Fast analytical flux reconstruction method for nodal space-time nuclear reactor analysis

Abstract

The reconstruction of the fine-mesh neutron flux distribution using coarse-mesh computational results is an important step in a nodal reactor analysis procedure. In this paper the problem is reformulated as a one-dimensional interpolation along the node boundaries followed by an approximate analytical solution of the associated Dirichlet problem. Finite difference techniques are employed for the calculation of boundary values and their derivatives for Cartesian and hexagonal fuel assemblies. Apart from the fact that this approach can be used for an arbitrary number of energy groups in any geometry an additional advantage is that it yields an estimate of the order of accuracy. The interior solution is based on weak-element approximations to elliptic problems and uses in its simplest variant as points of support only flux corner values in addition to the known surface fluxes. The high computational accuracy and efficiency is demonstrated by some results for Cartesian and hexagonal configurations.