Modelling and numerical study of the polyatomic bitemperature Euler system

Denise Aregba-Driollet; Stéphane Brull; Denise Aregba-Driollet; Stéphane Brull

doi:10.3934/nhm.2022018

Networks and Heterogeneous Media

2022, Volume 17, Issue 4: 593-611. doi: 10.3934/nhm.2022018

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Modelling and numerical study of the polyatomic bitemperature Euler system

Denise Aregba-Driollet ,
Stéphane Brull ^,

Univ. Bordeaux, CNRS, Bordeaux INP, IMB, UMR 5251, F-33400 Talence, France

Received: 01 April 2021 Revised: 01 January 2022 Published: 02 April 2022
Primary: 82C40; Secondary: 76X05, 65M08, 35L60

This paper is devoted to the study of the bitemperature Euler system in a polyatomic setting. Physically, this model describes a mixture of one species of ions and one species of electrons in the quasi-neutral regime. We firstly derive the model starting from a kinetic polyatomic model and performing next a fluid limit. This kinetic model is shown to satisfy fundamental properties. Some exact solutions are presented. Finally, a numerical scheme is derived and proved to coincide with an approximation designed in [3] and extended to second order and two space dimensions in [6]. Some numerical tests are presented.
- Nonconservative hyperbolic system,
- Euler type model for plasmas,
- BGK model,
- polyatomic,
- discrete BGK scheme
Citation: Denise Aregba-Driollet, Stéphane Brull. Modelling and numerical study of the polyatomic bitemperature Euler system[J]. Networks and Heterogeneous Media, 2022, 17(4): 593-611. doi: 10.3934/nhm.2022018

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Abstract

This paper is devoted to the study of the bitemperature Euler system in a polyatomic setting. Physically, this model describes a mixture of one species of ions and one species of electrons in the quasi-neutral regime. We firstly derive the model starting from a kinetic polyatomic model and performing next a fluid limit. This kinetic model is shown to satisfy fundamental properties. Some exact solutions are presented. Finally, a numerical scheme is derived and proved to coincide with an approximation designed in [3] and extended to second order and two space dimensions in [6]. Some numerical tests are presented.

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