Nonoscillatory schemes for kinetic model equations for gases with internal energy states

High-order accurate nonoscillatory schemes based on the discrete ordinate method and the characteristic flux difference splitting method are presented for solving the nonlinear Krook-type kinetic model equations for both monatomic gases and gases possessing internal degrees of freedom. The methods are tested for one-dimensional unsteady shock tube flow and for two-dimensional steady rarefied stream past a NACA 0012 airfoil at angles of attack. The computed results are found in good agreement both with theoretical solutions from Euler and Navier-Stokes calculations and with experimental results. Comparisons of results using kinetic models for both monatomic and diatomic gases are included.