Reduced-order modeling of radiation transport in binary stochastic media

Binary stochastic media arise in several radiation transport applications including photon, neutron, or charged particle transport through clouds, plasma-air structures, heterogeneous radiation shields, and BWR coolant. Methods for solving transport quantities in such media have generally focused on simple material homogenization or closures for the stochastic transport equation, but yield accurate results only in special mixing regimes. In this work we demonstrate an efficient representation of binary stochastic media for radiation transport applications using a Nataf transformation coupled with a Karhunen-Loeve expansion and further reduce the stochastic complexity using stochastic collocation. For some problems, this approach is more accurate than existing approximate methods while being less computationally expensive than brute force solution methods. Additionally, it can provide higher-order statistics of the solution response than currently used approximate methods, lends well to application in different mixing statistics, and provides a means by which to estimate and further resolve computational error. (authors)