# Multiscale Capability in Rattlesnake using Contiguous Discontinuous Discretization of Self-Adjoint Angular Flux Equation

## Abstract

In this report, we present a new upwinding scheme for the multiscale capability in Rattlesnake, the MOOSE based radiation transport application. Comparing with the initial implementation of multiscale utilizing Lagrange multipliers to impose strong continuity of angular flux on interface of in-between subdomains, this scheme does not require the particular domain partitioning. This upwinding scheme introduces discontinuity of angular flux and resembles the classic upwinding technique developed for solving first order transport equation using discontinuous finite element method (DFEM) on the subdomain interfaces. Because this scheme restores the causality of radiation streaming on the interfaces, significant accuracy improvement can be observed with moderate increase of the degrees of freedom comparing with the continuous method over the entire solution domain. Hybrid SN-PN is implemented and tested with this upwinding scheme. Numerical results show that the angular smoothing required by Lagrange multiplier method is not necessary for the upwinding scheme.

- Authors:

- Texas A & M Univ., College Station, TX (United States)
- 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:
- 1364491

- Report Number(s):
- INL/EXT-16-39793

TRN: US1703367

- DOE Contract Number:
- AC07-05ID14517

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 22 GENERAL STUDIES OF NUCLEAR REACTORS; FINITE ELEMENT METHOD; COMPARATIVE EVALUATIONS; DEGREES OF FREEDOM; RADIATION STREAMING; RADIATION TRANSPORT; multiscale; Rattlesnake; TREAT

### Citation Formats

```
Zheng, Weixiong, Wang, Yaqi, and DeHart, Mark D.
```*Multiscale Capability in Rattlesnake using Contiguous Discontinuous Discretization of Self-Adjoint Angular Flux Equation*. United States: N. p., 2016.
Web. doi:10.2172/1364491.

```
Zheng, Weixiong, Wang, Yaqi, & DeHart, Mark D.
```*Multiscale Capability in Rattlesnake using Contiguous Discontinuous Discretization of Self-Adjoint Angular Flux Equation*. United States. doi:10.2172/1364491.

```
Zheng, Weixiong, Wang, Yaqi, and DeHart, Mark D. Thu .
"Multiscale Capability in Rattlesnake using Contiguous Discontinuous Discretization of Self-Adjoint Angular Flux Equation". United States.
doi:10.2172/1364491. https://www.osti.gov/servlets/purl/1364491.
```

```
@article{osti_1364491,
```

title = {Multiscale Capability in Rattlesnake using Contiguous Discontinuous Discretization of Self-Adjoint Angular Flux Equation},

author = {Zheng, Weixiong and Wang, Yaqi and DeHart, Mark D.},

abstractNote = {In this report, we present a new upwinding scheme for the multiscale capability in Rattlesnake, the MOOSE based radiation transport application. Comparing with the initial implementation of multiscale utilizing Lagrange multipliers to impose strong continuity of angular flux on interface of in-between subdomains, this scheme does not require the particular domain partitioning. This upwinding scheme introduces discontinuity of angular flux and resembles the classic upwinding technique developed for solving first order transport equation using discontinuous finite element method (DFEM) on the subdomain interfaces. Because this scheme restores the causality of radiation streaming on the interfaces, significant accuracy improvement can be observed with moderate increase of the degrees of freedom comparing with the continuous method over the entire solution domain. Hybrid SN-PN is implemented and tested with this upwinding scheme. Numerical results show that the angular smoothing required by Lagrange multiplier method is not necessary for the upwinding scheme.},

doi = {10.2172/1364491},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Thu Sep 01 00:00:00 EDT 2016},

month = {Thu Sep 01 00:00:00 EDT 2016}

}