A stochastic first collision source for TWODANT

Ray effects are an inherent problem in discrete ordinates calculations. That is, in low scattering regions, such as voids or strong absorbers, the discrete ordinates solution will often exhibit maxima (rays) along the discrete directions. The problem is exacerbated by singular type sources, such as point sources, or sources which appear singular, such as spatially localized distributed sources. While ray effects do not typically affect integral quantities such as the eigenvalue, they can cause large errors in pointwise quantities such as the scalar flux. Although ray effects are mitigated by increasing the quadrature order or using biased quadrature sets, these solutions are computationally expensive and not always satisfactory. As an alternative, Alcouffe et al. used a semi-analytic solution for a point source along the centerline of a cylinder to determine the uncollided flux. The uncollided flux was then used to calculate the first collided source, which was in turn provided to the SN solver as a distributed fixed source. Thus, instead of seeing a singular point source and suffering the subsequent ray effects, the SN solver instead sees a widely distributed, fairly smooth fixed source. However, the semi-analytic first collision source (FCSRC) option in TWODANT was implemented only for a point source along the centerline in R -- Z geometry, and thus is of limited usefulness. We have now implemented a new FCSRC option in TWODANT where the uncollided flux is determined via ray tracing techniques in combination with a stochastic sampling of the source. As before, the uncollided flux is then used to provide a first collision source to the SN calculation. By using ray tracing and stochastic techniques to determine the uncollided flux, however, we are able to treat any fixed source input to TWODANT, including boundary sources, and for both X -- Y and R -- Z geometries