A numerical study of optimum boundary conditions for multigroup diffusion theory

Abstract

Using an energy dependent extrapolated endpoint Z0g as a variable parameter, a least-squares technique is used to minimise differences between the solutions of the multi-group transport and diffusion equations for one-dimensional slab geometry. The optimised Z0g values thus obtained are compared with the familiar prescriptions based on one-group theory, particularly the Milne condition cg Sigma trgZ0g=0.71. Applications to some moderating materials show that while the Milne formula is adequate for natural iron, a better prescription for light water would be cg Sigma trgZ0g=0.35. A similar analysis for extrapolation lengths lambda g yields an optimised fit of Sigma trg lambda g=0.62 for light water moderators.