An analytical spatial reconstruction scheme for the spectral diamond - spectral green's function - constant nodal method for one-speed X,Y-geometry SN eigenvalue problems - 251

In this paper the X,Y-geometry spectral diamond - spectral Green's function - constant nodal (SD-SGF-CN) method is used to determine the one-speed node-edge average angular fluxes in neutron fission reacting media. This hybrid spectral nodal method uses the spectral diamond (SD) auxiliary equations for the multiplying regions and the spectral Green's function (SGF) auxiliary equations for non-multiplying regions of the domain. Moreover, we consider constant approximations for the transverse-leakage terms in the transverse integrated SN nodal equations. We solve the SD-SGF-CN equations using the one-node block inversion (NBI) iterative scheme, which uses the most recent estimates available for the node-entering fluxes to evaluate the node-exiting fluxes in the directions that constitute the incoming fluxes for the adjacent node. Using these results, we offer an algorithm for analytical reconstruction of the coarse-mesh nodal solution within each spatial node, as localized numerical solutions are not generated by usual accurate nodal methods. Numerical results are presented to illustrate the accuracy of the offered algorithm. (authors)