Homogenization methodology for the low-order equations of the quasi-diffusion method

In this paper the development of spatial homogenization procedure is considered. Such procedure must preserve the averaged reaction rates, surface-averaged group currents, and eigenvalue. The coarse-mesh discretization of the low-order quasi-diffusion equations that is consistent with a fine-mesh discretization is presented. The resulting scheme preserves also the first and second spatial Legendre moments of the fine-mesh transport solution. The definition of discontinuity factors is formulated. The theorem of consistency is proven. The numerical solution of the proposed method reproduces accurately the large-scale behavior of the transport solution within assembly. Numerical results that demonstrate efficiency of the proposed methodology are presented. (author)