We describe in this paper the recent advances in spectral nodal methods applied to diffusion problems in Cartesian geometry for neutron multiplying systems. In particular, we present a constant spectral nodal method for two-energy group X,Y geometry applied to neutron diffusion eigenvalue problems. We consider an arbitrary rectangular spatial grid defined on a two-dimensional rectangular domain and we use a transverse integration procedure to transform the two-dimensional problem into two 'one-dimensional' problems wherein the transverse leakage terms are approximated by constants. As a result, we obtain the transverse-integrated constant nodal diffusion equations that we discretise using the spectral nodal method. The discretised balance diffusion equations together with appropriate auxiliary equations, continuity and boundary conditions form the two-energy group X,Y geometry spectral constant nodal diffusion equations. The auxiliary equations have parameters that are to be determined such that the analytical general solutions of the transverse-integrated constant nodal diffusion equations are preserved. We show numerical results to illustrate the method's accuracy for coarse-mesh calculations in homogeneous and heterogeneous domains.
Keywords: diffusion eigenvalue problems, spectral nodal methods, neutron multiplying systems, neutron diffusion