# A fully coupled Monte Carlo/discrete ordinates solution to the neutron transport equation. Final report

## Abstract

The neutron transport equation is solved by a hybrid method that iteratively couples regions where deterministic (S _{N}) and stochastic (Monte Carlo) methods are applied. Unlike previous hybrid methods, the Monte Carlo and S _{N} regions are fully coupled in the sense that no assumption is made about geometrical separation or decoupling. The hybrid method provides a new means of solving problems involving both optically thick and optically thin regions that neither Monte Carlo nor S _{N} is well suited for by themselves. The fully coupled Monte Carlo/S _{N} technique consists of defining spatial and/or energy regions of a problem in which either a Monte Carlo calculation or an S _{N} calculation is to be performed. The Monte Carlo region may comprise the entire spatial region for selected energy groups, or may consist of a rectangular area that is either completely or partially embedded in an arbitrary S _{N} region. The Monte Carlo and S _{N} regions are then connected through the common angular boundary fluxes, which are determined iteratively using the response matrix technique, and volumetric sources. The hybrid method has been implemented in the S _{N} code TWODANT by adding special-purpose Monte Carlo subroutines to calculate the responsemore »

- Authors:

- Univ. of Arizona, Tucson, AZ (United States)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Arizona Univ., Tucson, AZ (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 10136650

- Report Number(s):
- LA-SUB-94-61

ON: DE94009071; TRN: 94:007477

- DOE Contract Number:
- W-7405-ENG-36

- Resource Type:
- Thesis/Dissertation

- Resource Relation:
- Other Information: DN: Thesis submitted by R.S. Baker to the University of Arizona, Tucson, AZ; TH: Thesis (Ph.D.); PBD: 1990

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 97 MATHEMATICS AND COMPUTING; NEUTRON TRANSPORT THEORY; MONTE CARLO METHOD; ITERATIVE METHODS; CROSS SECTIONS; BENCHMARKS; RESPONSE MATRIX METHOD; PROGRESS REPORT; 663610; 990200; NEUTRON PHYSICS; MATHEMATICS AND COMPUTERS

### Citation Formats

```
Baker, Randal Scott.
```*A fully coupled Monte Carlo/discrete ordinates solution to the neutron transport equation. Final report*. United States: N. p., 1990.
Web. doi:10.2172/10136650.

```
Baker, Randal Scott.
```*A fully coupled Monte Carlo/discrete ordinates solution to the neutron transport equation. Final report*. United States. doi:10.2172/10136650.

```
Baker, Randal Scott. Mon .
"A fully coupled Monte Carlo/discrete ordinates solution to the neutron transport equation. Final report". United States. doi:10.2172/10136650. https://www.osti.gov/servlets/purl/10136650.
```

```
@article{osti_10136650,
```

title = {A fully coupled Monte Carlo/discrete ordinates solution to the neutron transport equation. Final report},

author = {Baker, Randal Scott},

abstractNote = {The neutron transport equation is solved by a hybrid method that iteratively couples regions where deterministic (SN) and stochastic (Monte Carlo) methods are applied. Unlike previous hybrid methods, the Monte Carlo and SN regions are fully coupled in the sense that no assumption is made about geometrical separation or decoupling. The hybrid method provides a new means of solving problems involving both optically thick and optically thin regions that neither Monte Carlo nor SN is well suited for by themselves. The fully coupled Monte Carlo/SN technique consists of defining spatial and/or energy regions of a problem in which either a Monte Carlo calculation or an SN calculation is to be performed. The Monte Carlo region may comprise the entire spatial region for selected energy groups, or may consist of a rectangular area that is either completely or partially embedded in an arbitrary SN region. The Monte Carlo and SN regions are then connected through the common angular boundary fluxes, which are determined iteratively using the response matrix technique, and volumetric sources. The hybrid method has been implemented in the SN code TWODANT by adding special-purpose Monte Carlo subroutines to calculate the response matrices and volumetric sources, and linkage subrountines to carry out the interface flux iterations. The common angular boundary fluxes are included in the SN code as interior boundary sources, leaving the logic for the solution of the transport flux unchanged, while, with minor modifications, the diffusion synthetic accelerator remains effective in accelerating SN calculations. The special-purpose Monte Carlo routines used are essentially analog, with few variance reduction techniques employed. However, the routines have been successfully vectorized, with approximately a factor of five increase in speed over the non-vectorized version.},

doi = {10.2172/10136650},

journal = {},

number = ,

volume = ,

place = {United States},

year = {1990},

month = {1}

}