Spectral nodal method for numerically solving two-energy group X,Y geometry neutron diffusion eigenvalue problems
by Dany S. Dominguez, Carlos R.G. Hernandez, Ricardo C. Barros
International Journal of Nuclear Energy Science and Technology (IJNEST), Vol. 5, No. 1, 2010

Abstract: 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.

Online publication date: Mon, 14-Dec-2009

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