  Kinetic schemes for compressible flow of gases are constructed by exploiting
the connection between Boltzmann equation and the Navier-Stokes equations. This
connection allows us to construct a flux splitting for the Navier-Stokes
equations based on the direction of molecular motion from which a numerical
flux can be obtained. The naive use of such a numerical flux function in a
discontinuous Galerkin (DG) discretization leads to an unstable scheme in the
viscous dominated case. Stable schemes are constructed by adding additional
terms either in a symmetric or non-symmetric manner which are motivated by the
DG schemes for elliptic equations. The novelty of the present scheme is the use
of kinetic fluxes to construct the stabilization terms. In the symmetric case,
interior penalty terms have to be added for stability and the resulting schemes
give optimal convergence rates in numerical experiments. The non-symmetric
schemes lead to a cell energy/entropy inequality but exhibit sub-optimal
convergence rates. These properties are studied by applying the schemes to a
scalar convection-diffusion equation and the 1-D compressible Navier-Stokes
equations. In the case of Navier-Stokes equations, entropy variables are used
to construct stable schemes.
