Analytical solution of the multigroup neutron diffusion equation coupled with an iterative method

Abstract

Many numerical methods are being used to solve the multigroup neutron diffusion equation for different types of nuclear reactors. These methods solve this equation quite accurately and determine the neutron flux and power distribution in the reactor as well as the eigenvalue of the reactor core. In this paper, we are proposing the integration of an analytical solution with an iterative method to determine the neutron flux distribution in the reactor and the effective eigenvalue. To do this, we solve the one-dimensional neutron diffusion equation for two energy groups, where the nuclear parameters are uniform in both nuclear fuel and reflector regions. The eigenvalue will be determined from the analytical solution using the power method iteratively until reaching convergence in both flux and eigenvalue. The results obtained in this paper are compared with results obtained from numerical methods used to validate the proposed method.

Keywords

• Neutron diffusion equation
• analytical solution
• iterative method
• eigenvalue
• slab reactor