Stochastic Lagrangian Method for Downscaling Problems in Computational Fluid Dynamics

Frédéric Bernardin 1 Mireille Bossy 2 Claire Chauvin 3 Jean Francois Jabir 4 Antoine Rousseau 3
1 CETE de Lyon - Centre d'études techniques de l'équipement de Lyon
2 TOSCA
INRIA Lorraine, CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, INPL - Institut National Polytechnique de Lorraine, CNRS - Centre National de la Recherche Scientifique : UMR7502
3 MOISE - Modelling, Observations, Identification for Environmental Sciences
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
4 CMM - Centre de modélisation mathématique
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.
Keywords : Langevin models PDF methods downscaling methods fluid dynamics particle methods
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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, EDP Sciences, 2010, Special Issue on Probabilistic methods and their applications, 44 (5), pp.885-920. ⟨10.1051/m2an/2010050⟩. ⟨inria-00410932v4⟩

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