Development of a 2D-Multigroup Code (NFDE-2D) based on the neutron spatial-fractional diffusion equation

Abstract

The first aim of this work is the numerical solution of the neutron spatial-fractional diffusion equation in two-dimension for energy multigroups using the shifted Grünwald–Letnikov approximation in the fractional derivatives. The second aim is related to illustrate a real application of fractional derivatives in the nuclear reactors. The novelty of this work is the discretization method of the neutron fractional diffusion equation in multigroup form for high heterogeneous multiplicative media where the effective multiplication factor (Keff) was rigorously calculated. When the classical Laplacian is converted to fractional Laplacian, the jump length statistics are unrestricted. For neutron population in the nuclear reactors there is a new version of the neutron diffusion equation which is established on the fractional space derivatives, called in this work as neutron fractional diffusion equation (NFDE). We have developed the NFDE-2D as a nuclear reactors core calculation code, which is validated with some numerical experiments where different orders of fractional derivative are considered. The results demonstrate that reactors exhibit the complex behavior against order of fractional derivative which is depended on the competition between neutron absorption and super-diffusion phenomena, which is comparable with the neutron transport theory.