Stochastic lagrangian method for downscaling problems in computational fluid dynamics
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 44 (2010) no. 5, pp. 885-920.

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.

Classification : 65C20,  65C35,  68U20,  35Q30
Mots clés : Langevin models, PDF methods, downscaling methods, fluid dynamics, particle methods
     author = {Bernardin, Fr\'ed\'eric and Bossy, Mireille and Chauvin, Claire and Jabir, Jean-Fran\c{c}ois and Rousseau, Antoine},
     title = {Stochastic lagrangian method for downscaling problems in computational fluid dynamics},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     pages = {885--920},
     publisher = {EDP-Sciences},
     volume = {44},
     number = {5},
     year = {2010},
     doi = {10.1051/m2an/2010046},
     mrnumber = {2731397},
     language = {en},
     url = {}
AU  - Bernardin, Frédéric
AU  - Bossy, Mireille
AU  - Chauvin, Claire
AU  - Jabir, Jean-François
AU  - Rousseau, Antoine
TI  - Stochastic lagrangian method for downscaling problems in computational fluid dynamics
JO  - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY  - 2010
DA  - 2010///
SP  - 885
EP  - 920
VL  - 44
IS  - 5
PB  - EDP-Sciences
UR  -
UR  -
UR  -
DO  - 10.1051/m2an/2010046
LA  - en
ID  - M2AN_2010__44_5_885_0
ER  - 
Bernardin, Frédéric; Bossy, Mireille; Chauvin, Claire; Jabir, Jean-François; Rousseau, Antoine. Stochastic lagrangian method for downscaling problems in computational fluid dynamics. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 44 (2010) no. 5, pp. 885-920. doi : 10.1051/m2an/2010046.

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