On the Neutron multi-group kinetic diffusion equation in a heterogeneous slab: An exact solution on a finite set of discrete points

Abstract

In the present work the one-dimensional neutron kinetic diffusion problem in a multi-layer slab was solved for the multi-energy-group model. One of the goals of this work is to obtain an approximate solution of the problem with error control and in form of an analytical expression. To this end the neutron flux is expanded in a Taylor series whose coefficients are found using the differential equation and the boundary and interface conditions. The global domain is segmented into several sub-domains, where size and polynomial order are adjusted as required by a predefined accuracy. The methodology is applied to a benchmark problem considering a variety of reactivity transients and the obtained results are compared to those found in the literature. Convergence of the series is shown as well as suprema and infima for the continuous functions are given.