Comparison of homogenized and enhanced diffusion solutions of model PWR problems

Model problem comparisons in slab geometry are made between two forms of homogenized diffusion theory and enhanced diffusion theory. The pin-cell discontinuity factors for homogenized diffusion calculations are derived from homogenized variational nodal P₁ response matrices and from standard finite differencing. Enhanced diffusion theory consists of applying quasi-reflected interface conditions to reduce variational nodal P_n response matrices to one degree of freedom per interface, without homogenization within the cell. As expected both homogenized diffusion methods preserve reaction rates exactly if the discontinuity factors are derived from the P ₁₁ reference solutions. If no reference lattice solution is available, discontinuity factors may be approximated from single cells with reflected boundary conditions; the computational effort is then comparable to calculating the enhanced diffusion response matrices. In this situation enhanced diffusion theory gives the most accurate results and finite difference discontinuity factors the least accurate.