A HighOrder LowOrder Algorithm with Exponentially Convergent Monte Carlo for Thermal Radiative Transfer
In this paper, we have implemented a new highorder loworder (HOLO) algorithm for solving thermal radiative transfer problems. The loworder (LO) system is based on the spatial and angular moments of the transport equation and a lineardiscontinuous finiteelement spatial representation, producing equations similar to the standard S _{2} equations. The LO solver is fully implicit in time and efficiently resolves the nonlinear temperature dependence at each time step. The highorder (HO) solver utilizes exponentially convergent Monte Carlo (ECMC) to give a globally accurate solution for the angular intensity to a fixedsource pureabsorber transport problem. This global solution is used to compute consistency terms, which require the HO and LO solutions to converge toward the same solution. The use of ECMC allows for the efficient reduction of statistical noise in the Monte Carlo solution, reducing inaccuracies introduced through the LO consistency terms. Finally, we compare results with an implicit Monte Carlo code for onedimensional gray test problems and demonstrate the efficiency of ECMC over standard Monte Carlo in this HOLO algorithm.
 Authors:

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 Texas A & M Univ., College Station, TX (United States). Dept. of Nuclear Engineering
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Publication Date:
 Report Number(s):
 LAUR1620497
Journal ID: ISSN 00295639; TRN: US1701348
 Grant/Contract Number:
 AC5206NA25396; NA0002376
 Type:
 Accepted Manuscript
 Journal Name:
 Nuclear Science and Engineering
 Additional Journal Information:
 Journal Volume: 185; Journal Issue: 1; Journal ID: ISSN 00295639
 Publisher:
 American Nuclear Society
 Research Org:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org:
 USDOE Office of Nuclear Energy (NE). Nuclear Energy University Programs (NEUP); USDOE National Nuclear Security Administration (NNSA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; Thermal Radiative Transfer, HOLO, IMC, Monte Carlo
 OSTI Identifier:
 1338753
Bolding, Simon R., Cleveland, Mathew Allen, and Morel, Jim E.. A HighOrder LowOrder Algorithm with Exponentially Convergent Monte Carlo for Thermal Radiative Transfer. United States: N. p.,
Web. doi:10.13182/NSE1636.
Bolding, Simon R., Cleveland, Mathew Allen, & Morel, Jim E.. A HighOrder LowOrder Algorithm with Exponentially Convergent Monte Carlo for Thermal Radiative Transfer. United States. doi:10.13182/NSE1636.
Bolding, Simon R., Cleveland, Mathew Allen, and Morel, Jim E.. 2016.
"A HighOrder LowOrder Algorithm with Exponentially Convergent Monte Carlo for Thermal Radiative Transfer". United States.
doi:10.13182/NSE1636. https://www.osti.gov/servlets/purl/1338753.
@article{osti_1338753,
title = {A HighOrder LowOrder Algorithm with Exponentially Convergent Monte Carlo for Thermal Radiative Transfer},
author = {Bolding, Simon R. and Cleveland, Mathew Allen and Morel, Jim E.},
abstractNote = {In this paper, we have implemented a new highorder loworder (HOLO) algorithm for solving thermal radiative transfer problems. The loworder (LO) system is based on the spatial and angular moments of the transport equation and a lineardiscontinuous finiteelement spatial representation, producing equations similar to the standard S2 equations. The LO solver is fully implicit in time and efficiently resolves the nonlinear temperature dependence at each time step. The highorder (HO) solver utilizes exponentially convergent Monte Carlo (ECMC) to give a globally accurate solution for the angular intensity to a fixedsource pureabsorber transport problem. This global solution is used to compute consistency terms, which require the HO and LO solutions to converge toward the same solution. The use of ECMC allows for the efficient reduction of statistical noise in the Monte Carlo solution, reducing inaccuracies introduced through the LO consistency terms. Finally, we compare results with an implicit Monte Carlo code for onedimensional gray test problems and demonstrate the efficiency of ECMC over standard Monte Carlo in this HOLO algorithm.},
doi = {10.13182/NSE1636},
journal = {Nuclear Science and Engineering},
number = 1,
volume = 185,
place = {United States},
year = {2016},
month = {10}
}