# Assessment of the Lagrange Discrete Ordinates Equations for Three-Dimensional 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

- OSTI Identifier:
- 1544721

- Report Number(s):
- LA-UR-18-27192

Journal ID: ISSN 0029-5639

- 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 0029-5639

- 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 Three-Dimensional 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 Three-Dimensional 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 Three-Dimensional Neutron Transport". United States. doi:10.1080/00295639.2018.1509569. https://www.osti.gov/servlets/purl/1544721.
```

```
@article{osti_1544721,
```

title = {Assessment of the Lagrange Discrete Ordinates Equations for Three-Dimensional 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}

}

*Citation information provided by*

Web of Science

Web of Science

Works referenced in this record:

##
Ray Effects in Discrete Ordinates Equations

journal, June 1968

- Lathrop, K. D.
- Nuclear Science and Engineering, Vol. 32, Issue 3

##
Lagrange Discrete Ordinates: A New Angular Discretization for the Three-Dimensional Linear Boltzmann Equation

journal, July 2015

- Ahrens, Cory D.
- Nuclear Science and Engineering, Vol. 180, Issue 3

##
Denovo: A New Three-Dimensional 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 Self-Shielding

journal, January 2015

- Wilson, S. C.; Slaybaugh, R. N.
- Nuclear Science and Engineering, Vol. 179, Issue 1

##
Analysis of the rowlands uranium oxide pin-cell benchmark with an updated WIMS-D library

journal, June 1998

- Trkov, Andrej
- Annals of Nuclear Energy, Vol. 25, Issue 10

##
Application of Quadruple Range Quadratures to Three-Dimensional Model Shielding Problems

journal, November 2009

- Jarrell, Joshua J.; Adams, Marvin L.; Risner, Joel M.
- Nuclear Technology, Vol. 168, Issue 2