Multigroup neutron diffusion equation with the finite volume method in reactors using MOX fuels

Abstract

The use of mixed oxide (MOX) fuel to partially fill the cores of commercial light water reactors (LWRs) gives rise to a reduction of the radioactive waste and production of more energy. However, the use of MOX fuels in LWRs changes the physics characteristics of the reactor core, since the variation with energy of the cross sections for the plutonium isotopes is more complex than for the uranium isotopes. Although the neutron diffusion theory could be applied to reactors using MOX fuels, more emphasis on treatment of the energy discretization should be placed. This energy discretization could be typically 4-8 energy groups, instead of the standard 2 energy group approach. In this work, the authors developed a finite volume method for discretizing the general multigroup neutron diffusion equation. This method solves the eigenvalue problem by using Krylov projection methods, in which the size of the vectors used for building the Krylov subspace does not depend on the number of energy groups, but it can solve the multigroup formulation with upscattering and fission production terms in several energy groups. The method was applied to MOX reactors for its validation.