Molecular extended thermodynamics: comparison between rarefied polyatomic and monatomic gas closures |
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| Authors: | Takashi Arima Tommaso Ruggeri Masaru Sugiyama Shigeru Taniguchi |
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| Affiliation: | 1.Department of Mechanical Engineering, Faculty of Engineering,Kanagawa University,Yokohama,Japan;2.Department of Mathematics,University of Bologna,Bologna,Italy;3.Alma Mater Research Center on Applied Mathematics AM2,University of Bologna,Bologna,Italy;4.Graduate School of Engineering,Nagoya Institute of Technology,Nagoya,Japan;5.Department of Creative Engineering, National Institute of Technology,Kitakyushu College,Kitakyushu,Japan |
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| 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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