# A high-order photon Monte Carlo method for radiative transfer in direct numerical simulation

## Abstract

A high-order photon Monte Carlo method is developed to solve the radiative transfer equation. The statistical and discretization errors of the computed radiative heat flux and radiation source term are isolated and quantified. Up to sixth-order spatial accuracy is demonstrated for the radiative heat flux, and up to fourth-order accuracy for the radiation source term. This demonstrates the compatibility of the method with high-fidelity direct numerical simulation (DNS) for chemically reacting flows. The method is applied to address radiative heat transfer in a one-dimensional laminar premixed flame and a statistically one-dimensional turbulent premixed flame. Modifications of the flame structure with radiation are noted in both cases, and the effects of turbulence/radiation interactions on the local reaction zone structure are revealed for the turbulent flame. Computational issues in using a photon Monte Carlo method for DNS of turbulent reacting flows are discussed.

- Authors:

- Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, 130 Research Building E, University Park, PA 16802 (United States)
- Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, 130 Research Building E, University Park, PA 16802 (United States). E-mail: dch12@psu.edu

- Publication Date:

- OSTI Identifier:
- 20991579

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Computational Physics; Journal Volume: 223; Journal Issue: 2; Other Information: DOI: 10.1016/j.jcp.2006.10.014; PII: S0021-9991(06)00479-7; Copyright (c) 2006 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; ACCURACY; COMPATIBILITY; COMPUTERIZED SIMULATION; EQUATIONS; ERRORS; FLAMES; HEAT FLUX; MONTE CARLO METHOD; ONE-DIMENSIONAL CALCULATIONS; PHOTONS; RADIANT HEAT TRANSFER; RADIATION SOURCES

### Citation Formats

```
Wu, Y., Modest, M.F., and Haworth, D.C.
```*A high-order photon Monte Carlo method for radiative transfer in direct numerical simulation*. United States: N. p., 2007.
Web. doi:10.1016/j.jcp.2006.10.014.

```
Wu, Y., Modest, M.F., & Haworth, D.C.
```*A high-order photon Monte Carlo method for radiative transfer in direct numerical simulation*. United States. doi:10.1016/j.jcp.2006.10.014.

```
Wu, Y., Modest, M.F., and Haworth, D.C. Tue .
"A high-order photon Monte Carlo method for radiative transfer in direct numerical simulation". United States.
doi:10.1016/j.jcp.2006.10.014.
```

```
@article{osti_20991579,
```

title = {A high-order photon Monte Carlo method for radiative transfer in direct numerical simulation},

author = {Wu, Y. and Modest, M.F. and Haworth, D.C.},

abstractNote = {A high-order photon Monte Carlo method is developed to solve the radiative transfer equation. The statistical and discretization errors of the computed radiative heat flux and radiation source term are isolated and quantified. Up to sixth-order spatial accuracy is demonstrated for the radiative heat flux, and up to fourth-order accuracy for the radiation source term. This demonstrates the compatibility of the method with high-fidelity direct numerical simulation (DNS) for chemically reacting flows. The method is applied to address radiative heat transfer in a one-dimensional laminar premixed flame and a statistically one-dimensional turbulent premixed flame. Modifications of the flame structure with radiation are noted in both cases, and the effects of turbulence/radiation interactions on the local reaction zone structure are revealed for the turbulent flame. Computational issues in using a photon Monte Carlo method for DNS of turbulent reacting flows are discussed.},

doi = {10.1016/j.jcp.2006.10.014},

journal = {Journal of Computational Physics},

number = 2,

volume = 223,

place = {United States},

year = {Tue May 01 00:00:00 EDT 2007},

month = {Tue May 01 00:00:00 EDT 2007}

}