A modified Sn method for calculating the uncollided flux from a point source without ray effects

Abstract

The purpose of this paper is to derive an advection-removal equation for the uncollided scalar flux from a point isotropic source of radiation that can be solved using Sn discretization and solution techniques, and converges to the analytic solution as the spatial mesh is refined. However, because of the singularity of the solution, a special solution procedure must be used within a fixed region of arbitrary size containing the source. The smaller the region, the finer the spatial mesh required to achieve adequate convergence outside the region. We present results from simple 2-D calculations to demonstrate the efficacy and basic properties of the approach. Finally, we conclude that this approach is useful, and that further investigation of this approach for point sources and localized volumetric sources is warranted.