Assessment of the Lagrange Discrete Ordinates Equations for ThreeDimensional Neutron Transport
Abstract
The Lagrange Discrete Ordinates (LDO) equations, developed by Ahrens as an alternative to the traditional discrete ordinates formulation, have been implemented in Denovo, a threedimensional radiation transport code developed by Oak Ridge National Laboratory. The LDO equations retain the formal structure of the classical discrete ordinates equations but treat particle scattering in a different way. Solutions of the LDO equations have an interpolatory structure such that the angular flux can be naturally evaluated at directions other than the discrete ordinates used in arriving at the solutions, and the ordinates themselves may be chosen in a strategic way for the problem under consideration. Of particular interest is that the LDO equations have been shown to mitigate ray effects at increased angular resolutions. In this paper we present scalar flux solutions of the LDO equations for a small number of test cases of interest and compare the results against flux solutions generated using standard quadrature types. The LDO equations’ flux solutions were found to be comparable to those resultant from the standard quadrature types in value; results from the LDO equations were also found to be commensurate with those of standard quadrature types when comparing the flux solutions in the context ofmore »
 Authors:

 Univ. of California, Berkeley, CA (United States)
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Publication Date:
 Research Org.:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC)
 OSTI Identifier:
 1544721
 Report Number(s):
 LAUR1827192
Journal ID: ISSN 00295639
 Grant/Contract Number:
 89233218CNA000001
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Nuclear Science and Engineering
 Additional Journal Information:
 Journal Volume: 193; Journal Issue: 3; Journal ID: ISSN 00295639
 Publisher:
 American Nuclear Society  Taylor & Francis
 Country of Publication:
 United States
 Language:
 English
 Subject:
 73 NUCLEAR PHYSICS AND RADIATION PHYSICS
Citation Formats
Rowland, Kelly L., Ahrens, Cory D., Hamilton, Steven, and Slaybaugh, R. N. Assessment of the Lagrange Discrete Ordinates Equations for ThreeDimensional Neutron Transport. United States: N. p., 2018.
Web. doi:10.1080/00295639.2018.1509569.
Rowland, Kelly L., Ahrens, Cory D., Hamilton, Steven, & Slaybaugh, R. N. Assessment of the Lagrange Discrete Ordinates Equations for ThreeDimensional Neutron Transport. United States. https://doi.org/10.1080/00295639.2018.1509569
Rowland, Kelly L., Ahrens, Cory D., Hamilton, Steven, and Slaybaugh, R. N. Thu .
"Assessment of the Lagrange Discrete Ordinates Equations for ThreeDimensional Neutron Transport". United States. https://doi.org/10.1080/00295639.2018.1509569. https://www.osti.gov/servlets/purl/1544721.
@article{osti_1544721,
title = {Assessment of the Lagrange Discrete Ordinates Equations for ThreeDimensional Neutron Transport},
author = {Rowland, Kelly L. and Ahrens, Cory D. and Hamilton, Steven and Slaybaugh, R. N.},
abstractNote = {The Lagrange Discrete Ordinates (LDO) equations, developed by Ahrens as an alternative to the traditional discrete ordinates formulation, have been implemented in Denovo, a threedimensional radiation transport code developed by Oak Ridge National Laboratory. The LDO equations retain the formal structure of the classical discrete ordinates equations but treat particle scattering in a different way. Solutions of the LDO equations have an interpolatory structure such that the angular flux can be naturally evaluated at directions other than the discrete ordinates used in arriving at the solutions, and the ordinates themselves may be chosen in a strategic way for the problem under consideration. Of particular interest is that the LDO equations have been shown to mitigate ray effects at increased angular resolutions. In this paper we present scalar flux solutions of the LDO equations for a small number of test cases of interest and compare the results against flux solutions generated using standard quadrature types. The LDO equations’ flux solutions were found to be comparable to those resultant from the standard quadrature types in value; results from the LDO equations were also found to be commensurate with those of standard quadrature types when comparing the flux solutions in the context of the experimental benchmark test case examined.},
doi = {10.1080/00295639.2018.1509569},
journal = {Nuclear Science and Engineering},
number = 3,
volume = 193,
place = {United States},
year = {2018},
month = {8}
}
Web of Science
Works referenced in this record:
Analysis of the rowlands uranium oxide pincell benchmark with an updated WIMSD library
journal, June 1998
 Trkov, Andrej
 Annals of Nuclear Energy, Vol. 25, Issue 10
Lagrange Discrete Ordinates: A New Angular Discretization for the ThreeDimensional Linear Boltzmann Equation
journal, July 2015
 Ahrens, Cory D.
 Nuclear Science and Engineering, Vol. 180, Issue 3
Improved Monte Carlo Variance Reduction for Space and Energy SelfShielding
journal, January 2015
 Wilson, S. C.; Slaybaugh, R. N.
 Nuclear Science and Engineering, Vol. 179, Issue 1
Application of Quadruple Range Quadratures to ThreeDimensional Model Shielding Problems
journal, November 2009
 Jarrell, Joshua J.; Adams, Marvin L.; Risner, Joel M.
 Nuclear Technology, Vol. 168, Issue 2
Ray Effects in Discrete Ordinates Equations
journal, June 1968
 Lathrop, K. D.
 Nuclear Science and Engineering, Vol. 32, Issue 3
Denovo: A New ThreeDimensional Parallel Discrete Ordinates Code in SCALE
journal, August 2010
 Evans, Thomas M.; Stafford, Alissa S.; Slaybaugh, Rachel N.
 Nuclear Technology, Vol. 171, Issue 2
Improved Monte Carlo Variance Reduction for Space and Energy SelfShielding
text, January 2015
 Wilson, S. C.; Slaybaugh, R. N.
 arXiv
Works referencing / citing this record:
Review of Hybrid Methods for DeepPenetration Neutron Transport
journal, April 2019
 Munk, Madicken; Slaybaugh, Rachel N.
 Nuclear Science and Engineering, Vol. 193, Issue 10