# A 2-D/1-D transverse leakage approximation based on azimuthal, Fourier moments

## Abstract

Here, the MPACT code being developed collaboratively by Oak Ridge National Laboratory and the University of Michigan is the primary deterministic neutron transport solver within the Virtual Environment for Reactor Applications Core Simulator (VERA-CS). In MPACT, the two-dimensional (2-D)/one-dimensional (1-D) scheme is the most commonly used method for solving neutron transport-based three-dimensional nuclear reactor core physics problems. Several axial solvers in this scheme assume isotropic transverse leakages, but work with the axial S _{N} solver has extended these leakages to include both polar and azimuthal dependence. However, explicit angular representation can be burdensome for run-time and memory requirements. The work here alleviates this burden by assuming that the azimuthal dependence of the angular flux and transverse leakages are represented by a Fourier series expansion. At the heart of this is a new axial SN solver that takes in a Fourier expanded radial transverse leakage and generates the angular fluxes used to construct the axial transverse leakages used in the 2-D-Method of Characteristics calculations.

- Authors:

- Univ. of Michigan, Ann Arbor, MI (United States); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Univ. of Michigan, Ann Arbor, MI (United States)

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1344985

- Grant/Contract Number:
- AC05-00OR22725

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Nuclear Science and Engineering

- Additional Journal Information:
- Journal Volume: 185; Journal Issue: 2; Journal ID: ISSN 0029-5639

- Publisher:
- American Nuclear Society - Taylor & Francis

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; 21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS

### Citation Formats

```
Stimpson, Shane G., Collins, Benjamin S., and Downar, Thomas.
```*A 2-D/1-D transverse leakage approximation based on azimuthal, Fourier moments*. United States: N. p., 2017.
Web. doi:10.1080/00295639.2016.1272360.

```
Stimpson, Shane G., Collins, Benjamin S., & Downar, Thomas.
```*A 2-D/1-D transverse leakage approximation based on azimuthal, Fourier moments*. United States. doi:10.1080/00295639.2016.1272360.

```
Stimpson, Shane G., Collins, Benjamin S., and Downar, Thomas. Thu .
"A 2-D/1-D transverse leakage approximation based on azimuthal, Fourier moments". United States.
doi:10.1080/00295639.2016.1272360. https://www.osti.gov/servlets/purl/1344985.
```

```
@article{osti_1344985,
```

title = {A 2-D/1-D transverse leakage approximation based on azimuthal, Fourier moments},

author = {Stimpson, Shane G. and Collins, Benjamin S. and Downar, Thomas},

abstractNote = {Here, the MPACT code being developed collaboratively by Oak Ridge National Laboratory and the University of Michigan is the primary deterministic neutron transport solver within the Virtual Environment for Reactor Applications Core Simulator (VERA-CS). In MPACT, the two-dimensional (2-D)/one-dimensional (1-D) scheme is the most commonly used method for solving neutron transport-based three-dimensional nuclear reactor core physics problems. Several axial solvers in this scheme assume isotropic transverse leakages, but work with the axial SN solver has extended these leakages to include both polar and azimuthal dependence. However, explicit angular representation can be burdensome for run-time and memory requirements. The work here alleviates this burden by assuming that the azimuthal dependence of the angular flux and transverse leakages are represented by a Fourier series expansion. At the heart of this is a new axial SN solver that takes in a Fourier expanded radial transverse leakage and generates the angular fluxes used to construct the axial transverse leakages used in the 2-D-Method of Characteristics calculations.},

doi = {10.1080/00295639.2016.1272360},

journal = {Nuclear Science and Engineering},

number = 2,

volume = 185,

place = {United States},

year = {Thu Jan 12 00:00:00 EST 2017},

month = {Thu Jan 12 00:00:00 EST 2017}

}

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