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

Ricerche di Matematica volume 66, pages1–13(2017)Cite this article

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.

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Notes

  1. 1.

    Throughout the paper, summation with respect to repeated indexes is assumed, where the range of the sum is to be understood in the context: when the index represents a spatial coordinate, the range of the sum is from 1 to 3; in all the other cases the sum is intended over the variability region of the repeated indexes.

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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.).

Author information

Affiliations

  1. Department of Mechanical Engineering, Faculty of Engineering, Kanagawa University, Yokohama, Japan

    Takashi Arima

  2. Department of Mathematics, University of Bologna, Bologna, Italy

    Tommaso Ruggeri

  3. Alma Mater Research Center on Applied Mathematics AM2, University of Bologna, Bologna, Italy

    Tommaso Ruggeri

  4. Graduate School of Engineering, Nagoya Institute of Technology, Nagoya, Japan

    Masaru Sugiyama

  5. Department of Creative Engineering, National Institute of Technology, Kitakyushu College, Kitakyushu, Japan

    Shigeru Taniguchi

Authors
  1. Takashi Arima
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  2. Tommaso Ruggeri
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  3. Masaru Sugiyama
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  4. Shigeru Taniguchi
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Correspondence to Tommaso Ruggeri.

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Arima, T., Ruggeri, T., Sugiyama, M. et al. Molecular extended thermodynamics: comparison between rarefied polyatomic and monatomic gas closures. Ricerche mat 66, 1–13 (2017). https://doi.org/10.1007/s11587-016-0279-7

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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