Stochastic Lagrangian method for downscaling problems in computational fluid dynamics

Frédéric Bernardin; Mireille Bossy; Claire Chauvin; Jean-François Jabir; Antoine Rousseau

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 44, Issue: 5, page 885-920
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Bernardin, Frédéric, et al. "Stochastic Lagrangian method for downscaling problems in computational fluid dynamics." ESAIM: Mathematical Modelling and Numerical Analysis 44.5 (2010): 885-920. <http://eudml.org/doc/250787>.

@article{Bernardin2010,
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. },
author = {Bernardin, Frédéric, Bossy, Mireille, Chauvin, Claire, Jabir, Jean-François, Rousseau, Antoine},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Langevin models; PDF methods; downscaling methods; fluid dynamics; particle methods},
language = {eng},
month = {8},
number = {5},
pages = {885-920},
publisher = {EDP Sciences},
title = {Stochastic Lagrangian method for downscaling problems in computational fluid dynamics},
url = {http://eudml.org/doc/250787},
volume = {44},
year = {2010},
}

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: Mathematical Modelling and Numerical Analysis
DA - 2010/8//
PB - EDP Sciences
VL - 44
IS - 5
SP - 885
EP - 920
AB - 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.
LA - eng
KW - Langevin models; PDF methods; downscaling methods; fluid dynamics; particle methods
UR - http://eudml.org/doc/250787
ER -

References

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