LAUSR

Abstract 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.