The infinite medium Green's function method for multigroup discrete ordinates transport problems in multi-layered slab geometry

Analytic solutions of the multigroup discrete ordinates transport equation with linearly anisotropic scattering and arbitrarily distributed source for multi-layered slab problems are obtained by using the infinite medium Gree n's function (IMGF) and Placzek's lemma, In this approach, the infinite med ium Green's function is derived analytically by using the spectral analysis for the multigroup discrete ordinates transport equation and its transpose d equation, and this infinite medium solution is related to the finite medi um solution by Placzek's lemma, The resulting equation leads to an exact re lation that represents the outgoing angular fluxes in terms of the incoming angular fluxes and the interior inhomogeneous source for each slab, For he terogeneous problems having multi-layered slabs, the slabs are coupled thro ugh the interface angular fluxes. Since all derivations are performed analy tically, the method gives exact solution with no truncation error. After th e interface angular fluxes are calculated by using an iterative method, the continuous spatial distribution of the angular flux (i.e. analytic solutio n) in each slab is given straightforwardly in terms of the IMGF and the bou ndary angular fluxes. (C) 2001 Elsevier Science Ltd. All rights reserved.