Seiichi Takeda

A Coarse-Mesh Correction of the Finite Difference Method for Neutron Diffusion Calculations

This study has been undertaken to evaluate an uncertainty in a finite difference method for two-dimensional neutron diffusion calculations and to provide a simple method to eliminate the uncertainty from k/sub eff/, control rod worth, and peak power density. An effect of a condensation of the energy groups is also studied. It is found that errors in k/sub eff/, control rod worth, and peak power density have linear relationships with the square of mesh spacing, and an extrapolation to zero mesh spacing, by using the linear relationships, is possible, eliminating the uncertainties of 0.7 percent ..delta..k/k in k/sub eff/, approximately 8 percent in control rod worth and approximately 2 percent in peak power density in a case of a mesh calculation as coarse as one mesh point per subassembly. When a basic multigroup cross-section set is condensed into a few-group cross-section set, the errors due to the condensation of the cross sections on k/sub eff/ and on control rod worth are shown to have linear relationships with the inverse square of the number of the condensed energy group. These relationships have been confirmed analytically with the application of perturbation theory.