Neutron Transport and Diffusion in Inhomogeneous Media. II

We construct an asymptotic solution of the neutron transport equation in a large heterogeneous medium using a multiscale method. The solution is asymptotic with respect to a small dimensionless parameter, ϵ, 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 ard are then averaged over the cell. We compare the asymptotic diffusion coefficients to other “homogenized” dif usion coefficients that have been proposed in the literature and show that a substantial numerical disagreement exists for a large class of problems. We also give a physical interpretation to the asymptotic solution and to the numerical results concerning the asymptotic diffusion coefficients.