[Un modèle approché stochastique pour la calibration dʼexpériences dʼécoulements instables]
Nous proposons une approche stochastique pour la calibration de tailles de zone de mélange dʼexpériences de tube à choc. La méthodologie repose sur la prise en compte de données initiales incertaines pour les équations dʼEuler. Dans ce travail, la position initiale de lʼinterface est considérée comme incertaine, modélisée par un processus stochastique. La taille de la zone de mélange est alors définie comme le support de la densité de probabilité du processus. Cette densité de probabilité, fonction du temps, est estimée par Chaos Polynomial généralisé non-intrusif, son support pouvant dans ce cas être évalué à moindre coût. Cette méthodologie repose sur un principe dʼergodicité (Wiener, 1938) et généralise lʼapproche par perturbations linéaires. Elle est appliquée dans ce papier à la calibration de résultats expérimentaux.
We propose a stochastic approach for calibration of mixing zone lengths in shock tube experiments. The methodology relies on taking into account uncertain initial data propagated through the basic multifluid Euler equations. In this work, the initial interface position is supposed uncertain, modeled by a stochastic process. The size of the mixing zone is then defined as the support of the probability density function of the stochastic process. This time dependent probability density function is estimated with non-intrusive generalized Polynomial Chaos, its support being in this case cheaply evaluated. This methodology relies on the application of an ergodic principle (Wiener, 1938) and generalizes linear perturbations analysis. It is applied in this Note to the calibration of several experimental results.
Accepté le :
Publié le :
@article{CRMATH_2012__350_5-6_319_0,
author = {Ga\"el Po\"ette and Didier Lucor and Herv\'e Jourdren},
title = {A stochastic surrogate model approach applied to calibration of unstable fluid flow experiments},
journal = {Comptes Rendus. Math\'ematique},
pages = {319--324},
publisher = {Elsevier},
volume = {350},
number = {5-6},
year = {2012},
doi = {10.1016/j.crma.2012.01.018},
language = {en},
}
TY - JOUR AU - Gaël Poëtte AU - Didier Lucor AU - Hervé Jourdren TI - A stochastic surrogate model approach applied to calibration of unstable fluid flow experiments JO - Comptes Rendus. Mathématique PY - 2012 SP - 319 EP - 324 VL - 350 IS - 5-6 PB - Elsevier DO - 10.1016/j.crma.2012.01.018 LA - en ID - CRMATH_2012__350_5-6_319_0 ER -
%0 Journal Article %A Gaël Poëtte %A Didier Lucor %A Hervé Jourdren %T A stochastic surrogate model approach applied to calibration of unstable fluid flow experiments %J Comptes Rendus. Mathématique %D 2012 %P 319-324 %V 350 %N 5-6 %I Elsevier %R 10.1016/j.crma.2012.01.018 %G en %F CRMATH_2012__350_5-6_319_0
Gaël Poëtte; Didier Lucor; Hervé Jourdren. A stochastic surrogate model approach applied to calibration of unstable fluid flow experiments. Comptes Rendus. Mathématique, Volume 350 (2012) no. 5-6, pp. 319-324. doi : 10.1016/j.crma.2012.01.018. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.01.018/
[1] The orthogonal development of non-linear functionals in series of Fourier–Hermite functionals, Ann. of Math., Volume 48 (1947), pp. 385-392
[2] Stochastic investigation of flows about airfoils at transonic speeds, AIAA Journal, Volume 48 (2010) no. 5, pp. 938-950
[3] Gaussian fields and random flow, J. Fluid. Mech., Volume 63 (1974), pp. 21-32
[4] A Godunov type method in Lagrangian coordinates for computing linearly-perturbed planar-symmetric flows of gas dynamics, J. Comp. Phys., Volume 198 (2004), pp. 80-105
[5] Arbitrary high-order schemes for the linear advection and wave equations: Application to hydrodynamics and aeroacoustics, C. R. Acad. Sci. Paris, Ser. I, Volume 342 (2006), pp. 441-446
[6] M. Gerritsma, P. Vos, J.-B. van der Steen, G. Karniadakis, Time dependent generalized polynomial chaos, preprint, 2009.
[7] Richtmyer–Meshkov turbulent mixing arising from an inclined material interface with realistic surface perturbations and reshocked flow, Phys. of Fluids, Volume 23 (2011), p. 046101
[8] Richtmyer–Meshkov instability growth: Experiment, simulation and theory, J. Fluid Mech., Volume 389 (1999), pp. 55-79
[9] A generalization of the Nataf transformation to distributions with elliptical copula, Prob. Eng. Mech., Volume 24 (2009) no. 2, pp. 172-178
[10] Predictability and uncertainty in CFD, Int. J. Numer. Methods Fluids, Volume 43 (2003), pp. 483-505
[11] Hydrodynamic instabilities in ablative tamped flows, Phys. Plas., Volume 13 (2006), p. 122701
[12] Treatment of uncertain interfaces in compressible flows, Comp. Meth. Appl. Math. Engrg., Volume 200 (2011), pp. 284-308
[13] Velocity measurements in turbulent gaseous mixtures induced by Richtmyer–Meshkov instability, Phys. of Fluids, Volume 10 (1998), p. 11
[14] Systèmes Hyperboliques de Lois de Conservation, partie I, Diderot, Paris, 1996
[15] A gPC based approach to uncertain transonic aerodynamics, CMAME, Volume 199 (2010), pp. 1091-1099
[16] Stochastic finite element expansion for random media, ASCE J. Eng. Mech., Volume 115 (1989) no. 5, pp. 1035-1053
[17] B. Sudret, Uncertainty propagation and sensitivity analysis in mechanical models, contribution to structural reliability and stochastic spectral methods, Habilitation à Diriger des Recherches, Université Blaise Pascal – Clermont II, 2007.
[18] Experiments on the Richtmyer–Meshkov instability of an air/SF6 interface, Shock Waves, Volume 4 (1995), pp. 247-252
[19] Beyond Wiener–Askey expansions: Handling arbitrary PDFs, SIAM J. Sci. Comp., Volume 27 (2006) no. 1–3
[20] Long-term behavior of polynomial chaos in stochastic flow simulations, CMAME, Volume 195 (2006), pp. 5582-5596
[21] The homogeneous chaos, Amer. J. Math., Volume 60 (1938), pp. 897-936
[22] Uncertainty quantification for chaotic computational fluid dynamics, J. Comp. Phys., Volume 217 (2006) no. 1, pp. 200-216
Cité par Sources :
Commentaires - Politique