Numerical simulation of two-dimensional fractional neutron diffusion model describing dynamical behaviour of sodium-cooled fast reactor

Abstract

This article proposes an efficient numerical technique for solving the two-dimensional fractional neutron diffusion (FND) model with time-dependent reactivity which describes neutron transport in a finite cylindrical nuclear reactor core. In this technique, the time discretization is based on the L1 scheme and the space discretization is based on Alternating Direction Implicit (ADI) difference scheme. The neutron flux distribution in the reactor is calculated. The effects of the order of fractional derivative and simulation time on the neutron flux profile are examined. The numerical results of fractional model are compared with those of the P1 model and the normal diffusion model. The elapsed computational time of the proposed numerical algorithm is provided to show the computational efficiency of the method. It is shown that the present method is of O(Δt+hr2+hz2) convergence, where Δt is the temporal step size and hr and hz are the spatial step sizes.