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Title: A stable 1D multigroup high-order low-order method

The high-order low-order (HOLO) method is a recently developed moment-based acceleration scheme for solving time-dependent thermal radiative transfer problems, and has been shown to exhibit orders of magnitude speedups over traditional time-stepping schemes. However, a linear stability analysis by Haut et al. (2015 Haut, T. S., Lowrie, R. B., Park, H., Rauenzahn, R. M., Wollaber, A. B. (2015). A linear stability analysis of the multigroup High-Order Low-Order (HOLO) method. In Proceedings of the Joint International Conference on Mathematics and Computation (M&C), Supercomputing in Nuclear Applications (SNA) and the Monte Carlo (MC) Method; Nashville, TN, April 19–23, 2015. American Nuclear Society.) revealed that the current formulation of the multigroup HOLO method was unstable in certain parameter regions. Since then, we have replaced the intensity-weighted opacity in the first angular moment equation of the low-order (LO) system with the Rosseland opacity. Furthermore, this results in a modified HOLO method (HOLO-R) that is significantly more stable.
Authors:
 [1] ;  [2] ;  [2] ;  [2]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of Michigan, Ann Arbor, MI (United States)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Report Number(s):
LA-UR-15-28071
Journal ID: ISSN 2332-4309
Grant/Contract Number:
AC52-06NA25396
Type:
Accepted Manuscript
Journal Name:
Journal of Computational and Theoretical Transport
Additional Journal Information:
Journal Name: Journal of Computational and Theoretical Transport; Journal ID: ISSN 2332-4309
Publisher:
Taylor and Francis
Research Org:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; thermal transfer, stability analysis, discontinuous Galerkin
OSTI Identifier:
1296672

Yee, Ben Chung, Wollaber, Allan Benton, Haut, Terry Scot, and Park, HyeongKae. A stable 1D multigroup high-order low-order method. United States: N. p., Web. doi:10.1080/23324309.2016.1187172.
Yee, Ben Chung, Wollaber, Allan Benton, Haut, Terry Scot, & Park, HyeongKae. A stable 1D multigroup high-order low-order method. United States. doi:10.1080/23324309.2016.1187172.
Yee, Ben Chung, Wollaber, Allan Benton, Haut, Terry Scot, and Park, HyeongKae. 2016. "A stable 1D multigroup high-order low-order method". United States. doi:10.1080/23324309.2016.1187172. https://www.osti.gov/servlets/purl/1296672.
@article{osti_1296672,
title = {A stable 1D multigroup high-order low-order method},
author = {Yee, Ben Chung and Wollaber, Allan Benton and Haut, Terry Scot and Park, HyeongKae},
abstractNote = {The high-order low-order (HOLO) method is a recently developed moment-based acceleration scheme for solving time-dependent thermal radiative transfer problems, and has been shown to exhibit orders of magnitude speedups over traditional time-stepping schemes. However, a linear stability analysis by Haut et al. (2015 Haut, T. S., Lowrie, R. B., Park, H., Rauenzahn, R. M., Wollaber, A. B. (2015). A linear stability analysis of the multigroup High-Order Low-Order (HOLO) method. In Proceedings of the Joint International Conference on Mathematics and Computation (M&C), Supercomputing in Nuclear Applications (SNA) and the Monte Carlo (MC) Method; Nashville, TN, April 19–23, 2015. American Nuclear Society.) revealed that the current formulation of the multigroup HOLO method was unstable in certain parameter regions. Since then, we have replaced the intensity-weighted opacity in the first angular moment equation of the low-order (LO) system with the Rosseland opacity. Furthermore, this results in a modified HOLO method (HOLO-R) that is significantly more stable.},
doi = {10.1080/23324309.2016.1187172},
journal = {Journal of Computational and Theoretical Transport},
number = ,
volume = ,
place = {United States},
year = {2016},
month = {7}
}