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A BGK Model for Gas Mixtures

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Abstract

The aim of this article is to construct a BGK operator for gas mixtures starting from the true Navier-Stokes equations. That is the ones having transport coefficients given by the hydrodynamical limit of the Boltzmann equation(s). Here the same hydrodynamical limit is obtained by introducing relaxation coefficients on certain moments of the distribution functions. Next the whole model is set by using entropy minimization under moments constraints. In our case the BGK operator allows to recover the exact Fick and Newton laws and satisfy the fundamental properties of the Boltzmann equations for inert gas mixtures.

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Authors and Affiliations

  1. Université Bordeaux, 351, cours de la Libération, 33405, Talence cedex, France

    Stéphane Brull

  2. IUSTI, Polytech Marseille, 5 rue Enrico Fermi, 13000, Marseille, France

    Jacques Schneider

  3. IMATH, University of Toulon, avenue de l’université, 83957, La Garde, France

    Vincent Pavan

Authors
  1. Stéphane Brull
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  2. Jacques Schneider
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  3. Vincent Pavan
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Correspondence to Stéphane Brull.

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Brull, S., Schneider, J. & Pavan, V. A BGK Model for Gas Mixtures. Acta Appl Math 132, 117–125 (2014). https://doi.org/10.1007/s10440-014-9893-0

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  • DOI: https://doi.org/10.1007/s10440-014-9893-0

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