Formal passage from kinetic theory to incompressible Navier–Stokes equations for a mixture of gases

Marzia Bisi; Laurent Desvillettes

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2014)

  • Volume: 48, Issue: 4, page 1171-1197
  • ISSN: 0764-583X

Abstract

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We present in this paper the formal passage from a kinetic model to the incompressible Navier−Stokes equations for a mixture of monoatomic gases with different masses. The starting point of this derivation is the collection of coupled Boltzmann equations for the mixture of gases. The diffusion coefficients for the concentrations of the species, as well as the ones appearing in the equations for velocity and temperature, are explicitly computed under the Maxwell molecule assumption in terms of the cross sections appearing at the kinetic level.

How to cite

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Bisi, Marzia, and Desvillettes, Laurent. "Formal passage from kinetic theory to incompressible Navier–Stokes equations for a mixture of gases." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 48.4 (2014): 1171-1197. <http://eudml.org/doc/273132>.

@article{Bisi2014,
abstract = {We present in this paper the formal passage from a kinetic model to the incompressible Navier−Stokes equations for a mixture of monoatomic gases with different masses. The starting point of this derivation is the collection of coupled Boltzmann equations for the mixture of gases. The diffusion coefficients for the concentrations of the species, as well as the ones appearing in the equations for velocity and temperature, are explicitly computed under the Maxwell molecule assumption in terms of the cross sections appearing at the kinetic level.},
author = {Bisi, Marzia, Desvillettes, Laurent},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {kinetic theory; incompressible Navier–Stokes equations; hydrodynamic limits; incompressible Navier-Stokes equation; gas mixture; hydrodynamic limit; Boltzmann equations},
language = {eng},
number = {4},
pages = {1171-1197},
publisher = {EDP-Sciences},
title = {Formal passage from kinetic theory to incompressible Navier–Stokes equations for a mixture of gases},
url = {http://eudml.org/doc/273132},
volume = {48},
year = {2014},
}

TY - JOUR
AU - Bisi, Marzia
AU - Desvillettes, Laurent
TI - Formal passage from kinetic theory to incompressible Navier–Stokes equations for a mixture of gases
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2014
PB - EDP-Sciences
VL - 48
IS - 4
SP - 1171
EP - 1197
AB - We present in this paper the formal passage from a kinetic model to the incompressible Navier−Stokes equations for a mixture of monoatomic gases with different masses. The starting point of this derivation is the collection of coupled Boltzmann equations for the mixture of gases. The diffusion coefficients for the concentrations of the species, as well as the ones appearing in the equations for velocity and temperature, are explicitly computed under the Maxwell molecule assumption in terms of the cross sections appearing at the kinetic level.
LA - eng
KW - kinetic theory; incompressible Navier–Stokes equations; hydrodynamic limits; incompressible Navier-Stokes equation; gas mixture; hydrodynamic limit; Boltzmann equations
UR - http://eudml.org/doc/273132
ER -

References

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