An analysis of the source-function integration technique for postprocessing PN angular fluxes

The source-function integration (SFI) technique for postprocessing PN solutions for radiation transport problems in plane geometry is investigated. New postprocessed formulas that display in a clear way the improvement introduced into the standard PN angular fluxes by the SFI technique are derived. In particular these formulas can be used to show that in the case where the angular dependency of the internal source can be represented exactly by a polynomial of order up to N and approximate boundary condition of the Mark type are used the standard and the postprocessed PN angular fluxes coincide at the N+1 values of the angular variable μ epsilon (Porson) [−1, 1] that corespond to the zeros of the Legendre polynomial PN+1(μ). A consequence of this property that is of interest for implementing iterative PN solutions to multilayer problems is discussed.