AREGBA-DRIOLLET, Denise; BREIL, J.; BRULL, Stéphane; DUBROCA, B.; ESTIBALS, Elise

doi:10.1051/m2an/2017007

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AREGBA-DRIOLLET, Denise
Institut de Mathématiques de Bordeaux [IMB]

BREIL, J.
Centre d'Etudes Lasers Intenses et Applications [CELIA]

BRULL, Stéphane
Équipe Calcul scientifique et Modélisation
Institut de Mathématiques de Bordeaux [IMB]

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ESAIM: Mathematical Modelling and Numerical Analysis. 2018, vol. 52, n° 4, p. 1353-1383

EDP Sciences

Résumé en anglais

This paper is devoted to the study of the nonconservative bitemperature Euler system. We firstly introduce an underlying two species kinetic model coupled with the Poisson equation. The bitemperature Euler system is then established from this kinetic model according to an hydrodynamic limit. A dissipative entropy is proved to exist and a solution is defined to be admissible if it satisfies the related dissipation property. Next, four different numerical methods are presented. Firstly, the kinetic model gives rise to kinetic schemes for the fluid system. The second approach belongs to the family of the discrete BGK schemes introduced by Aregba-Driollet and Natalini. Finally, a quasi-linear relaxation approach and a Lagrange-remap scheme are considered. 1991 Mathematics Subject Classification. 65M08, 35L60, 35L65. Secondary: 82D10, 76X05. The dates will be set by the publisher.< Réduire

Mots clés en anglais

nonconservative hyperbolic system

entropy dissipation

Relaxation method

hydrodynamic limit

kinetic schemes

BGK models

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Modelling and numerical approximation for the nonconservative bitemperature Euler model

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