# Generalized Coarse-Mesh Rebalance Method for Acceleration of Neutron Transport Calculations

## Abstract

This paper proposes a new acceleration method for neutron transport calculations: the generalized coarse-mesh rebalance (GCMR) method. The GCMR method is a unified scheme of the traditional coarse-mesh rebalance (CMR) and the coarse-mesh finite difference (CMFD) acceleration methods. Namely, by using an appropriate acceleration factor, formulation of the GCMR method becomes identical to that of the CMR or CMFD method. This also indicates that the convergence property of the GCMR method can be controlled by the acceleration factor since the convergence properties of the CMR and CMFD methods are generally different. In order to evaluate the convergence property of the GCMR method, a linearized Fourier analysis was carried out for a one-group homogeneous medium, and the results clarified the relationship between the acceleration factor and the spectral radius. It was also shown that the spectral radius of the GCMR method is smaller than those of the CMR and CMFD methods. Furthermore, the Fourier analysis showed that when an appropriate acceleration factor was used, the spectral radius of the GCMR method did not exceed unity in this study, which was in contrast to the results of the CMR or the CMFD method. Application of the GCMR method to practical calculations willmore »

- Authors:

- Nagoya University (Japan)

- Publication Date:

- OSTI Identifier:
- 20808479

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Nuclear Science and Engineering; Journal Volume: 151; Journal Issue: 3; Other Information: Copyright (c) 2006 American Nuclear Society (ANS), United States, All rights reserved. http://epubs.ans.org/; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; COMPUTER CALCULATIONS; COMPUTERIZED SIMULATION; FOURIER ANALYSIS; MESH GENERATION; NEUTRON TRANSPORT

### Citation Formats

```
Yamamoto, Akio.
```*Generalized Coarse-Mesh Rebalance Method for Acceleration of Neutron Transport Calculations*. United States: N. p., 2005.
Web.

```
Yamamoto, Akio.
```*Generalized Coarse-Mesh Rebalance Method for Acceleration of Neutron Transport Calculations*. United States.

```
Yamamoto, Akio. Tue .
"Generalized Coarse-Mesh Rebalance Method for Acceleration of Neutron Transport Calculations". United States.
doi:.
```

```
@article{osti_20808479,
```

title = {Generalized Coarse-Mesh Rebalance Method for Acceleration of Neutron Transport Calculations},

author = {Yamamoto, Akio},

abstractNote = {This paper proposes a new acceleration method for neutron transport calculations: the generalized coarse-mesh rebalance (GCMR) method. The GCMR method is a unified scheme of the traditional coarse-mesh rebalance (CMR) and the coarse-mesh finite difference (CMFD) acceleration methods. Namely, by using an appropriate acceleration factor, formulation of the GCMR method becomes identical to that of the CMR or CMFD method. This also indicates that the convergence property of the GCMR method can be controlled by the acceleration factor since the convergence properties of the CMR and CMFD methods are generally different. In order to evaluate the convergence property of the GCMR method, a linearized Fourier analysis was carried out for a one-group homogeneous medium, and the results clarified the relationship between the acceleration factor and the spectral radius. It was also shown that the spectral radius of the GCMR method is smaller than those of the CMR and CMFD methods. Furthermore, the Fourier analysis showed that when an appropriate acceleration factor was used, the spectral radius of the GCMR method did not exceed unity in this study, which was in contrast to the results of the CMR or the CMFD method. Application of the GCMR method to practical calculations will be easy when the CMFD acceleration is already adopted in a transport code. By multiplying a suitable acceleration factor to a coefficient (D{sup FD}) of a finite difference formulation, one can improve the numerical instability of the CMFD acceleration method.},

doi = {},

journal = {Nuclear Science and Engineering},

number = 3,

volume = 151,

place = {United States},

year = {Tue Nov 15 00:00:00 EST 2005},

month = {Tue Nov 15 00:00:00 EST 2005}

}