Formal passage from kinetic theory to incompressible Navier–Stokes equations for a mixture of gases. (15th July 2014)

• Record Type: Journal Article
• Authors: Bisi, Marzia; Desvillettes, Laurent
• Is Part Of: Mathematical modelling and numerical analysis. Volume 48:Part 4(2014)
• Page Start: 1171
• Page End: 1197
• Publication Date: 2014-07-15
• Subjects: Kinetic theory, -- incompressible Navier–Stokes equations, -- hydrodynamic limits; Numerical analysis -- Periodicals; Mathematical models -- Periodicals; 510
• DOI: 10.1051/m2an/2013135
• Languages: English
• ISSNs: 0764-583X

Abstract

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.