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Navier–Stokes Hydrodynamic Limit of BGK Kinetic Equations for an Inert Mixture of Polyatomic Gases

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From Particle Systems to Partial Differential Equations (PSPDE 2016)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 258))

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Abstract

We perform an hydrodynamic limit of BGK equations for an inert mixture of polyatomic gases, with molecular structure modelled by a set of discrete internal energy levels. An asymptotic Chapman–Enskog procedure provides consistent hydrodynamic equations at Navier–Stokes level for species number densities, global momentum and total (kinetic plus internal) energy. We explicitly compute diffusion velocities (with Fick matrix and Soret coefficients), pressure tensor (with the dynamical pressure typical of polyatomic gases), and heat flux (with Dufour effect).

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Acknowledgements

This work is performed in the frame of activities sponsored by INdAM–GNFM and by the University of Parma. M. Bisi acknowledges the kind invitation of the University of Minho to the conference From Particle Systems to Partial Differential Equations V (Braga, Portugal, November 2017), where some of these results have been presented.

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Authors and Affiliations

  1. Department of Mathematics, Physics and Computer Science, University of Parma, Parco Area delle Scienze 53/A, Parma, Italy

    Marzia Bisi & Giampiero Spiga

Authors
  1. Marzia Bisi
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  2. Giampiero Spiga
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Corresponding author

Correspondence to Marzia Bisi .

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Editors and Affiliations

  1. Center for Mathematical Analysis, Geometry and Dynamical Systems, Instituto Superior Técnico, University of Lisbon, Lisbon, Portugal

    Patrícia Gonçalves

  2. Center of Mathematics, University of Minho, Braga, Portugal

    Ana Jacinta Soares

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Bisi, M., Spiga, G. (2018). Navier–Stokes Hydrodynamic Limit of BGK Kinetic Equations for an Inert Mixture of Polyatomic Gases. In: Gonçalves, P., Soares, A. (eds) From Particle Systems to Partial Differential Equations . PSPDE 2016. Springer Proceedings in Mathematics & Statistics, vol 258. Springer, Cham. https://doi.org/10.1007/978-3-319-99689-9_1

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