Navier–Stokes Hydrodynamic Limit of BGK Kinetic Equations for an Inert Mixture of Polyatomic Gases
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).
KeywordsPolyatomic gases BGK models Hydrodynamic equations Transport coefficients
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.