Lambda modes comparison for different approximations of the neutron transport equation: Diffusion, SN and SP3

The methods presented in this paper solve the Simplified Spherical Harmonics approximation to the multidimensional neutron transport equation. 1D, 2D and 3D systems were modeled with Cartesian geometry using the finite difference method to discretize the spatial variables. The method is able to simulate any energy group discretization, including up-scattering terms. The Krylov Shur method was used to calculate the solution of the steady-state equation by solving a generalized eigenvalue problem. This methodology has the capability to calculate any number of eigenfunctions. A formulation review of the Simplified Spherical Harmonics is explained in this work, as well as, a study of the boundary conditions for different approaches of the finite difference method. The results calculated by this methodology are compared with the discrete ordinates and diffusion approximation methods, all of them, using the same spatial discretization in order to show the different accuracy of each method without influence of the method used for discretizing the spatial variable. The results show the validity of each method for different benchmark problems.