An asymptotic homogenized neutron diffusion approximation. I. Theory
Travis Trahan, Edward W. Larsen · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 2012
A monoenergetic, homogenized, anisotropic diffusion equation is derived asymptotically for large, 3-D, multiplying systems with a periodic lattice structure. The primary assumption is that the system is slightly perturbed from an infinite, periodic lattice, and that the length scale of a lattice element is small relative to the total system size. The perturbed flux is slightly buckled, and the leading order term is the product of a slowly varying amplitude component, and a rapidly varying periodic component. The amplitude function is the solution to the homogenized diffusion equation, while the periodic component is the solution to the unperturbed, infinite system, and can be found using any high-order transport method. The first order term acts as a correction term, and makes it possible to obtain a zero flux extrapolation distance for the diffusion equation by applying the Marshak boundary condition. (authors)