# Improved discrete ordinates calculations for an approximate model of neutral particle transport in ducts

## Abstract

An improved implementation of the discrete ordinates method for computing neutral particle transport in ducts is presented. The considered one-dimensional model makes use of two basic functions to represent the transverse and azimuthal dependencies of the particle angular flux in the duct. It is shown that if the problem is decomposed into uncollided and collided problems prior to using the discrete ordinates approximation, the number of ordinates necessary to achieve a desired degree of accuracy in the solution can be greatly reduced, especially for long ducts with significant wall absorption. Further savings in computer time can be attained by employing a composite quadrature based on a (nonstandard) half-range quadrature that can be generated in an effective and efficient way with one of the classical methods in the constructive theory of orthogonal polynomials.

- Authors:

- Centro Tecnico Aeroespacial, Sao Jose dos Campos, Sao Paulo (Brazil). Inst. de Estudos Avancados

- Publication Date:

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 687541

- Resource Type:
- Journal Article

- Journal Name:
- Nuclear Science and Engineering

- Additional Journal Information:
- Journal Volume: 133; Journal Issue: 1; Other Information: PBD: Sep 1999

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 66 PHYSICS; DISCRETE ORDINATE METHOD; NEUTRAL-PARTICLE TRANSPORT; DUCTS; ONE-DIMENSIONAL CALCULATIONS; QUADRATURES; PERFORMANCE

### Citation Formats

```
Garcia, R.D.M., and Ono, S.
```*Improved discrete ordinates calculations for an approximate model of neutral particle transport in ducts*. United States: N. p., 1999.
Web. doi:10.13182/NSE99-1.

```
Garcia, R.D.M., & Ono, S.
```*Improved discrete ordinates calculations for an approximate model of neutral particle transport in ducts*. United States. doi:10.13182/NSE99-1.

```
Garcia, R.D.M., and Ono, S. Wed .
"Improved discrete ordinates calculations for an approximate model of neutral particle transport in ducts". United States. doi:10.13182/NSE99-1.
```

```
@article{osti_687541,
```

title = {Improved discrete ordinates calculations for an approximate model of neutral particle transport in ducts},

author = {Garcia, R.D.M. and Ono, S.},

abstractNote = {An improved implementation of the discrete ordinates method for computing neutral particle transport in ducts is presented. The considered one-dimensional model makes use of two basic functions to represent the transverse and azimuthal dependencies of the particle angular flux in the duct. It is shown that if the problem is decomposed into uncollided and collided problems prior to using the discrete ordinates approximation, the number of ordinates necessary to achieve a desired degree of accuracy in the solution can be greatly reduced, especially for long ducts with significant wall absorption. Further savings in computer time can be attained by employing a composite quadrature based on a (nonstandard) half-range quadrature that can be generated in an effective and efficient way with one of the classical methods in the constructive theory of orthogonal polynomials.},

doi = {10.13182/NSE99-1},

journal = {Nuclear Science and Engineering},

number = 1,

volume = 133,

place = {United States},

year = {1999},

month = {9}

}