Calculation of [formula omitted] modes of the multi-group neutron transport equation using the discrete ordinates and Finite Difference Method.

• The solution of the 1D and 2D Neutron Transport Equation provide neutron distributions. • Discrete Ordinates method for the angular discretization is applied. • Finite Difference Method for the spatial discretization is applied. • Krylov-Schur method is applied to solve the eigenvalue problem. • Multiple eigenvalues and eigenfunctions can be calculated. The method explained in this paper solves the steady-state of the neutron transport equation for 1D and 2D systems modeled with Cartesian geometry, by using the Discrete Ordinates method S N for the angular discretization and the Finite Difference Method for the spatial discretization. The method applies the multi-group approach for any energy discretization, including upscattering terms. The method solves the steady-state equation by solving a generalized eigenvalue problem by means of a Krylov-Schur method. One of the main advantages of the method is the capability to calculate multiple eigenfunctions. The Discrete Ordinates methodology is used for the angular discretization, which uses a simple formulation involving the angles and direction cosines. The spatial discretization with Finite Difference Method is selected for its simplicity. The method is validated with several one-dimensional benchmark problems and four two dimensional benchmark problems. The results show good agreement with respect to the reference results for all the cases studied. [ABSTRACT FROM AUTHOR]