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Title: 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:
ORCiD logo [1];  [2]; ORCiD logo [2]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  2. 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
Report Number(s):
LLNL-JRNL-703665
Journal ID: ISSN 0021-9991
Grant/Contract Number:
AC52-07NA27344; NA0002376
Resource Type:
Journal Article: 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.. 2016. "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
}

Journal Article:
Free Publicly Available Full Text
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  • Cited by 1
  • This work 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 ismore » accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.« less
  • The S4 discrete-ordinates approximation is used to solve the radiative transfer equation in nonasymmetric (i.e., three-dimensional) cylindrical enclosures containing absorbing-emitting and scattering media, with and without the temperature profile known a priori. Because neither detailed experimental data nor predictions from a zone or Monte-Carlo model for three-dimensional cylindrical enclosures are available, cylindrical equivalents of three-dimensional rectangular enclosures, for which zone model predictions of radiative transfer are available, are used in model evaluation. Limited evaluation of the model shows that the discrete-ordinates method provides acceptable predictions of radiative transfer in nonaxisymmetric cylindrical enclosures. 12 refs.
  • A radiation code based on the method of lines (MOL) solution of the discrete ordinates method (DOM) for transient three-dimensional radiative heat transfer in rectangular enclosures for use in conjunction with a computational fluid dynamics (CFD) code based on the same approach was developed. Assessment of the predictive accuracy of the code by benchmarking its steady-state solutions against exact solutions on one- and three-dimensional test problems shows that the MOL solution of the DOM provides accurate and computationally efficient solutions for radiative heat fluxes and source terms and can be used with confidence in conjunction with CFD codes for transientmore » problems.« less
  • In this work concerning steady-state radiative-transfer calculations in plane-parallel media, the equivalence between the discrete ordinates method and the spherical harmonics method is proved. More specifically, it is shown that for standard radiative-transfer problems without the imposed restriction of azimuthal symmetry the two methods yield identical results for the radiation intensity when the quadrature scheme for the discrete ordinates method is defined by the zeros of the associated Legendre functions and when generalized Mark boundary conditions are used to define the spherical harmonics solution. It is also shown that, with these choices for a quadrature scheme and for the boundarymore » conditions, the two methods can be formulated so as to require the same computational effort. Finally a justification for using the generalized Mark boundary conditions in the spherical harmonics solution is given.« less