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:

 University of California, Berkeley, Nuclear Engineering Department, 4173 Etcheverry Hall, Berkeley, California 94720
 Los Alamos National Laboratory, X Theoretical Design Division, Primary Physics Group, Los Alamos, New Mexico 87545
 Oak Ridge National Laboratory, Radiation Transport and Criticality Group, P.O. Box 2008, Oak Ridge, Tennessee 378316170
 Publication Date:
 Research Org.:
 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC)
 OSTI Identifier:
 1580383
 DOE Contract Number:
 AC0205CH11231
 Resource Type:
 Journal Article
 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. doi: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. doi:10.1080/00295639.2018.1509569.
@article{osti_1580383,
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},
issn = {00295639},
number = 3,
volume = 193,
place = {United States},
year = {2018},
month = {8}
}
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