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Title: Solution of the non-classical linear Boltzmann equation for transport in multidimensional stochastic media

Journal Article · · Journal of Quantitative Spectroscopy and Radiative Transfer
 [1]
  1. Sandia National Lab. (SNL-CA), Livermore, CA (United States)

The non-classical linear Boltzmann equation (NCLBE) is a recently developed framework based on non-classical transport theory for modeling the expected value of particle flux in an arbitrary stochastic medium. Provided with a non-classical cross-section 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 non-classical cross-sections 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.

Research Organization:
Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
AC04-94AL85000
OSTI ID:
1530529
Alternate ID(s):
OSTI ID: 1691950
Report Number(s):
SAND-2019-7159J; 676747
Journal Information:
Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 235, Issue C; ISSN 0022-4073
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English

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