# Systematic assembly homogenization and local flux reconstruction for nodal method calculations. Final report, January 1, 1990--September 30, 1992

## Abstract

The report is divided into three parts. The main mathematical development of the new systematic simultaneous lattice-cell and fuel-assembly homogenization theory derived from the transport equation is summarized in Part I. Also included in Part I is the validation of this systematic homogenization theory and the resulting calculational procedures for coarse-mesh nodal diffusion methods that follow from it, in the form of their application to a simple one-dimensional test problem. The results of the application of this transport-equation-based systematic homogenization theory are summarized in Part II in which its superior accuracy over traditional flux and volume weighted homogenization procedures and over generalized equivalence theory is demonstrated for small and large practical two-dimensional PWR problems. The mathematical development of a second systematic homogenization theory -- this one derived starting from the diffusion equation -- is summarized in Part III where its application to a practical two-dimensional PWR model also is summarized and its superior accuracy over traditional homogenization methods and generalized equivalence theory is demonstrated for this problem.

- Authors:

- Publication Date:

- Research Org.:
- Virginia Univ., Charlottesville, VA (United States). Dept. of Mechanical, Aerospace and Nuclear Engineering

- Sponsoring Org.:
- USDOE, Washington, DC (United States)

- OSTI Identifier:
- 10168743

- Report Number(s):
- DOE/ER/12931-2; UVA-527406/MANE93/102

ON: DE93017839

- DOE Contract Number:
- FG02-90ER12931

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: PBD: May 1993

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 22 GENERAL STUDIES OF NUCLEAR REACTORS; 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; REACTOR LATTICES; NEUTRON TRANSPORT THEORY; NODAL EXPANSION METHOD; PROGRESS REPORT; MESH GENERATION; PWR TYPE REACTORS; NEUTRON DIFFUSION EQUATION; FUEL ASSEMBLIES; 220100; 663610; 990200; THEORY AND CALCULATION; NEUTRON PHYSICS; MATHEMATICS AND COMPUTERS

### Citation Formats

```
Dorning, J J.
```*Systematic assembly homogenization and local flux reconstruction for nodal method calculations. Final report, January 1, 1990--September 30, 1992*. United States: N. p., 1993.
Web. doi:10.2172/10168743.

```
Dorning, J J.
```*Systematic assembly homogenization and local flux reconstruction for nodal method calculations. Final report, January 1, 1990--September 30, 1992*. United States. doi:10.2172/10168743.

```
Dorning, J J. Sat .
"Systematic assembly homogenization and local flux reconstruction for nodal method calculations. Final report, January 1, 1990--September 30, 1992". United States. doi:10.2172/10168743. https://www.osti.gov/servlets/purl/10168743.
```

```
@article{osti_10168743,
```

title = {Systematic assembly homogenization and local flux reconstruction for nodal method calculations. Final report, January 1, 1990--September 30, 1992},

author = {Dorning, J J},

abstractNote = {The report is divided into three parts. The main mathematical development of the new systematic simultaneous lattice-cell and fuel-assembly homogenization theory derived from the transport equation is summarized in Part I. Also included in Part I is the validation of this systematic homogenization theory and the resulting calculational procedures for coarse-mesh nodal diffusion methods that follow from it, in the form of their application to a simple one-dimensional test problem. The results of the application of this transport-equation-based systematic homogenization theory are summarized in Part II in which its superior accuracy over traditional flux and volume weighted homogenization procedures and over generalized equivalence theory is demonstrated for small and large practical two-dimensional PWR problems. The mathematical development of a second systematic homogenization theory -- this one derived starting from the diffusion equation -- is summarized in Part III where its application to a practical two-dimensional PWR model also is summarized and its superior accuracy over traditional homogenization methods and generalized equivalence theory is demonstrated for this problem.},

doi = {10.2172/10168743},

journal = {},

number = ,

volume = ,

place = {United States},

year = {1993},

month = {5}

}