Galerkin and Generalized Least Squares finite element: A comparative study for multi-group diffusion solvers

In this paper, the solution of multi-group neutron/adjoint equation using Finite Element Method (FEM) for hexagonal and rectangular reactor cores is reported. The spatial discretization of the neutron diffusion equation is performed based on two different Finite Element Methods (FEMs) using unstructured triangular elements generated by Gambit software. Calculations are performed using Galerkin and Generalized Least Squares FEMs; based on which results are compared. Using the power iteration method for the neutron and adjoint calculations, the neutron and adjoint flux distributions with the corresponding eigenvalues are obtained. The results are then validated against the valid results for the IAEA-2D andBIBLIS-2D benchmark problems. The results of GFEM-2D (developed based on Galerkin FEM) and GELES-2D (developed based on Generalized Least Squares FEM) computer codes are also compared with results obtained from DONJON4 computer code. To investigate the validation of developed computer codes for the calculation with more than two energy groups, the calculations are performed for a benchmark problem with seven energy groups. To investigate the dependency of the results to the number of elements, a sensitivity analysis of the calculations to the number of elements is performed.