## High-order solution methods for grey discrete ordinates thermal radiative transfer

## Abstract

This paper presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation is accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.

- Authors:

- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Texas A & M Univ., College Station, TX (United States)

- Publication Date:

- Research Org.:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1334732

- Alternate Identifier(s):
- OSTI ID: 1397751

- Report Number(s):
- LLNL-JRNL-703665

Journal ID: ISSN 0021-9991

- Grant/Contract Number:
- AC52-07NA27344; NA0002376

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Computational Physics

- Additional Journal Information:
- Journal Volume: 327; Journal Issue: C; Journal ID: ISSN 0021-9991

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 22 GENERAL STUDIES OF NUCLEAR REACTORS; 97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; thermal radiation transport; discontinuous finite element method; Runge–Kutta; discrete ordinates

### Citation Formats

```
Maginot, Peter G., Ragusa, Jean C., and Morel, Jim E. High-order solution methods for grey discrete ordinates thermal radiative transfer. United States: N. p., 2016.
Web. doi:10.1016/j.jcp.2016.09.055.
```

```
Maginot, Peter G., Ragusa, Jean C., & Morel, Jim E. High-order solution methods for grey discrete ordinates thermal radiative transfer. United States. doi:10.1016/j.jcp.2016.09.055.
```

```
Maginot, Peter G., Ragusa, Jean C., and Morel, Jim E. Thu .
"High-order solution methods for grey discrete ordinates thermal radiative transfer". United States. doi:10.1016/j.jcp.2016.09.055. https://www.osti.gov/servlets/purl/1334732.
```

```
@article{osti_1334732,
```

title = {High-order solution methods for grey discrete ordinates thermal radiative transfer},

author = {Maginot, Peter G. and Ragusa, Jean C. and Morel, Jim E.},

abstractNote = {This paper presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation is accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.},

doi = {10.1016/j.jcp.2016.09.055},

journal = {Journal of Computational Physics},

number = C,

volume = 327,

place = {United States},

year = {2016},

month = {9}

}

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