Stochastic lagrangian method for downscaling problems in computational fluid dynamics

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

ESAIM: Modélisation mathématique et analyse numérique, Special Issue on Probabilistic methods and their applications, 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.

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