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

DOI : https://doi.org/10.1051/m2an/2010046
Classification:  65C20,  65C35,  68U20,  35Q30
Keywords: 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 cois 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},
     publisher = {EDP-Sciences},
     volume = {44},
     number = {5},
     year = {2010},
     pages = {885-920},
     doi = {10.1051/m2an/2010046},
     zbl = {pre05798937},
     mrnumber = {2731397},
     language = {en},
     url = {http://www.numdam.org/item/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: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 44 (2010) no. 5, pp. 885-920. doi : 10.1051/m2an/2010046. http://www.numdam.org/item/M2AN_2010__44_5_885_0/

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