Improvement of transport-corrected scattering stability and performance using a Jacobi inscatter algorithm for 2D-MOC
Abstract
The MPACT code, being developed collaboratively by the University of Michigan and Oak Ridge National Laboratory, is the primary deterministic neutron transport solver being deployed within the Virtual Environment for Reactor Applications (VERA) as part of the Consortium for Advanced Simulation of Light Water Reactors (CASL). In many applications of the MPACT code, transport-corrected scattering has proven to be an obstacle in terms of stability, and considerable effort has been made to try to resolve the convergence issues that arise from it. Most of the convergence problems seem related to the transport-corrected cross sections, particularly when used in the 2D method of characteristics (MOC) solver, which is the focus of this work. Here in this paper, the stability and performance of the 2-D MOC solver in MPACT is evaluated for two iteration schemes: Gauss-Seidel and Jacobi. With the Gauss-Seidel approach, as the MOC solver loops over groups, it uses the flux solution from the previous group to construct the inscatter source for the next group. Alternatively, the Jacobi approach uses only the fluxes from the previous outer iteration to determine the inscatter source for each group. Consequently for the Jacobi iteration, the loop over groups can be moved from the outermost loop$$-$$as is the case with the Gauss-Seidel sweeper$$-$$to the innermost loop, allowing for a substantial increase in efficiency by minimizing the overhead of retrieving segment, region, and surface index information from the ray tracing data. Several test problems are assessed: (1) Babcock & Wilcox 1810 Core I, (2) Dimple S01A-Sq, (3) VERA Progression Problem 5a, and (4) VERA Problem 2a. The Jacobi iteration exhibits better stability than Gauss-Seidel, allowing for converged solutions to be obtained over a much wider range of iteration control parameters. Additionally, the MOC solve time with the Jacobi approach is roughly 2.0-2.5× faster per sweep. While the performance and stability of the Jacobi iteration are substantially improved compared to the Gauss-Seidel iteration, it does yield a roughly 8$$-$$10% increase in the overall memory requirement.
- Authors:
-
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Univ. of Michigan, Ann Arbor, MI (United States). Dept. of Nuclear Engineering and Radiological Sciences
- Publication Date:
- Research Org.:
- Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Consortium for Advanced Simulation of LWRs (CASL)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1349605
- Alternate Identifier(s):
- OSTI ID: 1397019
- Grant/Contract Number:
- AC05-00OR22725; AC0500OR22725
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Annals of Nuclear Energy (Oxford)
- Additional Journal Information:
- Journal Name: Annals of Nuclear Energy (Oxford); Journal Volume: 105; Journal Issue: C; Journal ID: ISSN 0306-4549
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; Transport correction; MOC; Jacobi; Gauss-Seidel; Stability
Citation Formats
Stimpson, Shane, Collins, Benjamin, and Kochunas, Brendan. Improvement of transport-corrected scattering stability and performance using a Jacobi inscatter algorithm for 2D-MOC. United States: N. p., 2017.
Web. doi:10.1016/j.anucene.2017.02.024.
Stimpson, Shane, Collins, Benjamin, & Kochunas, Brendan. Improvement of transport-corrected scattering stability and performance using a Jacobi inscatter algorithm for 2D-MOC. United States. https://doi.org/10.1016/j.anucene.2017.02.024
Stimpson, Shane, Collins, Benjamin, and Kochunas, Brendan. Fri .
"Improvement of transport-corrected scattering stability and performance using a Jacobi inscatter algorithm for 2D-MOC". United States. https://doi.org/10.1016/j.anucene.2017.02.024. https://www.osti.gov/servlets/purl/1349605.
@article{osti_1349605,
title = {Improvement of transport-corrected scattering stability and performance using a Jacobi inscatter algorithm for 2D-MOC},
author = {Stimpson, Shane and Collins, Benjamin and Kochunas, Brendan},
abstractNote = {The MPACT code, being developed collaboratively by the University of Michigan and Oak Ridge National Laboratory, is the primary deterministic neutron transport solver being deployed within the Virtual Environment for Reactor Applications (VERA) as part of the Consortium for Advanced Simulation of Light Water Reactors (CASL). In many applications of the MPACT code, transport-corrected scattering has proven to be an obstacle in terms of stability, and considerable effort has been made to try to resolve the convergence issues that arise from it. Most of the convergence problems seem related to the transport-corrected cross sections, particularly when used in the 2D method of characteristics (MOC) solver, which is the focus of this work. Here in this paper, the stability and performance of the 2-D MOC solver in MPACT is evaluated for two iteration schemes: Gauss-Seidel and Jacobi. With the Gauss-Seidel approach, as the MOC solver loops over groups, it uses the flux solution from the previous group to construct the inscatter source for the next group. Alternatively, the Jacobi approach uses only the fluxes from the previous outer iteration to determine the inscatter source for each group. Consequently for the Jacobi iteration, the loop over groups can be moved from the outermost loop$-$as is the case with the Gauss-Seidel sweeper$-$to the innermost loop, allowing for a substantial increase in efficiency by minimizing the overhead of retrieving segment, region, and surface index information from the ray tracing data. Several test problems are assessed: (1) Babcock & Wilcox 1810 Core I, (2) Dimple S01A-Sq, (3) VERA Progression Problem 5a, and (4) VERA Problem 2a. The Jacobi iteration exhibits better stability than Gauss-Seidel, allowing for converged solutions to be obtained over a much wider range of iteration control parameters. Additionally, the MOC solve time with the Jacobi approach is roughly 2.0-2.5× faster per sweep. While the performance and stability of the Jacobi iteration are substantially improved compared to the Gauss-Seidel iteration, it does yield a roughly 8$-$10% increase in the overall memory requirement.},
doi = {10.1016/j.anucene.2017.02.024},
journal = {Annals of Nuclear Energy (Oxford)},
number = C,
volume = 105,
place = {United States},
year = {Fri Mar 10 00:00:00 EST 2017},
month = {Fri Mar 10 00:00:00 EST 2017}
}
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