Corrected Implicit Monte Carlo
Abstract
Here in this work we develop a set of nonlinear correction equations to enforce a consistent timeimplicit emission temperature for the original semiimplicit IMC equations. We present two possible forms of correction equations: one results in a set of nonlinear, zerodimensional, nonnegative, explicit correction equations, and the other results in a nonlinear, nonnegative, Boltzman transport correction equation. The zerodimensional correction equations adheres to the maximum principle for the material temperature, regardless of frequencydependence, but does not prevent maximum principle violation in the photon intensity, eventually leading to material overheating. The Boltzman transport correction guarantees adherence to the maximum principle for frequencyindependent simulations, at the cost of evaluating a reduced source nonlinear Boltzman equation. Finally, we present numerical evidence suggesting that the Boltzman transport correction, in its current form, significantly improves time step limitations but does not guarantee adherence to the maximum principle for frequencydependent simulations.
 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 National Nuclear Security Administration (NNSA)
 OSTI Identifier:
 1416278
 Alternate Identifier(s):
 OSTI ID: 1775889
 Report Number(s):
 LAUR1722796
Journal ID: ISSN 00219991; TRN: US1800892
 Grant/Contract Number:
 AC5206NA25396
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Computational Physics
 Additional Journal Information:
 Journal Volume: 359; Journal ID: ISSN 00219991
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; Thermal radiative transfer; Implicit Monte Carlo; HOLO
Citation Formats
Cleveland, Mathew Allen, and Wollaber, Allan Benton. Corrected Implicit Monte Carlo. United States: N. p., 2018.
Web. doi:10.1016/j.jcp.2017.12.038.
Cleveland, Mathew Allen, & Wollaber, Allan Benton. Corrected Implicit Monte Carlo. United States. https://doi.org/10.1016/j.jcp.2017.12.038
Cleveland, Mathew Allen, and Wollaber, Allan Benton. Tue .
"Corrected Implicit Monte Carlo". United States. https://doi.org/10.1016/j.jcp.2017.12.038. https://www.osti.gov/servlets/purl/1416278.
@article{osti_1416278,
title = {Corrected Implicit Monte Carlo},
author = {Cleveland, Mathew Allen and Wollaber, Allan Benton},
abstractNote = {Here in this work we develop a set of nonlinear correction equations to enforce a consistent timeimplicit emission temperature for the original semiimplicit IMC equations. We present two possible forms of correction equations: one results in a set of nonlinear, zerodimensional, nonnegative, explicit correction equations, and the other results in a nonlinear, nonnegative, Boltzman transport correction equation. The zerodimensional correction equations adheres to the maximum principle for the material temperature, regardless of frequencydependence, but does not prevent maximum principle violation in the photon intensity, eventually leading to material overheating. The Boltzman transport correction guarantees adherence to the maximum principle for frequencyindependent simulations, at the cost of evaluating a reduced source nonlinear Boltzman equation. Finally, we present numerical evidence suggesting that the Boltzman transport correction, in its current form, significantly improves time step limitations but does not guarantee adherence to the maximum principle for frequencydependent simulations.},
doi = {10.1016/j.jcp.2017.12.038},
journal = {Journal of Computational Physics},
number = ,
volume = 359,
place = {United States},
year = {2018},
month = {1}
}
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