Angular moments models for rarefied gas dynamics. Numerical comparisons with kinetic and Navier-Stokes equations

Sébastien Guisset

doi:10.3934/krm.2020025

Article Contents

2020, Volume 13, Issue 4: 739-758. Doi: 10.3934/krm.2020025

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Angular moments models for rarefied gas dynamics. Numerical comparisons with kinetic and Navier-Stokes equations

Sébastien Guisset^,

CEA-DAM Ile-de-France, France

^* Corresponding author: Sébastien Guisset
^* Corresponding author: Sébastien Guisset

Received: August 2019

Revised: January 2020

Published: May 2020

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Abstract

Angular moments models based on a minimum entropy problem have been largely used to describe the transport of photons [14] or charged particles [18]. In this communication the $ M_1 $ and $ M_2 $ angular moments models are presented for rarefied gas dynamics applications. After introducing the models studied, numerical simulations carried out in various collisional regimes are presented and illustrate the interest in considering angular moments models for rarefied gas dynamics applications. For each numerical test cases, the differences observed between the angular moments models and the well-known Navier-Stokes equations are discussed and compared with reference kinetic solutions.

Keywords:

Mathematics Subject Classification: Primary: 76P, 76N; Secondary: 65D, 65C.

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Figure 1. Density (top left), speed (top right), temperature (bottom left), heat flux (bottom right) profiles in the case $ \tau = 1/\nu = 0 $ (fluid regime) at time $ t = 15 $

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Figure 2. Representation of the density (top left), speed (top right), temperature (bottom left), heat flux (bottom right) in the case $ \tau = 1/\nu = 1 $ (close fluid regime) at time $ t = 5 $

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Figure 3. Representation of the density (top left), speed (top right), temperature (bottom left), heat flux (bottom right) in the case $ \tau = 1/\nu = 100 $ (rarefied regime) at time $ t = 5 $

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Figure 4. Representation of the density (top left), speed (top right), temperature (bottom left), heat flux (bottom right) in the case $ \tau = 1/\nu = 10^{4} $ (strongly rarefied regime) at time $ t = 5 $

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Figure 5. Representation of the density (top left), speed (top right), temperature (bottom left), heat flux (bottom right) in the case $ \tau = 1/\nu = 0 $ (fluid regime) at time $ t = 0.25 $

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Figure 6. Representation of the density (top left), speed (top right), temperature (bottom left), heat flux (bottom right) in the case $ \tau = 1/\nu = 10^{-2} $ (close of fluid regime) at time $ t = 0.1 $

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Figure 7. Representation of the density (top left), speed (top right), temperature (bottom left), heat flux (bottom right) in the case $ \tau = 1/\nu = 10^{-1} $ at time $ t = 0.1 $

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Figure 8. Representation of the density (top left), speed (top right), temperature (bottom left), heat flux (bottom right) in the case $ \tau = 1/\nu = 1 $ (intermediate regimes) at time $ t = 0.1 $

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Figure 9. Representation of the density (top left), speed (top right), temperature (bottom left), heat flux (bottom right) in the case $ \tau = 1/\nu = 0 $ (fluid regime) at time $ t = 0.2 $

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Figure 10. Representation of the density (top left), speed (top right), temperature (bottom left), heat flux (bottom right) in the case $ \tau = 1/\nu = 10^{-1} $ at time $ t = 0.1 $

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Figure 11. Representation of the density (top left), speed (top right), temperature (bottom left), heat flux (bottom right) in the case $ \tau = 1/\nu = 1 $ at time $ t = 0.1 $

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Figure 12. Representation of the inverse of the shock thickness as function of the Mach number (speed of the in-going flow)

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