Abstract
Accurate solution of neutron transport problems in the discrete ordinates (SN) formulations is relevant in many areas of engineering and nuclear science. Several researches have led to a variety of numerical differencing schemes in order to generate even more accurate numerical solutions. However, most differencing schemes seem to become unstable for sufficiently large spatial cell width and negative solutions may arise, which are non-physical results. In this work, we present a spectral analysis of the Extended Linear Discontinuous (ELD) and the classical Linear Discontinuous (LD) difference schemes for one-dimensional monoenergetic SN problems with isotropic scattering in non-multiplying media. This analysis can predict analytic threshold values for the discretization cell width, beyond which SN numerical solutions become unstable. Analytical threshold values were calculated by means of the spectrum of spatially discretized SN equations and tested by solving two model problems to compare the practical results with the theoretical predictions offered in this paper.
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