# Feasibility of a wavelet expansion method to treat energy in cell calculations

## Abstract

This paper discusses the application of the Discrete Wavelet Transform (DWT) for the functional expansion of the energy variable in a cell calculation. The motivation of the work is the desire to obtain a self-shielding methodology in which the treatment of the energy variable in a given material region can be automatically adapted to the complexity of the cross section in that region. Unfortunately, the work presented in this paper shows that it is generally not possible to obtain the desired adaptivity. The most fundamental reason is that in a multi-region system, the energy dependence of the flux in a given material region is a function of the energy dependent cross sections and sources in all material regions through which the neutrons have crossed before entering into the present material. The complexity of the energy dependence of the cross section in a material region is thus not necessarily linked to the energy dependence of the flux in that region. If one sacrifices the objective of adaptivity, then an accurate method can be obtained using the DWT as a functional expansion. However, the resulting system of equations is more complicated than the direct solution of a hyper-fine group calculation. The conclusionmore »

- Authors:

- Research Inst. of Nuclear Engineering, Univ. of Fukui, Kanawa-cho 1-2-4, T914-0055, Fukui-ken, Tsuruga-shi (Japan)

- Publication Date:

- Research Org.:
- American Nuclear Society, 555 North Kensington Avenue, La Grange Park, IL 60526 (United States)

- OSTI Identifier:
- 22107761

- Resource Type:
- Conference

- Resource Relation:
- Conference: ICAPP '12: 2012 International Congress on Advances in Nuclear Power Plants, Chicago, IL (United States), 24-28 Jun 2012; Other Information: Country of input: France; 8 refs.; Related Information: In: Proceedings of the 2012 International Congress on Advances in Nuclear Power Plants - ICAPP '12| 2799 p.

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 22 GENERAL STUDIES OF NUCLEAR REACTORS; CROSS SECTIONS; ENERGY DEPENDENCE; EQUATIONS; EXPANSION; NEUTRONS; NUCLEAR POWER PLANTS; SELF-SHIELDING; WAVELENGTHS

### Citation Formats

```
Van Rooijen, W. F. G.
```*Feasibility of a wavelet expansion method to treat energy in cell calculations*. United States: N. p., 2012.
Web.

```
Van Rooijen, W. F. G.
```*Feasibility of a wavelet expansion method to treat energy in cell calculations*. United States.

```
Van Rooijen, W. F. G. Sun .
"Feasibility of a wavelet expansion method to treat energy in cell calculations". United States.
```

```
@article{osti_22107761,
```

title = {Feasibility of a wavelet expansion method to treat energy in cell calculations},

author = {Van Rooijen, W. F. G.},

abstractNote = {This paper discusses the application of the Discrete Wavelet Transform (DWT) for the functional expansion of the energy variable in a cell calculation. The motivation of the work is the desire to obtain a self-shielding methodology in which the treatment of the energy variable in a given material region can be automatically adapted to the complexity of the cross section in that region. Unfortunately, the work presented in this paper shows that it is generally not possible to obtain the desired adaptivity. The most fundamental reason is that in a multi-region system, the energy dependence of the flux in a given material region is a function of the energy dependent cross sections and sources in all material regions through which the neutrons have crossed before entering into the present material. The complexity of the energy dependence of the cross section in a material region is thus not necessarily linked to the energy dependence of the flux in that region. If one sacrifices the objective of adaptivity, then an accurate method can be obtained using the DWT as a functional expansion. However, the resulting system of equations is more complicated than the direct solution of a hyper-fine group calculation. The conclusion is thus that the DWT approach is not very practical. (authors)},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2012},

month = {7}

}