# Convergence analysis of the angular-dependent rebalance iteration method in X-Y geometry

## Abstract

Recently, the angular dependent rebalance (ADR) method was developed for acceleration of the scattering source iteration (SI) and applied to various spatial differencing schemes of the discrete ordinates transport method in one- and two-dimensional geometries. In ADR, the lower-order equation is derived by integrating the rebalance form of the discretized transport equation over a coarse angular space. As a result, the lower-order equation resembles the transport equation, and the ADR method can be very easily implemented for various numerical transport methods in general geometry. However, it is difficult to theoretically analyze the stability of the ADR method since the ADR method is nonlinear. The authors study the convergence properties of the ADR iteration method via Cefus and Larsen`s approach (linearization and Fourier analysis) for step characteristic (SC) and constant-constant (C-C) spatial differencing schemes in infinite homogeneous X-Y geometry. The results show that the ADR method is unconditionally stable in such an ideal situation, giving confidence in the observed stability in finite heterogeneous problems.

- Authors:

- KAIST (Korea, Republic of)

- Publication Date:

- OSTI Identifier:
- 678128

- Report Number(s):
- CONF-990605-

Journal ID: TANSAO; ISSN 0003-018X; TRN: 99:009113

- Resource Type:
- Journal Article

- Journal Name:
- Transactions of the American Nuclear Society

- Additional Journal Information:
- Journal Volume: 80; Conference: 1999 annual meeting of the American Nuclear Society (ANS), Boston, MA (United States), 6-10 Jun 1999; Other Information: PBD: 1999

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 66 PHYSICS; DISCRETE ORDINATE METHOD; ITERATIVE METHODS; CONVERGENCE; ONE-DIMENSIONAL CALCULATIONS; TWO-DIMENSIONAL CALCULATIONS; MESH GENERATION

### Citation Formats

```
Hong, S.G., and Cho, N.Z.
```*Convergence analysis of the angular-dependent rebalance iteration method in X-Y geometry*. United States: N. p., 1999.
Web.

```
Hong, S.G., & Cho, N.Z.
```*Convergence analysis of the angular-dependent rebalance iteration method in X-Y geometry*. United States.

```
Hong, S.G., and Cho, N.Z. Wed .
"Convergence analysis of the angular-dependent rebalance iteration method in X-Y geometry". United States.
```

```
@article{osti_678128,
```

title = {Convergence analysis of the angular-dependent rebalance iteration method in X-Y geometry},

author = {Hong, S.G. and Cho, N.Z.},

abstractNote = {Recently, the angular dependent rebalance (ADR) method was developed for acceleration of the scattering source iteration (SI) and applied to various spatial differencing schemes of the discrete ordinates transport method in one- and two-dimensional geometries. In ADR, the lower-order equation is derived by integrating the rebalance form of the discretized transport equation over a coarse angular space. As a result, the lower-order equation resembles the transport equation, and the ADR method can be very easily implemented for various numerical transport methods in general geometry. However, it is difficult to theoretically analyze the stability of the ADR method since the ADR method is nonlinear. The authors study the convergence properties of the ADR iteration method via Cefus and Larsen`s approach (linearization and Fourier analysis) for step characteristic (SC) and constant-constant (C-C) spatial differencing schemes in infinite homogeneous X-Y geometry. The results show that the ADR method is unconditionally stable in such an ideal situation, giving confidence in the observed stability in finite heterogeneous problems.},

doi = {},

journal = {Transactions of the American Nuclear Society},

number = ,

volume = 80,

place = {United States},

year = {1999},

month = {9}

}