Development of a 3D-Multigroup program to simulate anomalous diffusion phenomena in the nuclear reactors

•The new version of neutron diffusion equation for simulating anomalous diffusion is presented.•Application of fractional calculus in the nuclear reactor is revealed.•A 3D-Multigroup program is developed based on the fractional operators.•The super-diffusion and sub-diffusion phenomena are modeled in the nuclear reactors core.

The diffusion process is categorized in three parts, normal diffusion, super-diffusion and sub-diffusion. The classical neutron diffusion equation is used to model normal diffusion. A new scheme of derivatives is required to model anomalous diffusion phenomena. The fractional space derivatives are employed to model anomalous diffusion processes where a plume of particles spreads at an inconsistent rate with the classical Brownian motion model. In the fractional diffusion equation, the fractional Laplacians are used; therefore the statistical jump length of neutrons is unrestricted. It is clear that the fractional Laplacians are capable to model the anomalous phenomena in nuclear reactors. We have developed a NFDE-3D (neutron fractional diffusion equation) as a core calculation code to model normal and anomalous diffusion phenomena. The NFDE-3D is validated against the LMW-LWR reactor. The results demonstrate that reactors exhibit complex behavior versus order of the fractional derivatives which depends on the competition between neutron absorption and super-diffusion phenomenon.