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Stochastic Lagrangian method for downscaling problems in computational fluid dynamics

Published online by Cambridge University Press:  26 August 2010

Frédéric Bernardin ,
Mireille Bossy ,
Claire Chauvin ,
Jean-François Jabir  and
Antoine Rousseau
Frédéric Bernardin
Affiliation:
CETE de Lyon, LRPC, Clermont-Ferrand, France. Frederic.Bernardin@developpement-durable.gouv.fr
Mireille Bossy
Affiliation:
INRIA, TOSCA, Sophia Antipolis, France. Mireille.Bossy@sophia.inria.fr
Claire Chauvin
Affiliation:
INRIA, MOISE, Grenoble, France. Claire.Chauvin@inria.fr
Jean-François Jabir
Affiliation:
CMM Universidad de Chile, Blanco Encalada 2120, Santiago, Chile. jjabir@dim.uchile.cl
Antoine Rousseau
Affiliation:
INRIA & Laboratoire Jean Kuntzmann, 51 rue des Maths, BP 53, 38041 Grenoble Cedex 9, France. Antoine.Rousseau@inria.fr
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Abstract

This work aims at introducing modelling, 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 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 modelsPDF methodsdownscaling methodsfluid dynamicsparticle methods
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 44 , Issue 5: Special Issue on Probabilistic methods and their applications , September 2010 , pp. 885 - 920
Copyright
© EDP Sciences, SMAI, 2010

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