# An asymptotic preserving unified gas kinetic scheme for gray radiative transfer equations

## Abstract

The solutions of radiative transport equations can cover both optical thin and optical thick regimes due to the large variation of photon's mean-free path and its interaction with the material. In the small mean free path limit, the nonlinear time-dependent radiative transfer equations can converge to an equilibrium diffusion equation due to the intensive interaction between radiation and material. In the optical thin limit, the photon free transport mechanism will emerge. In this paper, we are going to develop an accurate and robust asymptotic preserving unified gas kinetic scheme (AP-UGKS) for the gray radiative transfer equations, where the radiation transport equation is coupled with the material thermal energy equation. The current work is based on the UGKS framework for the rarefied gas dynamics [14], and is an extension of a recent work [12] from a one-dimensional linear radiation transport equation to a nonlinear two-dimensional gray radiative system. The newly developed scheme has the asymptotic preserving (AP) property in the optically thick regime in the capturing of diffusive solution without using a cell size being smaller than the photon's mean free path and time step being less than the photon collision time. Besides the diffusion limit, the scheme can capture themore »

- Authors:

- Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088 (China)
- Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon (Hong Kong)

- Publication Date:

- OSTI Identifier:
- 22465611

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Computational Physics; Journal Volume: 285; Other Information: Copyright (c) 2015 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICAL METHODS AND COMPUTING; ASYMPTOTIC SOLUTIONS; DIFFUSION EQUATIONS; EXACT SOLUTIONS; MEAN FREE PATH; NONLINEAR PROBLEMS; ONE-DIMENSIONAL CALCULATIONS; PHOTON COLLISIONS; RADIANT HEAT TRANSFER; RADIATION TRANSPORT; TIME DEPENDENCE; TRANSPORT THEORY; TWO-DIMENSIONAL SYSTEMS

### Citation Formats

```
Sun, Wenjun, E-mail: sun_wenjun@iapcm.ac.cn, Jiang, Song, E-mail: jiang@iapcm.ac.cn, and Xu, Kun, E-mail: makxu@ust.hk.
```*An asymptotic preserving unified gas kinetic scheme for gray radiative transfer equations*. United States: N. p., 2015.
Web. doi:10.1016/J.JCP.2015.01.008.

```
Sun, Wenjun, E-mail: sun_wenjun@iapcm.ac.cn, Jiang, Song, E-mail: jiang@iapcm.ac.cn, & Xu, Kun, E-mail: makxu@ust.hk.
```*An asymptotic preserving unified gas kinetic scheme for gray radiative transfer equations*. United States. doi:10.1016/J.JCP.2015.01.008.

```
Sun, Wenjun, E-mail: sun_wenjun@iapcm.ac.cn, Jiang, Song, E-mail: jiang@iapcm.ac.cn, and Xu, Kun, E-mail: makxu@ust.hk. Sun .
"An asymptotic preserving unified gas kinetic scheme for gray radiative transfer equations". United States.
doi:10.1016/J.JCP.2015.01.008.
```

```
@article{osti_22465611,
```

title = {An asymptotic preserving unified gas kinetic scheme for gray radiative transfer equations},

author = {Sun, Wenjun, E-mail: sun_wenjun@iapcm.ac.cn and Jiang, Song, E-mail: jiang@iapcm.ac.cn and Xu, Kun, E-mail: makxu@ust.hk},

abstractNote = {The solutions of radiative transport equations can cover both optical thin and optical thick regimes due to the large variation of photon's mean-free path and its interaction with the material. In the small mean free path limit, the nonlinear time-dependent radiative transfer equations can converge to an equilibrium diffusion equation due to the intensive interaction between radiation and material. In the optical thin limit, the photon free transport mechanism will emerge. In this paper, we are going to develop an accurate and robust asymptotic preserving unified gas kinetic scheme (AP-UGKS) for the gray radiative transfer equations, where the radiation transport equation is coupled with the material thermal energy equation. The current work is based on the UGKS framework for the rarefied gas dynamics [14], and is an extension of a recent work [12] from a one-dimensional linear radiation transport equation to a nonlinear two-dimensional gray radiative system. The newly developed scheme has the asymptotic preserving (AP) property in the optically thick regime in the capturing of diffusive solution without using a cell size being smaller than the photon's mean free path and time step being less than the photon collision time. Besides the diffusion limit, the scheme can capture the exact solution in the optical thin regime as well. The current scheme is a finite volume method. Due to the direct modeling for the time evolution solution of the interface radiative intensity, a smooth transition of the transport physics from optical thin to optical thick can be accurately recovered. Many numerical examples are included to validate the current approach.},

doi = {10.1016/J.JCP.2015.01.008},

journal = {Journal of Computational Physics},

number = ,

volume = 285,

place = {United States},

year = {Sun Mar 15 00:00:00 EDT 2015},

month = {Sun Mar 15 00:00:00 EDT 2015}

}