## Hybrid super homogenization and discontinuity factor method for continuous finite element diffusion

## Abstract

This paper presents a novel homogenization equivalence technique aiming to simultaneously leveragethe simplicity of the Super Homogenization (SPH) method to reproduce reference reaction rates andthe ability to preserve reference leakage rates at desired surfaces through Discontinuity Factors (DF).The need for this new class of methods arises from the inability of the current state-of-the-art SPH technology to properly reproduce the reactor multiplication factor for problems with significant leakage. This work shows that this defect lies in the use of normalization factors in the SPH algorithm: while they are necessary with purely reflecting problems to ensure uniqueness of the solution, they introduce homogenization inconsistencies if at least one vacuum boundary condition is present. Two solutions to this problem are presented in this work: (i) to simply remove the normalization factor or (ii) to introduce additional degrees of freedom in the form of DFs in such a way that the normalization factors can still constrain the problem. While the former clearly offers unrivaled simplicity and can lead to very satisfactory results for leakage-dominated cores or if spatial restriction of the SPH regions is applied – as demonstrated for the High Temperature Test Reactor, the latter is more robust and does not require tomore »

- Authors:

- Idaho National Lab. (INL), Idaho Falls, ID (United States)

- Publication Date:

- Research Org.:
- Idaho National Lab. (INL), Idaho Falls, ID (United States)

- Sponsoring Org.:
- USDOE Office of Nuclear Energy (NE)

- OSTI Identifier:
- 1498269

- Report Number(s):
- INL/JOU-18-51060-Rev000

Journal ID: ISSN 0306-4549

- Grant/Contract Number:
- AC07-05ID14517

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Annals of Nuclear Energy (Oxford)

- Additional Journal Information:
- Journal Name: Annals of Nuclear Energy (Oxford); Journal Volume: 128; Journal Issue: C; Journal ID: ISSN 0306-4549

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; 22 GENERAL STUDIES OF NUCLEAR REACTORS; Finite Element Method; Super Homogenization (SPH); Discontinuity Factors; Rattlesnake Transport Code; Multiphysics Object Oriented Simulation Environment (MOOSE); High Temperature Test Reactor (HTTR)

### Citation Formats

```
Labouré, Vincent, Wang, Yaqi, Ortensi, Javier, Schunert, Sebastian, Gleicher, Frederick, DeHart, Mark, and Martineau, Richard. Hybrid super homogenization and discontinuity factor method for continuous finite element diffusion. United States: N. p., 2019.
Web. doi:10.1016/j.anucene.2019.01.003.
```

```
Labouré, Vincent, Wang, Yaqi, Ortensi, Javier, Schunert, Sebastian, Gleicher, Frederick, DeHart, Mark, & Martineau, Richard. Hybrid super homogenization and discontinuity factor method for continuous finite element diffusion. United States. doi:10.1016/j.anucene.2019.01.003.
```

```
Labouré, Vincent, Wang, Yaqi, Ortensi, Javier, Schunert, Sebastian, Gleicher, Frederick, DeHart, Mark, and Martineau, Richard. Fri .
"Hybrid super homogenization and discontinuity factor method for continuous finite element diffusion". United States. doi:10.1016/j.anucene.2019.01.003. https://www.osti.gov/servlets/purl/1498269.
```

```
@article{osti_1498269,
```

title = {Hybrid super homogenization and discontinuity factor method for continuous finite element diffusion},

author = {Labouré, Vincent and Wang, Yaqi and Ortensi, Javier and Schunert, Sebastian and Gleicher, Frederick and DeHart, Mark and Martineau, Richard},

abstractNote = {This paper presents a novel homogenization equivalence technique aiming to simultaneously leveragethe simplicity of the Super Homogenization (SPH) method to reproduce reference reaction rates andthe ability to preserve reference leakage rates at desired surfaces through Discontinuity Factors (DF).The need for this new class of methods arises from the inability of the current state-of-the-art SPH technology to properly reproduce the reactor multiplication factor for problems with significant leakage. This work shows that this defect lies in the use of normalization factors in the SPH algorithm: while they are necessary with purely reflecting problems to ensure uniqueness of the solution, they introduce homogenization inconsistencies if at least one vacuum boundary condition is present. Two solutions to this problem are presented in this work: (i) to simply remove the normalization factor or (ii) to introduce additional degrees of freedom in the form of DFs in such a way that the normalization factors can still constrain the problem. While the former clearly offers unrivaled simplicity and can lead to very satisfactory results for leakage-dominated cores or if spatial restriction of the SPH regions is applied – as demonstrated for the High Temperature Test Reactor, the latter is more robust and does not require to scale the fission terms with the reference eigenvalue.},

doi = {10.1016/j.anucene.2019.01.003},

journal = {Annals of Nuclear Energy (Oxford)},

number = C,

volume = 128,

place = {United States},

year = {2019},

month = {2}

}