Solution of the nonclassical linear Boltzmann equation for transport in multidimensional stochastic media
Abstract
The nonclassical linear Boltzmann equation (NCLBE) is a recently developed framework based on nonclassical transport theory for modeling the expected value of particle flux in an arbitrary stochastic medium. Provided with a nonclassical crosssection for a given statistical description of a medium, any transport problem in that medium may be solved. Previous work has been limited in the types of material variability considered and has not explicitly introduced finite boundaries and sources. In this work the solution approach for the NCLBE in multidimensional media with finite boundaries is outlined. The discrete ordinates method with an implicit discretization of the pathlength variable is used to leverage sweeping methods for the transport operator. In addition, several convenient approximations for nonclassical crosssections are introduced based on existing theories of stochastic media. The solution approach is verified against random realizations of a Gaussian process medium in a square enclosure.
 Authors:

 Sandia National Lab. (SNLCA), Livermore, CA (United States)
 Publication Date:
 Research Org.:
 Sandia National Lab. (SNLCA), Livermore, CA (United States)
 Sponsoring Org.:
 USDOE National Nuclear Security Administration (NNSA)
 OSTI Identifier:
 1530529
 Report Number(s):
 SAND20197159J
Journal ID: ISSN 00224073; 676747
 Grant/Contract Number:
 AC0494AL85000
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Quantitative Spectroscopy and Radiative Transfer
 Additional Journal Information:
 Journal Volume: 235; Journal Issue: C; Journal ID: ISSN 00224073
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Citation Formats
Frankel, Ari. Solution of the nonclassical linear Boltzmann equation for transport in multidimensional stochastic media. United States: N. p., 2019.
Web. doi:10.1016/j.jqsrt.2019.06.015.
Frankel, Ari. Solution of the nonclassical linear Boltzmann equation for transport in multidimensional stochastic media. United States. doi:10.1016/j.jqsrt.2019.06.015.
Frankel, Ari. Mon .
"Solution of the nonclassical linear Boltzmann equation for transport in multidimensional stochastic media". United States. doi:10.1016/j.jqsrt.2019.06.015. https://www.osti.gov/servlets/purl/1530529.
@article{osti_1530529,
title = {Solution of the nonclassical linear Boltzmann equation for transport in multidimensional stochastic media},
author = {Frankel, Ari},
abstractNote = {The nonclassical linear Boltzmann equation (NCLBE) is a recently developed framework based on nonclassical transport theory for modeling the expected value of particle flux in an arbitrary stochastic medium. Provided with a nonclassical crosssection for a given statistical description of a medium, any transport problem in that medium may be solved. Previous work has been limited in the types of material variability considered and has not explicitly introduced finite boundaries and sources. In this work the solution approach for the NCLBE in multidimensional media with finite boundaries is outlined. The discrete ordinates method with an implicit discretization of the pathlength variable is used to leverage sweeping methods for the transport operator. In addition, several convenient approximations for nonclassical crosssections are introduced based on existing theories of stochastic media. The solution approach is verified against random realizations of a Gaussian process medium in a square enclosure.},
doi = {10.1016/j.jqsrt.2019.06.015},
journal = {Journal of Quantitative Spectroscopy and Radiative Transfer},
number = C,
volume = 235,
place = {United States},
year = {2019},
month = {6}
}