Improvements in the ADO Method for a One-Dimensional Model of Neutral Particle Transport in Ducts

Garcia, R. D. M.

doi:10.1080/00411450.2014.910227

Cited by 4 publications

(2 citation statements)

References 16 publications

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“…Assuming classical Lambertian duct wall scattering, neutral particles, such as photons and neutrons move through a duct filled with a nonparticipating medium. Through a clever moments formulation, several investigators, including Ed Larsen, Roberto Garcia and MMR Williams [2][3][4][5][6][7][8][9][10][11][12], investigated solutions to the resulting moments equations via basis functions. In several very informative articles, Garcia [6,11] and co-authors studied the solution for up to three basis functions with conventional numerical discrete ordinates (NDO) and the analytical discrete ordinates (ADO) methods.…”

Section: Introductionmentioning

confidence: 99%

Particle Transport in a 3D Duct by Adding and Doubling

Ganapol

2017

Journal of Computational and Theoretical Transport

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Particle transport through a duct by Lambertian reflection from duct walls is again considered. This popular transport example has been solved by most numerical transport methods except notably one− the method of doubling. We shall show that the method of doubling provides every bit as, or more, accurate reflectances and transmittances as the numerical discrete ordinates (NDO) and analytical discrete ordinates (ADO) methods with less mathematical and numerical effort.

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Section: Introductionmentioning

confidence: 99%

Particle Transport in a 3D Duct by Adding and Doubling

Ganapol

2017

Journal of Computational and Theoretical Transport

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“…For the N = 2 and N = 3 cases, the maximum percent deviation reported for reflection probabilities are 9% and 5%, and 1.3% and 0.27 % for the transmission probabilities. Besides these works developing more accurate models, there has also been research into efficient solution techniques for these one-dimensional models [11,12,13,14,15,16,17].…”

Section: Introductionmentioning

confidence: 99%

Approximate One-Dimensional Models for Monoenergetic Neutral Particle Transport in Ducts with Wall Migration

Gonzalez

McClarren

2017

Journal of Computational and Theoretical Transport

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The problem of monoenergetic neutral particle transport in a duct, where particles travel inside the duct walls, is treated using an approximate one-dimensional model. The onedimensional model uses three-basis functions, as part of a previously derived weighted-residual procedure, to account for the geometry of particle transport in a duct system (where particle migration into the walls is not considered). Our model introduces two stochastic parameters to account for particle-wall interactions: an albedo approximation yielding the fraction of particles that return to the duct after striking the walls, and a mean-distance travelled in the walls transverse to the duct by particles that re-enter the duct. Our model produces a set of three transport equations with a non-local scattering kernel. We solve these equations using discrete ordinates with source iteration. Numerical results for the reflection and transmission probabilities of neutron transport in ducts of circular cross section are compared to Monte Carlo results computed using the MCNP code.

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Analytical Discrete-Ordinates Solution for 3D Particle Transport in Ducts as Described by a 1D Model with Three Basis Functions

Garcia¹

2016

Journal of Computational and Theoretical Transport

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An analytical discrete-ordinates (ADO) solution is developed for an approximate model of particle transport in ducts. The model is based on the use of three basis functions to represent the transverse and azimuthal-angle dependencies of the angular flux in the duct and a weighted residual procedure that reduces the original 3D transport problem to a three-group-like 1D problem. Numerical results of benchmark quality for the reflection and transmission probabilities are tabulated for the cases of isotropic incidence and incidence described by the Dirac delta distribution.

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Improvements in the ADO Method for a One-Dimensional Model of Neutral Particle Transport in Ducts

Cited by 4 publications

References 16 publications

Particle Transport in a 3D Duct by Adding and Doubling

Particle Transport in a 3D Duct by Adding and Doubling

Approximate One-Dimensional Models for Monoenergetic Neutral Particle Transport in Ducts with Wall Migration

Analytical Discrete-Ordinates Solution for 3D Particle Transport in Ducts as Described by a 1D Model with Three Basis Functions

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