[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.
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@article{CRMATH_2012__350_5-6_319_0,
author = {Po\"ette, Ga\"el and Lucor, Didier and Jourdren, Herv\'e},
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},
url = {http://www.numdam.org/articles/10.1016/j.crma.2012.01.018/}
}
TY - JOUR AU - Poëtte, Gaël AU - Lucor, Didier AU - Jourdren, Hervé 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 UR - http://www.numdam.org/articles/10.1016/j.crma.2012.01.018/ DO - 10.1016/j.crma.2012.01.018 LA - en ID - CRMATH_2012__350_5-6_319_0 ER -
%0 Journal Article %A Poëtte, Gaël %A Lucor, Didier %A Jourdren, Hervé %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 %U http://www.numdam.org/articles/10.1016/j.crma.2012.01.018/ %R 10.1016/j.crma.2012.01.018 %G en %F CRMATH_2012__350_5-6_319_0
Poëtte, Gaël; Lucor, Didier; Jourdren, Hervé. A stochastic surrogate model approach applied to calibration of unstable fluid flow experiments. Comptes Rendus. Mathématique, Tome 350 (2012) no. 5-6, pp. 319-324. doi : 10.1016/j.crma.2012.01.018. http://www.numdam.org/articles/10.1016/j.crma.2012.01.018/
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