Consistent Coarse-Mesh Discretization of the Low-Order Equations of the Quasi-Diffusion Method

In this paper, the development of a spatial homogenization procedure is considered. Such procedure must preserve the averaged reaction rates, surface-averaged group currents, and eigenvalue. The homogenization fits naturally into the framework of the quasidiffusion (QD) method that is based on the idea of successive averaging of the transport equation over angular and energy variables. The averaging over the spatial variable is the next logical step. We have developed an approach for exact spatial averaging of the discretized QD low-order equations and generating of a coarse-mesh discretization that is consistent with the given fine-mesh discretization. The presented technique can be applied to any number of spatial zones. This is a rigorous mathematical result. The proposed method uses the quantities that are similar by their definitions to discontinuity factors; however, the resulting solution preserves continuity of both the scalar flux and the current on interfaces. The procedure of spatial decomposition based on albedo boundary conditions was formulated. The proposed methodology creates a theoretical background for homogenization of spatial regions. The presented approach of consistent coarse-mesh discretization can be extended to multigroup and multidimensional problems, as well as to different kind of discretization methods.