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Ricerche di Matematica

, Volume 66, Issue 1, pp 1–13 | Cite as

Molecular extended thermodynamics: comparison between rarefied polyatomic and monatomic gas closures

  • Takashi Arima
  • Tommaso RuggeriEmail author
  • Masaru Sugiyama
  • Shigeru Taniguchi
Article
  • 124 Downloads

Abstract

Molecular extended thermodynamics is justified at the mesoscopic level by the moment equations associated with the Boltzmann equation. For polyatomic gases we have a binary hierarchy of moments in contrast with the usual single hierarchy for monatomic gases. In this paper, taking one-dimensional space variables for simplicity, we review the closure of the system of the moment equations for polyatomic gases with the use of the maximum entropy principle, which is equivalent to the entropy principle. Then we consider the singular limit where the degrees of freedom of a molecule approach 3, and we prove that, by imposing appropriate initial conditions, the solutions for polyatomic gases converge to the ones for monatomic gases. As examples of the singular limit, the asymptotic behaviors of linear waves and light scattering based on the linearized system of field equations are briefly presented.

Keywords

Extended Thermodynamics Rarefied Polyatomic Gases  Rarefied Monatomic Gases Singular Limit Kinetic Theory and Moments 

Mathematics Subject Classification

82C35 Irreversible thermodynamics, including Onsager-Machlup theory 76N15 Gas dynamics, general 82C40 Kinetic theory of gases 

Notes

Acknowledgments

This work was partially supported by Japan Society of Promotion of Science (JSPS) No. 15K21452 (T.A.) and No. 25390150 (M.S.), and by National Group of Mathematical Physics GNFM-INdAM and by University of Bologna: FARB 2012 Project Extended Thermodynamics of Non-Equilibrium Processes from Macro- to Nano-Scale (T.R.).

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Copyright information

© Università degli Studi di Napoli "Federico II" 2016

Authors and Affiliations

  • Takashi Arima
    • 1
  • Tommaso Ruggeri
    • 2
    • 3
    Email author
  • Masaru Sugiyama
    • 4
  • Shigeru Taniguchi
    • 5
  1. 1.Department of Mechanical Engineering, Faculty of EngineeringKanagawa UniversityYokohamaJapan
  2. 2.Department of MathematicsUniversity of BolognaBolognaItaly
  3. 3.Alma Mater Research Center on Applied Mathematics AM2University of BolognaBolognaItaly
  4. 4.Graduate School of EngineeringNagoya Institute of TechnologyNagoyaJapan
  5. 5.Department of Creative Engineering, National Institute of TechnologyKitakyushu CollegeKitakyushuJapan

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