Spatial Homogenization of Transport Discretization Schemes

Abstract

Neutron transport problems for whole reactor core calculations result in a very large amount of unknowns. Some difficulties related to dimensionality of this kind of problem can be resolved by solving a well-posed homogenized transport problem on a coarse grid. We apply homogenization methodology to develop discretization schemes for solving k-eigenvalue problems on coarse meshes in 1D slab geometry. The step characteristic (SC) method is used for fine-mesh transport calculations. We develop spatially homogenized transport schemes on a basis of two different transport discretization methods: SC and linear discontinuous schemes. The basic approach is to formulate a discretization that is spatially consistent with the given fine-mesh transport discretization. The presented numerical results demonstrate features of the developed methods in preserving grid functions of the angular flux computed with the SC method on fine spatial meshes. We study sensitivity of the proposed schemes to various types of perturbations in spatially averaged cross sections and other homogenization parameters.