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Multiscale Phenomena in Continuum Mechanics: Mesoscopic Justification of Rational Extended Thermodynamics of Gases with Internal Structure

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Views on Microstructures in Granular Materials

Part of the book series: Advances in Mechanics and Mathematics ((ACM,volume 44))

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Abstract

In many physical systems one encounters situations where phenomena occur at different scales. An example is the modeling of a rarefied gas at varying Knudsen number (Kn). Large Kn corresponds to a case where the Boltzmann equation is the most appropriate model while, for small Kn, one can obtain the Euler or Navier–Stokes–Fourier system. At intermediate regime, using the mathematical methods of Rational Extended Thermodynamics (RET), one can obtain the closure of hyperbolic moment system associated with the Boltzmann equation for monatomic gas. This methodology can be extended to polyatomic gas by considering a distribution function depending on an extra variable that takes into account the internal motion of polyatomic molecule (rotation and vibration). In this survey paper we consider first the state-of-the-art of RET and at the end we give a summary on the recent results about more refined version of RET of polyatomic gas in which molecular rotational and vibrational relaxation processes are treated individually.

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Notes

  1. 1.

    In this paper there are some misprints and therefore interested reader can check also Chapter 6 of the book [8].

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Acknowledgement

This work was supported by National Group of Mathematical Physics GNFM-INdAM.

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Authors and Affiliations

  1. Department of Mathematics and Alma Mater Research Center on Applied Mathematics AM2, University of Bologna, Bologna, Italy

    Tommaso Ruggeri

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  1. Tommaso Ruggeri
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Correspondence to Tommaso Ruggeri .

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Editors and Affiliations

  1. Department of Civil, Energy, Environment, and Materials Engineering (DICEAM), University ‘Mediterranea’ of Reggio Calabria, Reggio Calabria, Italy

    Pasquale Giovine

  2. Department of Civil and Environmental Engineering, University of Florence, Firenze, Italy

    Paolo Maria Mariano

  3. Department of Civil, Energy, Environment, and Materials Engineering (DICEAM), University of Reggio Calabria, Reggio Calabria, Italy

    Giuseppe Mortara

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Ruggeri, T. (2020). Multiscale Phenomena in Continuum Mechanics: Mesoscopic Justification of Rational Extended Thermodynamics of Gases with Internal Structure. In: Giovine, P., Mariano, P.M., Mortara, G. (eds) Views on Microstructures in Granular Materials. Advances in Mechanics and Mathematics(), vol 44. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-49267-0_10

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