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August  2020, 13(4): 739-758. doi: 10.3934/krm.2020025

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

 CEA-DAM Ile-de-France, France

* Corresponding author: Sébastien Guisset

Received  August 2019 Revised  January 2020 Published  May 2020

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.

Citation: Sébastien Guisset. Angular moments models for rarefied gas dynamics. Numerical comparisons with kinetic and Navier-Stokes equations. Kinetic & Related Models, 2020, 13 (4) : 739-758. doi: 10.3934/krm.2020025
##### References:

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##### References:
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 $t = 15$
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 $t = 5$
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 $t = 5$
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 $t = 5$
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 $t = 0.25$
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 $t = 0.1$
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 $t = 0.1$
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 $t = 0.1$
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 $t = 0.2$
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 $t = 0.1$
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 $t = 0.1$
Representation of the inverse of the shock thickness as function of the Mach number (speed of the in-going flow)
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