Development of the S3-HACNEM Simulator Program in order to Solving the Forward and Adjoint Neutron Diffusion Equation for Rectangular Geometry Reactor Cores

In nuclear reactor calculations, such as burn-up and fuel management, transient analysis, and pin power reconstruction, methods are being developed that are optimal, and are both cost-efficient and time-efficient. In this paper, the discretization of the neutron diffusion equation with a high-order average current nodal expansion method is shown, which can calculate in optimum time and with acceptable accuracy. The discretization of the Forward and Adjoint neutron diffusion equation is performed for two-dimensional rectangular geometry in two energy groups and then the S3-HACNEM reactor core simulator is developed. To verify, the calculations for the BIBLIS-2D reactor core are performed and compared with valid references. It results that the computational error improves from 9.67% to 0.58% by increasing the flux expansion order from quadratic polynomials to fourth-degree polynomials.