Conditional Point Sampling: A stochastic media transport algorithm with full geometric sampling memory. (September 2021) - Vu, Emily H.; Olson, Aaron J.
Highlights: Conditional Point Sampling is an algorithm for stochastic media radiation transport. Multi-point autocorrelation relationships are solved for 1D Markovian-mixed media. Conditional Point Sampling accuracy hinges on a conditional probability function. Conditional Point Sampling can be errorless for 1D, binary, Markovian-mixed media. Embedded Variance Deconvolution enables computation of variance caused by mixing. Embedded Variance Deconvolution computes parametric variance (caused by mixing). Abstract: Current methods for stochastic media transport are either computationally expensive or, by nature, approximate. Moreover, none of the well-developed, benchmarked approximate methods can compute the variance caused by the stochastic mixing, a quantity especially important to safety calculations. Therefore, we derive and apply a new conditional probability function (CPF) for use in the recently developed stochastic media transport algorithm Conditional Point Sampling (CoPS), which 1) leverages the full intra-particle memory of CoPS to yield errorless computation of stochastic media outputs in 1D, binary, Markovian-mixed media, and 2) leverages the full inter-particle memory of CoPS and the recently developed Embedded Variance Deconvolution method to yield computation of the variance in transport outputs caused by stochastic material mixing. Numerical results demonstrate errorless stochastic media transport as compared to reference benchmark solutions with the new CPF for this class of stochastic mixing as well as the ability to compute the variance caused by the stochastic mixing via CoPS. Using previously derived, non-errorless CPFs, CoPS is further found to be more accurate than the atomic mix approximation, Chord Length Sampling (CLS), and most of memory-enhanced versions of CLS surveyed. In addition, we study the compounding behavior of CPF error as a function of cohort size (where a cohort is a group of histories that share intra-particle memory) and recommend that small cohorts be used when computing the variance in transport outputs caused by stochastic mixing.