Neutron transport and diffusion in inhomogeneous media. II

An asymptotic solution of the neutron transport equation is constructed in a large heterogeneous medium using a multiscale method. The solution is asymptotic with respect to a small dimensionless parameter, epsilon, which is defined as the ratio of a mean-free-path to the diameter of the medium. The leading term of the solution is the product of two functions, one determined by a cell calculation and the other as the solution of a diffusion equation. The coefficients in the diffusion equation contain functions that are determined by cell calculations and are then averaged over the cell. The asymptotic diffusion coefficients are compared to other homogenized diffusion coefficients that have been proposed in the literature. A substantial numerical disagreement exists for a large class of problems. A physical interpretation is given to the asymptotic solution and to the numerical results concerning the asymptotic diffusion coefficients.