BRULL, Stéphane; DUBROCA, Bruno; PRIGENT, Corentin

doi:10.3934/krm.2020002

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BRULL, Stéphane
Institut de Mathématiques de Bordeaux [IMB]

DUBROCA, Bruno

Laboratoire des Composites Thermostructuraux [LCTS]

PRIGENT, Corentin
Institut de Mathématiques de Bordeaux [IMB]

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Kinetic and Related Models. 2020, vol. 13, n° 1

Résumé en anglais

We are interested in the numerical approximation of the bi-temperature Euler equations, which is a non conservative hyperbolic system introduced in [4]. We consider a conservative underlying kinetic model, the Vlasov-BGK-Poisson system. We perform a scaling on this system in order to obtain its hydrodynamic limit. We present a deterministic numerical method to approximate this kinetic system. The method is shown to be Asymptotic-Preserving in the hydrodynamic limit, which means that any stability condition of the method is independant of any parameter ε, with ε→0. We prove that the method is, under appropriate choices, consistant with the solution for bi-temperature Euler. Finally, our method is compared to methods for the fluid model (HLL, Suliciu).< Réduire

Mots clés en anglais

Bgk model

asympotic preserving scheme

nonconservative hyperbolic system

plasma physics

kinetic scheme

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A kinetic approach of the bi-temperature euler model

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