An improved random walk algorithm for the implicit Monte Carlo method
Abstract
In this paper, we introduce a modified Implicit Monte Carlo (IMC) Random Walk (RW) algorithm, which increases simulation efficiency for multigroup radiative transfer problems with strongly frequencydependent opacities. To date, the RW method has only been implemented in “fullygray” form; that is, the multigroup IMC opacities are groupcollapsed over the full frequency domain of the problem to obtain a gray diffusion problem for RW. This formulation works well for problems with large spatial cells and/or opacities that are weakly dependent on frequency; however, the efficiency of the RW method degrades when the spatial cells are thin or the opacities are a strong function of frequency. To address this inefficiency, we introduce a RW frequency group cutoff in each spatial cell, which divides the frequency domain into optically thick and optically thin components. In the modified algorithm, opacities for the RW diffusion problem are obtained by groupcollapsing IMC opacities below the frequency group cutoff. Particles with frequencies above the cutoff are transported via standard IMC, while particles below the cutoff are eligible for RW. This greatly increases the total number of RW steps taken per IMC timestep, which in turn improves the efficiency of the simulation. We refer to this newmore »
 Authors:

 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Publication Date:
 Research Org.:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1459827
 Alternate Identifier(s):
 OSTI ID: 1399043
 Report Number(s):
 LAUR1625113
Journal ID: ISSN 00219991; TRN: US1901807
 Grant/Contract Number:
 AC5206NA25396
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Computational Physics
 Additional Journal Information:
 Journal Volume: 328; Journal ID: ISSN 00219991
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; implicit Monte Carlo; random walk; hybrid methods
Citation Formats
Keady, Kendra P., and Cleveland, Mathew A. An improved random walk algorithm for the implicit Monte Carlo method. United States: N. p., 2016.
Web. doi:10.1016/j.jcp.2016.09.056.
Keady, Kendra P., & Cleveland, Mathew A. An improved random walk algorithm for the implicit Monte Carlo method. United States. doi:10.1016/j.jcp.2016.09.056.
Keady, Kendra P., and Cleveland, Mathew A. Tue .
"An improved random walk algorithm for the implicit Monte Carlo method". United States. doi:10.1016/j.jcp.2016.09.056. https://www.osti.gov/servlets/purl/1459827.
@article{osti_1459827,
title = {An improved random walk algorithm for the implicit Monte Carlo method},
author = {Keady, Kendra P. and Cleveland, Mathew A.},
abstractNote = {In this paper, we introduce a modified Implicit Monte Carlo (IMC) Random Walk (RW) algorithm, which increases simulation efficiency for multigroup radiative transfer problems with strongly frequencydependent opacities. To date, the RW method has only been implemented in “fullygray” form; that is, the multigroup IMC opacities are groupcollapsed over the full frequency domain of the problem to obtain a gray diffusion problem for RW. This formulation works well for problems with large spatial cells and/or opacities that are weakly dependent on frequency; however, the efficiency of the RW method degrades when the spatial cells are thin or the opacities are a strong function of frequency. To address this inefficiency, we introduce a RW frequency group cutoff in each spatial cell, which divides the frequency domain into optically thick and optically thin components. In the modified algorithm, opacities for the RW diffusion problem are obtained by groupcollapsing IMC opacities below the frequency group cutoff. Particles with frequencies above the cutoff are transported via standard IMC, while particles below the cutoff are eligible for RW. This greatly increases the total number of RW steps taken per IMC timestep, which in turn improves the efficiency of the simulation. We refer to this new method as PartiallyGray Random Walk (PGRW). We present numerical results for several multigroup radiative transfer problems, which show that the PGRW method is significantly more efficient than standard RW for several problems of interest. In general, PGRW decreases runtimes by a factor of ~2–4 compared to standard RW, and a factor of ~3–6 compared to standard IMC. While PGRW is slower than frequencydependent Discrete Diffusion Monte Carlo (DDMC), it is also easier to adapt to unstructured meshes and can be used in spatial cells where DDMC is not applicable. Finally, this suggests that it may be optimal to employ both DDMC and PGRW in a single simulation.},
doi = {10.1016/j.jcp.2016.09.056},
journal = {Journal of Computational Physics},
number = ,
volume = 328,
place = {United States},
year = {2016},
month = {10}
}
Web of Science