Cylindrical Kernel Density Estimators For Monte Carlo Neutron Transport Reactor Physics Problems
- Department of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, MI (United States)
Kernel Density Estimators (KDEs) have been investigated as an alternative to histogram tallies in Monte Carlo radiation transport simulations for capturing spatially-resolved quantities such as scalar flux and reaction rate densities. KDEs are non-parametric estimators that show potential for producing smooth estimates of quantities of interest with reduced variance compared to traditional histogram tallies. Furthermore, KDEs obtain estimates of the underlying distribution at user-defined points without requiring an underlying mesh, thus making KDEs an attractive potential alternative to histogram tallies. Recent work has introduced the Mean Free Path based KDE (MFP KDE) in order to capture distributions with large curvature at material interfaces, e.g. absorption reaction rates in UO{sub 2} fuel in light water reactors. However, the multivariate MFP KDE produces inaccuracies in the form of localized spikes in problems with material cross sections that contain large resonances. Since the MFP KDE works well in one dimension, it is hypothesized that a different MFP KDE formulation where the normalization coefficient only contains one factor of the cross section would be able to capture these distributions with large curvature without producing spikes in the estimate. This can be accomplished by using a cylindrical KDE whose 2-D support area is wedge-shaped and applying the MFP KDE to the radial component of the cylindrical KDE. These cylindrical KDEs use 2-D (r,θ) cylindrical coordinates with no dependence in axial dimension z. This paper derives the cylindrical KDE and the cylindrical MFP KDE and tests them on a reactor physics pin-cell benchmark problem, producing accurate estimates of flux and reaction rate densities with differences less than 0.5% when compared to a reference histogram. (authors)
- OSTI ID:
- 23042657
- Journal Information:
- Transactions of the American Nuclear Society, Vol. 115; Conference: 2016 ANS Winter Meeting and Nuclear Technology Expo, Las Vegas, NV (United States), 6-10 Nov 2016; Other Information: Country of input: France; 7 refs.; available from American Nuclear Society - ANS, 555 North Kensington Avenue, La Grange Park, IL 60526 (US); ISSN 0003-018X
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
ABSORPTION
BENCHMARKS
COMPUTERIZED SIMULATION
CROSS SECTIONS
CYLINDRICAL CONFIGURATION
DENSITY
KERNELS
MEAN FREE PATH
MONTE CARLO METHOD
MULTIVARIATE ANALYSIS
NEUTRON TRANSPORT
NUCLEAR FUELS
REACTION KINETICS
REACTOR PHYSICS
URANIUM DIOXIDE
WATER COOLED REACTORS
WATER MODERATED REACTORS