# Discrete Ordinates Approximations to the First- and Second-Order Radiation Transport Equations

## Abstract

The conventional discrete ordinates approximation to the Boltzmann transport equation can be described in a matrix form. Specifically, the within-group scattering integral can be represented by three components: a moment-to-discrete matrix, a scattering cross-section matrix and a discrete-to-moment matrix. Using and extending these entities, we derive and summarize the matrix representations of the second-order transport equations.

- Authors:

- Publication Date:

- Research Org.:
- Sandia National Labs., Albuquerque, NM (US); Sandia National Labs., Livermore, CA (US)

- Sponsoring Org.:
- US Department of Energy (US)

- OSTI Identifier:
- 800996

- Report Number(s):
- SAND2002-1880

TRN: US0206081

- DOE Contract Number:
- AC04-94AL85000

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: PBD: 1 Jun 2002

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; BOLTZMANN EQUATION; DISCRETE ORDINATE METHOD; RADIATION TRANSPORT; SCATTERING; TRANSPORT THEORY; MOMENTS METHOD

### Citation Formats

```
FAN, WESLEY C, DRUMM, CLIFTON R, and POWELL, JENNIFER L.
```*Discrete Ordinates Approximations to the First- and Second-Order Radiation Transport Equations*. United States: N. p., 2002.
Web. doi:10.2172/800996.

```
FAN, WESLEY C, DRUMM, CLIFTON R, & POWELL, JENNIFER L.
```*Discrete Ordinates Approximations to the First- and Second-Order Radiation Transport Equations*. United States. doi:10.2172/800996.

```
FAN, WESLEY C, DRUMM, CLIFTON R, and POWELL, JENNIFER L. Sat .
"Discrete Ordinates Approximations to the First- and Second-Order Radiation Transport Equations". United States. doi:10.2172/800996. https://www.osti.gov/servlets/purl/800996.
```

```
@article{osti_800996,
```

title = {Discrete Ordinates Approximations to the First- and Second-Order Radiation Transport Equations},

author = {FAN, WESLEY C and DRUMM, CLIFTON R and POWELL, JENNIFER L},

abstractNote = {The conventional discrete ordinates approximation to the Boltzmann transport equation can be described in a matrix form. Specifically, the within-group scattering integral can be represented by three components: a moment-to-discrete matrix, a scattering cross-section matrix and a discrete-to-moment matrix. Using and extending these entities, we derive and summarize the matrix representations of the second-order transport equations.},

doi = {10.2172/800996},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Sat Jun 01 00:00:00 EDT 2002},

month = {Sat Jun 01 00:00:00 EDT 2002}

}

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