Kinetic schemes and boundary conditions for moment equations

Abstract.

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 moments. It is shown that the required distance of grid points must be considerably smaller than the mean free path. Thus, the kinetic scheme is useful only in the case of large Knudsen numbers. Results of the numerical calculation 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.