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Title: A solution of the monoenergetic neutral particle transport equation for adjacent half-spaces with anisotropic scattering

Abstract

We present highly accurate solutions to the neutral particle transport equation in a half-space. While our initial motivation was in response to a recently published solution based on Chandrasekhar's H-function, the presentation to follow has taken on a more comprehensive tone. The solution by H-functions certainly did achieved high accuracy but was limited to isotropic scattering and emission from spatially uniform and linear sources. Moreover, the overly complicated nature of the H-function approach strongly suggests that its extension to anisotropic scattering and general sources is not at all practical. For this reason, an all encompassing theory for the determination of highly precise benchmarks, including anisotropic scattering for a variety of spatial source distributions, is presented for particle transport in a half-space. We illustrate the approach via a collection of cases including tables of 7-place flux benchmarks to guide transport methods developers. The solution presented can be applied to a considerable number of one and two half-space transport problems with variable sources and represents a state-of-the-art benchmark solution.

Authors:
 [1]; ;  [2]
  1. Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ (United States)
  2. Montecuccolino Laboratory, University of Bologna, Via dei Colli, 16, I-40136 Bologna (Italy)
Publication Date:
OSTI Identifier:
22572333
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 316; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACCELERATION; ACCURACY; ANISOTROPY; BENCHMARKS; CONVERGENCE; DEVELOPERS; DISCRETE ORDINATE METHOD; DISTRIBUTION; MATHEMATICAL SOLUTIONS; NEUTRAL PARTICLES; NEUTRAL-PARTICLE TRANSPORT; SCATTERING; TRANSPORT THEORY

Citation Formats

Ganapol, B.D., E-mail: ganapol@cowboy.ame.arizona.edu, Mostacci, D., and Previti, A.. A solution of the monoenergetic neutral particle transport equation for adjacent half-spaces with anisotropic scattering. United States: N. p., 2016. Web. doi:10.1016/J.JCP.2016.02.049.
Ganapol, B.D., E-mail: ganapol@cowboy.ame.arizona.edu, Mostacci, D., & Previti, A.. A solution of the monoenergetic neutral particle transport equation for adjacent half-spaces with anisotropic scattering. United States. doi:10.1016/J.JCP.2016.02.049.
Ganapol, B.D., E-mail: ganapol@cowboy.ame.arizona.edu, Mostacci, D., and Previti, A.. 2016. "A solution of the monoenergetic neutral particle transport equation for adjacent half-spaces with anisotropic scattering". United States. doi:10.1016/J.JCP.2016.02.049.
@article{osti_22572333,
title = {A solution of the monoenergetic neutral particle transport equation for adjacent half-spaces with anisotropic scattering},
author = {Ganapol, B.D., E-mail: ganapol@cowboy.ame.arizona.edu and Mostacci, D. and Previti, A.},
abstractNote = {We present highly accurate solutions to the neutral particle transport equation in a half-space. While our initial motivation was in response to a recently published solution based on Chandrasekhar's H-function, the presentation to follow has taken on a more comprehensive tone. The solution by H-functions certainly did achieved high accuracy but was limited to isotropic scattering and emission from spatially uniform and linear sources. Moreover, the overly complicated nature of the H-function approach strongly suggests that its extension to anisotropic scattering and general sources is not at all practical. For this reason, an all encompassing theory for the determination of highly precise benchmarks, including anisotropic scattering for a variety of spatial source distributions, is presented for particle transport in a half-space. We illustrate the approach via a collection of cases including tables of 7-place flux benchmarks to guide transport methods developers. The solution presented can be applied to a considerable number of one and two half-space transport problems with variable sources and represents a state-of-the-art benchmark solution.},
doi = {10.1016/J.JCP.2016.02.049},
journal = {Journal of Computational Physics},
number = ,
volume = 316,
place = {United States},
year = 2016,
month = 7
}