Kinetic schemes and boundary conditions for moment equations

A numerical scheme for moment equations of kinetic theory, due to LeTallec & Perlat, is considered for the calculation of stationary heat transfer in the Grad 13 moment system and linearized extended thermodynamics of 14 mome nts. It is shown that the required distance of grid points must be consider ably smaller than the mean free path. Thus, the kinetic scheme is useful on ly in the case of targe Knudsen numbers. Results of the numerical calculati on for 13 and 14 moments are compared with an analytical solution for heat transfer with 13 moments. The results indicate that the boundary conditions do not guarantee conservation of energy at the walls. In order to overcome this deficiency a modification of the boundary conditions is presented and discussed.