Asymptotic, multigroup flux reconstruction and consistent discontinuity factors

Abstract

Recent theoretical work has led to an asymptotically derived expression for reconstructing the neutron flux from lattice functions and multigroup diffusion solutions. The leading-order asymptotic term is the standard expression for flux reconstruction, i.e., it is the product of a shape function, obtained through a lattice calculation, and the multigroup diffusion solution. The first-order asymptotic correction term is significant only where the gradient of the diffusion solution is not small. Inclusion of this first-order correction term can significantly improve the accuracy of the reconstructed flux. One may define discontinuity factors (DFs) to make certain angular moments of the reconstructed flux continuous across interfaces between assemblies in 1-D. Indeed, the standard assembly discontinuity factors make the zeroth moment (scalar flux) of the reconstructed flux continuous. The inclusion of the correction term in the flux reconstruction provides an additional degree of freedom that can be used to make two angular moments of the reconstructed flux continuous across interfaces by using current DFs in addition to flux DFs. Numerical results demonstrate that using flux and current DFs together can be more accurate than using only flux DFs, and that making the second angular moment continuous can be more accurate than making the zeroth moment continuous.