Multigroup Neutron Transport Using a Collision-Based Hybrid Method

Abstract

A collision-based hybrid algorithm for the discrete ordinates approximation of the neutron transport equation is extended to the isotropic multigroup setting. The algorithm uses discrete energy and angle grids at two different resolutions and approximates the fission and scattering sources on the coarser grids. The coupling of a collided transport equation, discretized on the coarse grid, with an uncollided transport equation, discretized on the fine grid, yields an algorithm that, in most cases, is more efficient than the traditional multigroup approach. The improvement over existing techniques is demonstrated for time-dependent problems with different materials, geometries, and energy groups.

Keywords:

• Neutron transport
• hybrid methods
• multigroup approximation

Acknowledgments

The work of Ben Whewell and Ryan McClarren is supported by the Center for Exascale Monte-Carlo Neutron Transport (CEMeNT), a PSAAP-III project funded by the U.S. Department of Energy grant number DE-NA003967. The work of Cory Hauck is sponsored by the Office of Advanced Scientific Computing Research, U.S. Department of Energy, and performed at the Oak Ridge National Laboratory, which is managed by UT-Battelle, LLC under contract number DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains, and the publisher, by accepting the article for publication, acknowledges, that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan).

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Notes

^a For Monte Carlo, ε² is used in place of ε in Eq. (45)(45) $\mathrm{F}\mathrm{O}\mathrm{M}=\frac{1}{\epsilon \tau },$(45) as it is the variance in a statistical estimate.

Additional information

Funding

This work was supported by the U.S. Department of Energy [DE-AC05-00OR22725]; U.S. Department of Energy [DE-NA003967].