[Généralisation de l'identité de Bohm quantique : condition CFL hyperbolique pour équations d'Euler–Korteweg]
Dans cette note, on propose une importante généralisation de l'identité dite du potentiel de Bohm quantique. Cette dernière permet de définir une formulation augmentée des systèmes d'Euler–Korteweg, qui est sous forme conservative dans le cas multi-dimensionnel. Une conséquence très importante de cette formulation est la construction de schémas avec stabilité entropique sous condition CFL hyperbolique du système d'Euler–Korteweg. Cette généralisation de l'identité de Bohm évite donc le développement d'ondes parasites pour ces systèmes de type dispersif et est aussi importante, par exemple, dans l'étude des équations de Navier–Stokes compressibles à viscosités dégénérées.
In this note, we propose a surprising and important generalization of the quantum Bohm potential identity. This formula allows us to design an original conservative extended formulation of Euler–Korteweg systems and the construction of a numerical scheme with entropy stability property under a hyperbolic CFL condition in the multi-dimensional setting. To the authors' knowledge, this generalization of the quantum Bohm identity strongly improves what is already known for simulation of such a dispersive system and is also important for theoretical studies on compressible Navier–Stokes equations with degenerate viscosities.
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@article{CRMATH_2016__354_1_39_0,
author = {Bresch, Didier and Couderc, Fr\'ed\'eric and Noble, Pascal and Vila, Jean-Paul},
title = {A generalization of the quantum {Bohm} identity: {Hyperbolic} {CFL} condition for {Euler{\textendash}Korteweg} equations},
journal = {Comptes Rendus. Math\'ematique},
pages = {39--43},
publisher = {Elsevier},
volume = {354},
number = {1},
year = {2016},
doi = {10.1016/j.crma.2015.09.020},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2015.09.020/}
}
TY - JOUR AU - Bresch, Didier AU - Couderc, Frédéric AU - Noble, Pascal AU - Vila, Jean-Paul TI - A generalization of the quantum Bohm identity: Hyperbolic CFL condition for Euler–Korteweg equations JO - Comptes Rendus. Mathématique PY - 2016 SP - 39 EP - 43 VL - 354 IS - 1 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2015.09.020/ DO - 10.1016/j.crma.2015.09.020 LA - en ID - CRMATH_2016__354_1_39_0 ER -
%0 Journal Article %A Bresch, Didier %A Couderc, Frédéric %A Noble, Pascal %A Vila, Jean-Paul %T A generalization of the quantum Bohm identity: Hyperbolic CFL condition for Euler–Korteweg equations %J Comptes Rendus. Mathématique %D 2016 %P 39-43 %V 354 %N 1 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2015.09.020/ %R 10.1016/j.crma.2015.09.020 %G en %F CRMATH_2016__354_1_39_0
Bresch, Didier; Couderc, Frédéric; Noble, Pascal; Vila, Jean-Paul. A generalization of the quantum Bohm identity: Hyperbolic CFL condition for Euler–Korteweg equations. Comptes Rendus. Mathématique, Tome 354 (2016) no. 1, pp. 39-43. doi : 10.1016/j.crma.2015.09.020. http://www.numdam.org/articles/10.1016/j.crma.2015.09.020/
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