Modelling and numerical study of the polyatomic bitemperature Euler system

Denise Aregba-Driollet; Stéphane Brull

doi:10.3934/nhm.2022018

Article Contents

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

This issue Previous Article A periodic homogenization problem with defects rare at infinity Next Article An atomistic derivation of von-Kármán plate theory

Modelling and numerical study of the polyatomic bitemperature Euler system

Denise Aregba-Driollet and
Stéphane Brull^,

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

^* Corresponding author: Stéphane Brull
^* Corresponding author: Stéphane Brull

Received: April 2021

Revised: January 2022

Early access: April 2022

Published: August 2022

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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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Mathematics Subject Classification: Primary: 82C40; Secondary: 76X05, 65M08, 35L60.

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Figure 1. Double rarefaction. Left: density. Right: velocity

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Figure 2. Double rarefaction. Left: electronic temperature. Right : ionic temperature

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Figure 3. Total density (left) and electronic temperature (right) at time $ t = 4.0901\times 10^{-7} $s for an implosion test case with $ \nu_{ei} $ given by the NRL formulary with a grid of 500 by 500 points

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Figure 4. Implosion test case with $ \nu_{ei} $ given by the NRL formulary with a grid of 500 by 500 points. Density along the first bisector at 4 different times: the peak occurs for $ t = 9.2 \times 10^{-7} $ sec

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Figure 5. Implosion test case with $ \nu_{ei} $ given by the NRL formulary with a grid of 500 by 500 points. Left: isovalues of the density when the peak occurs. Right: isovalues of the electronic and ionic temperatures when the peak occurs

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