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Title: Monte Carlo chord length sampling for d-dimensional Markov binary mixtures

Journal Article · · Journal of Quantitative Spectroscopy and Radiative Transfer
 [1];  [2];  [3];  [1];  [2];  [1]
  1. Univ. Paris-Saclay, Gif-sur-Yvette (France). Den-Service d'Etudes des Reacteurs et de Mathematiques Appliquees (SERMA), CEA
  2. Oregon State Univ., Corvallis, OR (United States). School of Nuclear Science & Engineering
  3. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
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The Chord Length Sampling (CLS) algorithm is a powerful Monte Carlo method that models the effects of stochastic media on particle transport by generating on-the-fly 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 speed-up with respect to transport in quenched disorder, where ensemble-averaging 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 one-dimensional geometries, of the rod or slab type. In this work we extend these results to Markov media in two-dimensional (extruded) and three-dimensional 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.

Research Organization:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Organization:
USDOE; Electricite de France (EDF)
Grant/Contract Number:
AC52-07NA27344
OSTI ID:
1418910
Alternate ID(s):
OSTI ID: 1549235
Report Number(s):
LLNL-JRNL-735817; TRN: US1801312
Journal Information:
Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 204, Issue C; ISSN 0022-4073
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 6 works
Citation information provided by
Web of Science

References (27)

Benchmark results for particle transport in a binary Markov statistical medium journal October 1989
A benchmark comparison of Monte Carlo particle transport algorithms for binary stochastic mixtures journal March 2011
A generalized linear Boltzmann equation for non-classical particle transport journal March 2011
Linear transport theory in a random medium journal October 1986
Linear kinetic theory in stochastic media journal November 1989
Renewal theory for transport processes in binary statistical mixtures journal April 1988
Transport in two-dimensional scattering stochastic media: Simulations and models journal June 2000
Photon propagation in heterogeneous optical media with spatial correlations: enhanced mean-free-paths and wider-than-exponential free-path distributions journal February 2004
Scale-dependent droplet clustering in turbulent clouds journal May 2001
Stochastic Radiative Transfer in Partially Cloudy Atmosphere journal July 1993
Transport in renewal statistical media: Benchmarking and comparison with models journal May 1994
Modification to a previous higher order model for particle transport in binary stochastic media journal November 1995
Application of Monte Carlo Chord-Length Sampling Algorithms to Transport through a Two-Dimensional Binary Stochastic Mixture journal March 2003
Equivalence of generic equation method and the phenomenological model for linear transport problems in a two‐state random scattering medium journal July 1989
An application of reactor noise techniques to neutron transport problems in a random medium journal January 1989
Chord length sampling method for analyzing stochastic distribution of fuel particles in continuous energy simulations journal March 2013
Benchmark solutions for transport in d-dimensional Markov binary mixtures journal March 2017
Monte Carlo particle transport in random media: The effects of mixing statistics journal July 2017
TRIPOLI-4®, CEA, EDF and AREVA reference Monte Carlo code journal August 2015
Random Polygons Determined by Random Lines in a Plane journal October 1964
The Random Division of Space journal December 1972
A Random Set Process in the Plane with a Markovian Property journal December 1965
Statistical simulation of an exponentially correlated many-dimensional random field journal January 2011
Monte Carlo Simulation of Fully Markovian Stochastic Geometries journal January 2011
On the Chord Length Sampling in 1-D Binary Stochastic Media journal December 2011
Finite-size effects and percolation properties of Poisson geometries journal July 2016
Benchmark solutions for transport in $d$-dimensional Markov binary mixtures text January 2016

Cited By (1)

A Reciprocal Formulation of Nonexponential Radiative Transfer. 3: Binary Mixtures preprint January 2019

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