Development of two-dimensional, multigroup neutron diffusion computer code based on GFEM with unstructured triangle elements

Various methods for solving the forward/adjoint equation in hexagonal and rectangular geometries are known in the literatures. In this paper, the solution of multigroup forward/adjoint equation using Finite Element Method (FEM) for hexagonal and rectangular reactor cores is reported. The spatial discretization of equations is based on Galerkin FEM (GFEM) using unstructured triangle elements. Calculations are performed for both linear and quadratic approximations of the shape function; based on which results are compared. Using power iteration method for the forward and adjoint calculations, the forward and adjoint fluxes with the corresponding eigenvalues are obtained. The results are then benchmarked against the valid results for IAEA-2D, BIBLIS-2D and IAEA-PWR benchmark problems. Convergence rate of GFEM in linear and quadratic approximations of the shape function are calculated and results are quantitatively compared. A sensitivity analysis of the calculations to the number and arrangement of elements has been performed.

► We develop a 2-D, multigroup neutron/adjoint diffusion computer code based on GFEM. ► The spatial discretization is performed using unstructured triangle elements. ► Multiplication factor, flux/adjoint and power distribution are outputs of the code. ► Sensitivity analysis to the number, arrangement and size of elements is performed. ► We proved that the developed code is a reliable tool to solve diffusion equation.