Publications

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Conditional Point Sampling (CoPS) is a newly developed Monte Carlo method for computing radiation transport quantities in stochastic media. The algorithm involves a growing list of point-wise material designations during simulation that causes potentially unbounded increases in memory and runtime, making the calculation of probability density functions (PDFs) computationally expensive. In this work, we adapt CoPS by omitting material points used in the computation from being stored in persisting memory if they are within a user-defined “amnesia radius” from neighboring material points already defined within a realization. We conduct numerical studies to investigate trade-offs between accuracy, required computer memory, and computation time. We demonstrate CoPS's ability to produce accurate mean leakage results and PDFs of leakage results while improving memory and runtime through use of an amnesia radius. We show that a limit on required computer memory per cohort of histories and average runtime per history is imposed as a function of a non-zero amnesia radius. We find that, for the benchmark set investigated, using an amnesia radius of ra = 0.01 introduces minimal error (a 0.006 increase in CoPS3PO root mean squared relative error) in results while improving memory and runtime by an order of magnitude for a cohort size of 100.

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Radiation transport in stochastic media is a problem found in a multitude of applications, and the need for tools that are capable of thoroughly modeling this type of problem remains. A collection of approximate methods have been developed to produce accurate mean results, but the demand for methods that are capable of quantifying the spread of results caused by the randomness of material mixing remains. In this work, the new stochastic media transport algorithm Conditional Point Sampling is expanded using Embedded Variance Deconvolution such that it can compute the variance caused by material mixing. The accuracy of this approach is assessed for 1D, binary, Markovian-mixed media by comparing results to published benchmark values, and the behavior of the method is numerically studied as a function of user parameters. We demonstrate that this extension of Conditional Point Sampling is able to compute the variance caused by material mixing with accuracy dependent on the accuracy of the conditional probability function used.

Radiation transport in stochastic media is a challenging problem type relevant for applications such as meteorological modeling, heterogeneous radiation shields, BWR coolant, and pebble-bed reactor fuel. A commonly cited challenge for methods performing transport in stochastic media is to simultaneously be accurate and efficient. Conditional Point Sampling (CoPS), a new method for transport in stochastic media, was recently shown to have accuracy comparable to the most accurate approximate methods for a common 1D benchmark set. In this paper, we use a pseudo-interface-based approach to extend CoPS to application in multi-D for Markovian-mixed media, compare its accuracy with published results for other approximate methods, and examine its accuracy and efficiency as a function of user options. CoPS is found to be the most accurate of the compared methods on the examined benchmark suite for transmittance and comparable in accuracy with the most accurate methods for reflectance and internal flux. Numerical studies examine accuracy and efficiency as a function of user parameters providing insight for effective parameter selection and further method development. Since the authors did not implement any of the other approximate methods, there is not yet a valid comparison for efficiency with the other methods.

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