A Stable 1D Multigroup High-Order Low-Order Method

作者：Yee B C^*; Wollaber A B; Haut T S; Park H

来源：Journal of Computational and Theoretical Transport, 2017, 46(1): 46-76.

DOI：10.1080/23324309.2016.1187172

• Discontinuous Galerkin
• high-order low-order (HOLO)
• stability analysis
• thermal radiative transfer

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 timestepping schemes. However, a linear stability analysis by Haut et al. (2015) 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. This results in a modified HOLO method (HOLO-R) that is significantly more stable.
This paper has two primary components. First, we present results from a linear stability analysis of the HOLO-R method for a 2group problem. These results show that HOLO-R is stable in all regions of the parameter space we considered, and strongly suggest that HOLO-R is unconditionally stable. The predicted decay factors from the stability analysis are verified with numerically computed decay factors from a spectralHOLO-R code. Second, we describe a preliminary (unoptimized) implementation of HOLO-R in Capsaicin - a deterministic, discrete-ordinates radiation transport code at Los Alamos National Laboratory. The results from this implementation further verify the stability of the HOLO-R method. Moreover, in the simulation of a 50-group, nonlinear Marshak wave problem, away from the 2-group, linearized stability analysis, we assess HOLO-R's accuracy, efficiency, and robustness as compared to current methods in Capsaicin. To our knowledge, this is the first implementation of HOLO that uses amass-lumped discontinuous Galerkin spatial discretization for both the highorder (HO) and LO systems, and details of this discretization are provided in the Appendix.

• 出版日期2017
• 单位Los Alamos