Chapman-Enskog Expansion for a Discrete Velocity Model of a Gas Mixture With Bi-Molecular Chemical Reactions

We propose a new discrete velocity model of the Boltzmann equation for a mixture of four gases admitting particle elastic collisions and bi-molecular chemical reactions. We first prove an H-theorem and determine the thermodynamical equilibrium state. A Chapman-Enskog expansion on the kinetic equations is then performed, deriving both the Euler and the Navier-Stokes equations of the model. Finally the transport coefficients of diffusivity and viscosity are provided as well.