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.
Mots-clés : Langevin models, PDF methods, downscaling methods, fluid dynamics, particle methods
@article{M2AN_2010__44_5_885_0,
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: 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 = {http://www.numdam.org/articles/10.1051/m2an/2010046/}
}
TY - JOUR 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: Modélisation mathématique et analyse numérique PY - 2010 SP - 885 EP - 920 VL - 44 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2010046/ DO - 10.1051/m2an/2010046 LA - en ID - M2AN_2010__44_5_885_0 ER -
%0 Journal Article %A Bernardin, Frédéric %A Bossy, Mireille %A Chauvin, Claire %A Jabir, Jean-François %A Rousseau, Antoine %T Stochastic lagrangian method for downscaling problems in computational fluid dynamics %J ESAIM: Modélisation mathématique et analyse numérique %D 2010 %P 885-920 %V 44 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2010046/ %R 10.1051/m2an/2010046 %G en %F M2AN_2010__44_5_885_0
Bernardin, Frédéric; Bossy, Mireille; Chauvin, Claire; Jabir, Jean-François; Rousseau, Antoine. Stochastic lagrangian method for downscaling problems in computational fluid dynamics. ESAIM: Modélisation mathématique et analyse numérique, Special Issue on Probabilistic methods and their applications, Tome 44 (2010) no. 5, pp. 885-920. doi : 10.1051/m2an/2010046. http://www.numdam.org/articles/10.1051/m2an/2010046/
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