Three-dimensional solutions of the Boltzmann equation: heat transport at long mean free paths.

A kinetic transport model for arbitrary meshes is presented and the method is applied to heat transfer in a rare gas between parallel plates at different temperatures. The method uses "propagating" rays for tracking the transport of particles throughout the phase space in three-dimensional spatial meshes. Two collision operators are tested with the model, a simple monoenergetic operator and the Bhatnagar-Gross-Krook (BGK) model. Results are generated for several Knudsen numbers in the transition regime. The results of the kinetic simulation, which employ the BGK operator, compare favorably with those of a finite-difference solution of the Boltzmann equation using the BGK collision operator [T. Ohwada, Phys. Fluids 8, 2153 (1996)]. In addition, the results for both collision models exhibit fair agreement with experimental data of Teagan and Springer [Phys. Fluids. 11, 497 (1968)].