[Un système multi-fluide compressible avec de nouveaux termes de relaxation physiques]
Dans cet article, nous étudions la propagation d'oscillations de densité dans les solutions des équations de Navier-Stokes compressibles fluides à viscosité variable. Nous appliquons cette analyse à la dérivation rigoureuse d'un système de type Baer-Nunziatio pour les écoulements multi-fluide. Le modèle obtenu inclut de nouveaux termes de relaxation dans les équations sur les fractions volumiques des composants du mélange. Ces termes résultent des différences entre les lois de viscosité et de pression dans les différents composants.
In this paper, we study the propagation of density-oscillations in solutions to density-dependent compressible Navier Stokes system. As a consequence to this analysis, we derive rigorously a generalization of the one-velocity Baer-Nunziato model for multifluid flows. The derived model includes a new relaxation term, in the PDE that governs the volume fraction of the component fluids, that encodes the change of viscosity and pressure between them.
Keywords: Compressible Navier-Stokes, density-dependent viscosity, multifluid flows, Baer-Nunziato, homogenization, Young measures, effective flux, relaxation terms.
Mot clés : Navier-Stokes compressible, viscosité variable, systèmes multi-fluides, Baer-Nunziato, homogénéisation, mesures de Young, flux effectif, termes de relaxation.
@article{ASENS_2019__52_1_257_0,
author = {Bresch, Didier and Hillairet, Matthieu},
title = {A {Compressible} {Multifluid} {System} with {New} {Physical} {Relaxation} {Terms}},
journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
pages = {255--295},
publisher = {Soci\'et\'e Math\'ematique de France. Tous droits r\'eserv\'es},
volume = {Ser. 4, 52},
number = {1},
year = {2019},
doi = {10.24033/asens.2387},
zbl = {1421.35241},
language = {en},
url = {http://www.numdam.org/articles/10.24033/asens.2387/}
}
TY - JOUR AU - Bresch, Didier AU - Hillairet, Matthieu TI - A Compressible Multifluid System with New Physical Relaxation Terms JO - Annales scientifiques de l'École Normale Supérieure PY - 2019 SP - 255 EP - 295 VL - 52 IS - 1 PB - Société Mathématique de France. Tous droits réservés UR - http://www.numdam.org/articles/10.24033/asens.2387/ DO - 10.24033/asens.2387 LA - en ID - ASENS_2019__52_1_257_0 ER -
%0 Journal Article %A Bresch, Didier %A Hillairet, Matthieu %T A Compressible Multifluid System with New Physical Relaxation Terms %J Annales scientifiques de l'École Normale Supérieure %D 2019 %P 255-295 %V 52 %N 1 %I Société Mathématique de France. Tous droits réservés %U http://www.numdam.org/articles/10.24033/asens.2387/ %R 10.24033/asens.2387 %G en %F ASENS_2019__52_1_257_0
Bresch, Didier; Hillairet, Matthieu. A Compressible Multifluid System with New Physical Relaxation Terms. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 52 (2019) no. 1, pp. 255-295. doi : 10.24033/asens.2387. http://www.numdam.org/articles/10.24033/asens.2387/
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