## This content will become publicly available on June 24, 2020

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

## Abstract

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.

- Authors:

- Sandia National Lab. (SNL-CA), Livermore, CA (United States)

- Publication Date:

- Research Org.:
- Sandia National Lab. (SNL-CA), Livermore, CA (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1530529

- Report Number(s):
- SAND-2019-7159J

Journal ID: ISSN 0022-4073; 676747

- Grant/Contract Number:
- AC04-94AL85000

- 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 0022-4073

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Frankel, Ari. Solution of the non-classical 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 non-classical 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 non-classical linear Boltzmann equation for transport in multidimensional stochastic media". United States. doi:10.1016/j.jqsrt.2019.06.015.
```

```
@article{osti_1530529,
```

title = {Solution of the non-classical linear Boltzmann equation for transport in multidimensional stochastic media},

author = {Frankel, Ari},

abstractNote = {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.},

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}

}