Application of Monte Carlo Chord-Length Sampling Algorithms to Transport through a Two-Dimensional Binary Stochastic Mixture

Donovan, Timothy J.; Danon, Y.

doi:10.13182/nse03-a2332

Cited by 29 publications

(19 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This approach was followed by Donovan and Danon [8] in the generation of their two-dimensional benchmark results and by Ji and Martin [11] in the generation of their three-dimensional benchmark results.…”

Section: Generation Of Benchmark Solutionsmentioning

confidence: 99%

“…Murata, Mori, and Nakagawa [7] examined the use of similar algorithms for modeling spherical fuels in high-temperature gas-cooled reactors. Donovan and Danon [8] applied the Levermore-Pomraning algorithm proposed by Zimmerman (Algorithm A) to the specific case of a two-dimensional binary stochastic mixture composed of circular disks of one material randomly distributed in a background matrix material. Donovan and Danon generally refer to these types of Monte Carlo algorithms as "chord length sampling" (CLS) algorithms.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A benchmark comparison of Monte Carlo particle transport algorithms for binary stochastic mixtures

Brantley

2011

Journal of Quantitative Spectroscopy and Radiative Transfer

View full text Add to dashboard Cite

We numerically investigate the accuracy of two Monte Carlo algorithms originally proposed by Zimmerman [1] and Zimmerman and Adams [2] for particle transport through binary stochastic mixtures. We assess the accuracy of these algorithms using a standard suite of planar geometry incident angular flux benchmark problems and a new suite of interior source benchmark problems. In addition to comparisons of the ensemble-averaged leakage values, we compare the ensemble-averaged material scalar flux distributions. Both Monte Carlo transport algorithms robustly produce physically-realistic scalar flux distributions for the benchmark transport problems examined. The base Monte Carlo algorithm reproduces the standard Levermore-Pomraning model [3,4] results. The improved Monte Carlo algorithm generally produces significantly more accurate leakage values and also significantly more accurate material scalar flux distributions. We also present deterministic atomic mix solutions of the benchmark problems for comparison with the benchmark and the Monte Carlo solutions. Both Monte Carlo algorithms are generally significantly more accurate than the atomic mix approximation for the benchmark suites examined.

show abstract

Section: Generation Of Benchmark Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A benchmark comparison of Monte Carlo particle transport algorithms for binary stochastic mixtures

Brantley

2011

Journal of Quantitative Spectroscopy and Radiative Transfer

View full text Add to dashboard Cite

show abstract

“…Matrix cell number idum (2) i, the number of concentric spheres making up the stochastic sphere. idum(2+1 to 2+i) The cell numbers of the stochastic sphere idum(3+i)…”

Section: Modifications To Mcnpmentioning

confidence: 99%

“…The average chord length in the matrix material rdum (2) The radius of the stochastic sphere rdum (3) X coordinate of the representative stochastic sphere rdum (4) Y coordinate of the representative stochastic sphere rdum (5) Z coordinate of the representative stochastic sphere…”

Section: Rdum(1)mentioning

confidence: 99%

Implementation of Chord Length Sampling for Transport Through a Binary Stochastic Mixture

Donovan¹,

Sutton²,

Danon³

2002

View full text Add to dashboard Cite

Neutron transport through a special case stochastic mixture is examined, in which spheres of constant radius are uniformly mixed in a matrix material. A Monte Carlo algorithm previously proposed and examined in 2-D has been implemented in a test version of MCNP. The Limited Chord Length Sampling (LCLS) technique provides a means for modeling a binary stochastic mixture as a cell in MCNP. When inside a matrix cell, LCLS uses chord-length sampling to sample the distance to the next stochastic sphere. After a surface crossing into a stochastic sphere, transport is treated explicitly until the particle exits or is killed. Results were computed for a simple model with two different fixed neutron source distributions and three sets of material number densities. Stochastic spheres were modeled as black absorbers and varying degrees of scattering were introduced in the matrix material. Tallies were computed using the LCLS capability and by averaging results obtained from multiple realizations of the random geometry. Results were compared for accuracy and figures of merit were compared to indicate the efficiency gain of the LCLS method over the benchmark method. Results show that LCLS provides very good accuracy if the scattering optical thickness of the matrix is small (≤1). Comparisons of figures of merit show an advantage to LCLS varying between factors of 141 and 5. LCLS efficiency and accuracy relative to the benchmark both decrease as scattering is increased in the matrix.

show abstract

“…However, for such reactors, as the pebble bed reactor, the double heterogeneity of the fuel particles randomly placed in the core makes a full Monte Carlo simulation impossible. To overcome these geometrical difficulties, several authors [1][2][3] propose an alternative method that consists of simulating the trajectory of the neutrons by sampling the distributions of chords in different materials. Simple models of stochastic media 4) assume that the chord length distribution inside each material is exponential (i.e.…”

mentioning

confidence: 99%

Monte Carlo Simulation of Fully Markovian Stochastic Geometries

Lepage

Delaby

Malvagi

et al. 2011

Progress in Nuclear Science and Technology

View full text Add to dashboard Cite

The interest in resolving the equation of transport in stochastic media has continued to increase these last years. For binary stochastic media it is often assumed that the geometry is Markovian, which is never the case in usual environments. In the present paper, based on rigorous mathematical theorems, we construct fully two-dimensional Markovian stochastic geometries and we study their main properties. In particular, we determine a percolation threshold p c equal to 0.586±0.002 for such geometries. Finally, Monte Carlo simulations are performed through these geometries and the results compared to homogeneous geometries.

show abstract

Application of Monte Carlo Chord-Length Sampling Algorithms to Transport through a Two-Dimensional Binary Stochastic Mixture

Cited by 29 publications

References 11 publications

A benchmark comparison of Monte Carlo particle transport algorithms for binary stochastic mixtures

A benchmark comparison of Monte Carlo particle transport algorithms for binary stochastic mixtures

Implementation of Chord Length Sampling for Transport Through a Binary Stochastic Mixture

Monte Carlo Simulation of Fully Markovian Stochastic Geometries

Contact Info

Product

Resources

About