BOUNDARY CONDITIONS FOR SOLVING THE BOLTZMANN EQUATION IN PERIODIC LATTICES
G. Ya. Rumyantsev · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 1963
A previously described method (Atomnaya Energ., 13: developed and applied for the exact solution of the Boltzmann transport equation. The results of this study of the transport equation involving heterogeneous periodic lattices made it possible to consider only a single cell; the partial solutions of the single-velocity Boltzmann equation were then used for deriving a generalized solution for the whole medium. In the solution of two-dimensional problems, advantage may be taken of certain simplifying conditions, assuming that all rectangular cells are squares and making use of an asymptotic nonhomogeneous solution. It is often sufficient to find only the effective macroscopic parameters of the homogenized medium. The effective macroscopic parameters of the neutron diffusion process must be determined at various angles to the axis of the lattice. (TTT)