Monte Carlo chord length sampling for ddimensional Markov binary mixtures
Abstract
The Chord Length Sampling (CLS) algorithm is a powerful Monte Carlo method that models the effects of stochastic media on particle transport by generating onthefly the material interfaces seen by the random walkers during their trajectories. This annealed disorder approach, which formally consists of solving the approximate Levermore–Pomraning equations for linear particle transport, enables a considerable speedup with respect to transport in quenched disorder, where ensembleaveraging of the Boltzmann equation with respect to all possible realizations is needed. However, CLS intrinsically neglects the correlations induced by the spatial disorder, so that the accuracy of the solutions obtained by using this algorithm must be carefully verified with respect to reference solutions based on quenched disorder realizations. When the disorder is described by Markov mixing statistics, such comparisons have been attempted so far only for onedimensional geometries, of the rod or slab type. In this work we extend these results to Markov media in twodimensional (extruded) and threedimensional geometries, by revisiting the classical set of benchmark configurations originally proposed by Adams, Larsen and Pomraning and extended by Brantley. In particular, we examine the discrepancies between CLS and reference solutions for scalar particle flux and transmission/reflection coefficients as a function of the materialmore »
 Authors:

 Univ. ParisSaclay, GifsurYvette (France). DenService d'Etudes des Reacteurs et de Mathematiques Appliquees (SERMA), CEA
 Oregon State Univ., Corvallis, OR (United States). School of Nuclear Science & Engineering
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Publication Date:
 Research Org.:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org.:
 USDOE; Electricite de France (EDF)
 OSTI Identifier:
 1418910
 Alternate Identifier(s):
 OSTI ID: 1549235
 Report Number(s):
 LLNLJRNL735817
Journal ID: ISSN 00224073; TRN: US1801312
 Grant/Contract Number:
 AC5207NA27344
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Quantitative Spectroscopy and Radiative Transfer
 Additional Journal Information:
 Journal Volume: 204; Journal Issue: C; Journal ID: ISSN 00224073
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 22 GENERAL STUDIES OF NUCLEAR REACTORS; 97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; Chord Length Sampling; Markov geometries; Benchmark; Monte Carlo; Tripoli4®; Mercury
Citation Formats
Larmier, Coline, Lam, Adam, Brantley, Patrick, Malvagi, Fausto, Palmer, Todd, and Zoia, Andrea. Monte Carlo chord length sampling for ddimensional Markov binary mixtures. United States: N. p., 2017.
Web. doi:10.1016/j.jqsrt.2017.09.014.
Larmier, Coline, Lam, Adam, Brantley, Patrick, Malvagi, Fausto, Palmer, Todd, & Zoia, Andrea. Monte Carlo chord length sampling for ddimensional Markov binary mixtures. United States. doi:10.1016/j.jqsrt.2017.09.014.
Larmier, Coline, Lam, Adam, Brantley, Patrick, Malvagi, Fausto, Palmer, Todd, and Zoia, Andrea. Wed .
"Monte Carlo chord length sampling for ddimensional Markov binary mixtures". United States. doi:10.1016/j.jqsrt.2017.09.014. https://www.osti.gov/servlets/purl/1418910.
@article{osti_1418910,
title = {Monte Carlo chord length sampling for ddimensional Markov binary mixtures},
author = {Larmier, Coline and Lam, Adam and Brantley, Patrick and Malvagi, Fausto and Palmer, Todd and Zoia, Andrea},
abstractNote = {The Chord Length Sampling (CLS) algorithm is a powerful Monte Carlo method that models the effects of stochastic media on particle transport by generating onthefly the material interfaces seen by the random walkers during their trajectories. This annealed disorder approach, which formally consists of solving the approximate Levermore–Pomraning equations for linear particle transport, enables a considerable speedup with respect to transport in quenched disorder, where ensembleaveraging of the Boltzmann equation with respect to all possible realizations is needed. However, CLS intrinsically neglects the correlations induced by the spatial disorder, so that the accuracy of the solutions obtained by using this algorithm must be carefully verified with respect to reference solutions based on quenched disorder realizations. When the disorder is described by Markov mixing statistics, such comparisons have been attempted so far only for onedimensional geometries, of the rod or slab type. In this work we extend these results to Markov media in twodimensional (extruded) and threedimensional geometries, by revisiting the classical set of benchmark configurations originally proposed by Adams, Larsen and Pomraning and extended by Brantley. In particular, we examine the discrepancies between CLS and reference solutions for scalar particle flux and transmission/reflection coefficients as a function of the material properties of the benchmark specifications and of the system dimensionality.},
doi = {10.1016/j.jqsrt.2017.09.014},
journal = {Journal of Quantitative Spectroscopy and Radiative Transfer},
number = C,
volume = 204,
place = {United States},
year = {2017},
month = {9}
}
Web of Science