Consistent Spatial Approximation of the Low-Order Quasi-Diffusion Equations on Coarse Grids

Spatial discretization methods have been developed for the low-order quasi-diffusion equations on coarse grids and corresponding homogenization procedure for full-core reactor calculations. The proposed methods reproduce accurately the complicated large-scale behavior of the transport solution within assemblies. The developed discretization is spatially consistent with a fine-mesh discretization of the transport equation in the sense that it preserves a set of spatial moments of the fine-mesh transport solution over either coarse-mesh cells or its subregions, as well as the surface currents and eigenvalue. To demonstrate accuracy of the proposed methods, numerical results are presented of calculations of test problems that simulate the interaction of mixed-oxide and uranium assemblies.