Nonrecursive residual Monte Carlo method for SN transport discretization error estimation

In this paper, we present a nonrecursive residual Monte Carlo method for estimating discretization errors associated with the SN transport solution to radiation transport problems. Although this technique is general, we applied it to the mono-energetic 1-D SN equation with linear-discontinuous finite element method spatial discretization as a demonstration of the theory for the purpose of this study. Two angular flux representations: conforming and simplified representations were considered in this analysis, and the results were compared. It is shown that the simplified representation dramatically reduces the memory footprint and computational complexity of residual source generation and sampling while accurately capturing the error associated with certain types of responses.