Kinetic theory for a discrete velocity gas and application to the shock structure

A model gas is composed of identical particles with velocities restricted to a given finite set of p vectors where only binary collisions are considered. The Boltzmann equation is replaced by a system of p nonlinear coupled differential equations. These equations possess the essential properties of the Boltzmann equation. In particular, the Chapman−Enskog method can be applied. The model with six coplanar velocities is used for the problem of shock structure: The shock structure as given by the associated Navier−Stokes equations is compared with the structure which is known for the exact system. The thickness of the shock structure profile obtained from the associated Navier−Stokes equation is smaller than the thickness obtained from exact equations. These results agree well with those found by other methods.