Publications

A generalized Levermore-Pomraning closure for stochastic media transport problems

Pautz, Shawn D.; Franke, Brian C.

Stochastic media transport problems have long posed challenges for accurate modeling. Brute force Monte Carlo or deterministic sampling of realizations can be expensive in order to achieve the desired accuracy. The well-known Levermore-Pomraning (LP) closure is very simple and inexpensive, but is inaccurate in many circumstances. We propose a generalization to the LP closure that may help bridge the gap between the two approaches. Our model consists of local calculations to approximately determine the relationship between ensemble-averaged angular fluxes and the corresponding averages at material interfaces. The expense and accuracy of the method are related to how "local" the model is and how much local detail it contains. We show through numerical results that our approach is more accurate than LP for benchmark problems, provided that we capture enough local detail. Thus we identify two approaches to using ensemble calculations for stochastic media calculations: direct averaging of ensemble results for transport quantities of interest, or indirect use via a generalized LP equation to determine those same quantities; in some cases the latter method is more efficient. However, the method is subject to creating ill-posed problems if insufficient local detail is included in the model.