Kernel Density Estimation Techniques for Monte Carlo Reactor Analysis.

Abstract

Kernel density estimators (KDEs) are developed to estimate neutron scalar flux and reaction rate densities in Monte Carlo neutron transport simulations of pressurized water reactor benchmark problems in continuous energy. Previous work introduced the collision and track-length KDE for estimating scalar flux in radiation transport problems as an alternative to traditional histogram tallies. However, these estimators were not developed to estimate reaction rates and they were they not tested in continuous energy reactor physics problems. This dissertation expands upon previous work by developing KDEs that are capable of accurately estimating reaction rates in reactor physics problems.

The current state of the art in KDEs is applied to estimate reaction rates in reactor physics problems, with significant bias observed at material interfaces. The Mean Free Path (MFP) KDE is introduced in order to reduce this bias, with results showing no significant bias in 1-D problems. The multivariate MFP KDE is derived and applied to 2-D benchmark problems. Results show that the multivariate MFP KDE produces results with significant variance resulting from particle events at resonance energies. The fractional MFP KDE is developed to reduce this variance.

An approximation to the MFP KDE is introduced to improve computational performance of the algorithm at the cost of introducing additional bias into the estimates. A volume-average KDE is derived in order to directly compare KDE and histogram results and is used to determine the bias introduced by the approximation to the MFP KDE.

A KDE is derived for cylindrical coordinates, and the cylindrical MFP KDE is derived to capture distributions in reactor pincell problems. The cylindrical MFP KDE is applied to estimate distributions on an IFBA pincell, a quarter assembly of pincells, a depleted pincell, and on an unstructured mesh representation of a pincell. The results indicate that the cylindrical MFP KDE and fractional MFP KDE are capable of accurately capturing reaction rates in reactor physics benchmark problems.

This dissertation also describes the acceleration of the KDE via heterogeneous computing with GPUs. The algorithm development is described along with optimization strategies on the GPU. Speedups of 1.4-5 are observed for several benchmark problems.