Multigroup pin power reconstruction with two-dimensional source expansion and corner flux discontinuity

A pin power reconstruction method that is readily applicable to multigroup problems with superior accuracy is presented for applications involving rectangular fuel assemblies. It employs a two-dimensional (2D), fourth order Legendre expansion of the source distribution that naturally leads to a group-decoupled, 2D semi-analytic solution of the neutron diffusion equation. The four surface average currents and four corner fluxes are used as the boundary conditions to uniquely specify the homogenous solution. The corner fluxes and source expansion coefficients are iteratively determined using the condition of corner point balance and the orthogonal property of the Lengedre functions. Corner discontinuity is incorporated in the calculation of the corner fluxes which turns out to be very effective in the cases of enrichment zoning. The accuracy of the proposed method is assessed by performing the two-step core calculations for the L336C5, C5G7MOX, and MOX core transient benchmark problems and then by comparing with the direct whole-core transport solutions. The results indicate that the proposed method is as accurate as the fully analytic method and works well irrespective the number of groups. However, it is also noted that somewhat larger errors are inevitable at the peripheral assemblies near the reflector in which the error associated with a prioi generation of the homogenized cross-sections and form functions is not trivial.