# Etude théorique et numérique de la déformation d'une interface séparant deux fluides non-miscibles à bas nombre de Mach

1 LETR - Laboratoire d'Etudes Thermiques des Réacteurs
DM2S - Département de Modélisation des Systèmes et Structures : DEN/DM2S/SFME/LETR
3 SIMPAF - SImulations and Modeling for PArticles and Fluids
LPP - Laboratoire Paul Painlevé - UMR 8524, Inria Lille - Nord Europe
Abstract : We aimed at studying non-miscible two-fluid flows in a bounded domain in order to better understand and to predict the overall process of bubbly flows in nuclear reactors. A system of PDEs has been derived from the Navier-Stokes equations under a low Mach number assumption and named DLMN. As a preliminary, we prove in this thesis existence and uniqueness results for two sets of PDEs endowed with smooth initial data (Sobolev spaces) and consisting of hyperbolic, parabolic and elliptic equations. In particular, we deal with an abstract bubble vibration model (ABV). In addition to the proof of the short time existence result, we show that there exist global solutions in dimension $1$ no matter what smooth initial data. We also demonstrate several properties satisfied by potential solutions. We then carry out numerical simulations by means of an unconditionally stable second-order scheme based on the method of characteristics (for smooth solutions) or a coupling between an antidiffusive scheme and an adaptive mesh refinement algorithm (in case of discontinuities).
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Cited literature [87 references]

https://tel.archives-ouvertes.fr/tel-00547865
Contributor : Yohan Penel <>
Submitted on : Friday, December 17, 2010 - 3:29:10 PM
Last modification on : Friday, November 27, 2020 - 2:18:02 PM
Long-term archiving on: : Monday, November 5, 2012 - 2:35:17 PM

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• HAL Id : tel-00547865, version 1

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Yohan Penel. Etude théorique et numérique de la déformation d'une interface séparant deux fluides non-miscibles à bas nombre de Mach. Mathématiques [math]. Université Paris-Nord - Paris XIII, 2010. Français. ⟨tel-00547865⟩

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