A Fick Law's recovering BGK model for a mixture of monoatomic and polyatomic gases

Stéphane Brull; Kévin Guillon; Philippe Thieullen

doi:10.3934/krm.2024006

Article Contents

2024, Volume 17, Issue 6: 914-938. Doi: 10.3934/krm.2024006

This issue Previous Article On the stabilization of a kinetic model by feedback-like control fields in a Monte Carlo framework Next Article Global weak solutions for a nonlocal multispecies Fokker–Planck–Landau system

A Fick Law's recovering BGK model for a mixture of monoatomic and polyatomic gases

1.
Univ. Bordeaux, Bordeaux INP, CNRS, UMR 5251, F-33400 talence, France

^*Corresponding author: Stéphane Brull
^*Corresponding author: Stéphane Brull

Received: March 2023

Revised: December 2023

Early access: March 2024

Published online: March 2024

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Abstract

Through this paper, we extend the derivation of the Fick-relaxation BGK model operated in [16], whose aim was a relaxation operator recovering the Fick Law and the shear viscosity at hydrodynamic limit, for a mixture of monoatomic gases. Here, the framework deals with a mixture of monoatomic and polyatomic gases, and we need a model including the non translational degrees of freedom and internal energies. The attractors are computed from the resolution of an entropy minimisation problem. The model is shown to satisfy a H theorem. Next, we use a Chapman-Enskog expansion in order to compute the expression for the transport coefficients; that is, the phenomenological Fick matrix as both shear and volume viscosity.

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Mathematics Subject Classification: Primary: 82B40, 76P05, ; Secondary: 82C40, 82D05.

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References

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