Spectral nodal method for numerical solving two- group X,Y-geometry eigenvalue neutron diffusion problems

We describe in this paper the recent advances in spectral nodal method applied to diffusion problem in Cartesian geometry for neutron multiplying systems, exactly a spectral nodal method for two group energy x,y geometry diffusion eigenvalue problem. We considered an arbitrary rectangular spatial grid defined on a two-dimensional domain. In the two-dimensional problem we separated it in two 'one-dimensional' problems and we obtained transverse-integrated constant nodal diffusion equations. The balance diffusion equations, together with auxiliary equations and appropriate continuity and boundary conditions form the X,Y geometry two group energy spectral constant nodal diffusion equations. We show numerical results to illustrate the method's accuracy for coarse mesh calculations in homogeneous and heterogeneous mediums, and we compare the numerical result with those obtained by a finite difference method and analytical method. (Author)