Finite element formulation of the first- and second-order discrete ordinates equations for radiative heat transfer calculation in three-dimensional participating media

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Two finite element methods (FEMs), FEDOM1 and FEDOM2 (standing for the first and the second finite element discrete ordinates methods, respectively), are formulated and numerically tested. The reference second-order discrete equation is modified in its scattering terms and is applied to the problems of absorbing/emitting and anisotropically scattering media by using the FEM. Numerical features of the developed FEMs are compared with one of the discrete ordinates interpolation method (DOIM), which uses a finite difference scheme. Prediction results of radiative heat transfer by these two FEMs are compared with reference solutions and verified in three-dimensional enclosures containing participating media. The results of FEDOM1 and FEDOM2 agree well with exact solutions for the problem of absorbing/emitting medium with various range of optical thickness. Generally, the two FEMs show more accurate results than DOIM. And FEDOM1 shows more accurate results than FEDOM2 in most of the test problems. Both of the developed FEMs show reasonable results compared with published Monte Carlo solutions for the tested absorbing/emitting and anisotropically scattering media. Although the FEDOM2 is not as accurate as the FEDOM1, it shows its own advantages that it reduces CPU time and memory space of dependent variable to half. (c) 2008 Elsevier Ltd. All rights reserved.
Publisher
PERGAMON-ELSEVIER SCIENCE LTD
Issue Date
2008-07
Language
English
Article Type
Article
Keywords

ANISOTROPICALLY SCATTERING MEDIA; VOLUME METHOD; MULTIDIMENSIONAL GEOMETRIES; RECTANGULAR ENCLOSURES; INTERPOLATION

Citation

JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER, v.109, no.11, pp.2094 - 2107

ISSN
0022-4073
URI
http://hdl.handle.net/10203/25106
Appears in Collection
ME-Journal Papers(저널논문)
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