# American Institute of Mathematical Sciences

• Previous Article
Slow flocking dynamics of the Cucker-Smale ensemble with a chemotactic movement in a temperature field
• KRM Home
• This Issue
• Next Article
Strong solutions for the Alber equation and stability of unidirectional wave spectra
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:

show all references

##### 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)
 [1] Pavel I. Plotnikov, Jan Sokolowski. Optimal shape control of airfoil in compressible gas flow governed by Navier-Stokes equations. Evolution Equations & Control Theory, 2013, 2 (3) : 495-516. doi: 10.3934/eect.2013.2.495 [2] Pavel I. Plotnikov, Jan Sokolowski. Compressible Navier-Stokes equations. Conference Publications, 2009, 2009 (Special) : 602-611. doi: 10.3934/proc.2009.2009.602 [3] Jan W. Cholewa, Tomasz Dlotko. Fractional Navier-Stokes equations. Discrete & Continuous Dynamical Systems - B, 2018, 23 (8) : 2967-2988. doi: 10.3934/dcdsb.2017149 [4] Yong Yang, Bingsheng Zhang. On the Kolmogorov entropy of the weak global attractor of 3D Navier-Stokes equations:Ⅰ. Discrete & Continuous Dynamical Systems - B, 2017, 22 (6) : 2339-2350. doi: 10.3934/dcdsb.2017101 [5] Hermenegildo Borges de Oliveira. Anisotropically diffused and damped Navier-Stokes equations. Conference Publications, 2015, 2015 (special) : 349-358. doi: 10.3934/proc.2015.0349 [6] Hyukjin Kwean. Kwak transformation and Navier-Stokes equations. Communications on Pure & Applied Analysis, 2004, 3 (3) : 433-446. doi: 10.3934/cpaa.2004.3.433 [7] Vittorino Pata. On the regularity of solutions to the Navier-Stokes equations. Communications on Pure & Applied Analysis, 2012, 11 (2) : 747-761. doi: 10.3934/cpaa.2012.11.747 [8] C. Foias, M. S Jolly, I. Kukavica, E. S. Titi. The Lorenz equation as a metaphor for the Navier-Stokes equations. Discrete & Continuous Dynamical Systems - A, 2001, 7 (2) : 403-429. doi: 10.3934/dcds.2001.7.403 [9] Igor Kukavica. On regularity for the Navier-Stokes equations in Morrey spaces. Discrete & Continuous Dynamical Systems - A, 2010, 26 (4) : 1319-1328. doi: 10.3934/dcds.2010.26.1319 [10] Igor Kukavica. On partial regularity for the Navier-Stokes equations. Discrete & Continuous Dynamical Systems - A, 2008, 21 (3) : 717-728. doi: 10.3934/dcds.2008.21.717 [11] Susan Friedlander, Nataša Pavlović. Remarks concerning modified Navier-Stokes equations. Discrete & Continuous Dynamical Systems - A, 2004, 10 (1&2) : 269-288. doi: 10.3934/dcds.2004.10.269 [12] Hakima Bessaih, Benedetta Ferrario. Statistical properties of stochastic 2D Navier-Stokes equations from linear models. Discrete & Continuous Dynamical Systems - B, 2016, 21 (9) : 2927-2947. doi: 10.3934/dcdsb.2016080 [13] Ben Duan, Zhen Luo. Dynamics of vacuum states for one-dimensional full compressible Navier-Stokes equations. Communications on Pure & Applied Analysis, 2013, 12 (6) : 2543-2564. doi: 10.3934/cpaa.2013.12.2543 [14] Fang Li, Bo You, Yao Xu. Dynamics of weak solutions for the three dimensional Navier-Stokes equations with nonlinear damping. Discrete & Continuous Dynamical Systems - B, 2018, 23 (10) : 4267-4284. doi: 10.3934/dcdsb.2018137 [15] Jean-Pierre Raymond. Stokes and Navier-Stokes equations with a nonhomogeneous divergence condition. Discrete & Continuous Dynamical Systems - B, 2010, 14 (4) : 1537-1564. doi: 10.3934/dcdsb.2010.14.1537 [16] Yoshikazu Giga. A remark on a Liouville problem with boundary for the Stokes and the Navier-Stokes equations. Discrete & Continuous Dynamical Systems - S, 2013, 6 (5) : 1277-1289. doi: 10.3934/dcdss.2013.6.1277 [17] Siegfried Maier, Jürgen Saal. Stokes and Navier-Stokes equations with perfect slip on wedge type domains. Discrete & Continuous Dynamical Systems - S, 2014, 7 (5) : 1045-1063. doi: 10.3934/dcdss.2014.7.1045 [18] John W. Barrett, Endre Süli. Existence of global weak solutions to Fokker-Planck and Navier-Stokes-Fokker-Planck equations in kinetic models of dilute polymers. Discrete & Continuous Dynamical Systems - S, 2010, 3 (3) : 371-408. doi: 10.3934/dcdss.2010.3.371 [19] Ana Bela Cruzeiro. Navier-Stokes and stochastic Navier-Stokes equations via Lagrange multipliers. Journal of Geometric Mechanics, 2019, 11 (4) : 553-560. doi: 10.3934/jgm.2019027 [20] Xue-Li Song, Yan-Ren Hou. Attractors for the three-dimensional incompressible Navier-Stokes equations with damping. Discrete & Continuous Dynamical Systems - A, 2011, 31 (1) : 239-252. doi: 10.3934/dcds.2011.31.239

2019 Impact Factor: 1.311