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

Yasuyoshi Kato, Toshikazu Takeda, Seiichi Takeda

Nuclear Science and Engineering / Volume 61 / Number 2 / Pages 127-141

October 1976

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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 keff, 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 keff, 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% Δk/k in keff, ∼8% in control rod worth and ∼2% 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 keff and on control rod worth are shown to have linear relationships with the inverse square of the number of the condensed energy group. These relationship have been confirmed analytically with the application of perturbation theory.

 
 
 
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