM: Mathematical Modelling and Numerical Analysis, 2010, Special Issue on Probabilistic methods and their applications, 44 (5), pp.885-920. ⟨10.1051/m2an/2010050⟩. ⟨inria-00410932v4⟩
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