Abstract
A generalization is made of the methodological approach to the solution of the tramport equations in heterogeneous periodic lattices, which was presented in the diffusion approximation in [1], The boundary conditions at the outside surface of the cell are derived for making an accurate solution of the one velocity Boltzmann kinetic equations, which permits considering a single cell of the heterogeneons medium. A short discussion is given of methods of solving the problem with these boundary conditions and of the question of eigenvalues.
A general solution for the whole heterogeneous medium in accurate and macroscopic (averaged) form is made up of the special solutions found for a single celt, using the same principle as in [1].
The boundary conditions formulated for a plane one dimensional lattice may be extended to a two dimensional lattice.
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Additional information
Translated from Atomnaya Énergiya, Vol. 14, No. 4, pp. 371–374, April, 1963.
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Rumyantsev, G.Y. Boundary conditions for the solution of Boltzmann's equation in periodic lattices. At Energy 14, 377–381 (1964). https://doi.org/10.1007/BF01114508
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DOI: https://doi.org/10.1007/BF01114508