The present article introduces a new method to solve the radiative transfer equation (RTE). First, a finite element discretization of the solid angle dependence is derived, wherein the coefficients of the finite element approximation are functions of the spatial coordinates. The angular basis functions are defined according to finite element principles on subdivisions of the octahedron. In a second step, these spatially dependent coefficients are discretized by spatial finite elements. This approach is very attractive, since it provides a concise derivation for approximations of the angular dependence with an arbitrary number of angular nodes. In addition, the usage of high-order angular basis functions is straightforward. In the current paper the governing equations are first derived independently of the actual angular approximation. Then, the design principles for the angular mesh are discussed and the parameterization of the piecewise angular basis functions is derived. In the following, the method is applied to two-dimensional test cases which are commonly used for the validation of approximation methods of the RTE. The results reveal that the proposed method is a promising alternative to the well-established practices like the Discrete Ordinates Method (DOM) and provides highly accurate approximations. A test case known to exhibit the ray effect in the DOM verifies the ability of the new method to avoid ray effects.
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ASME 2009 Heat Transfer Summer Conference collocated with the InterPACK09 and 3rd Energy Sustainability Conferences
July 19–23, 2009
San Francisco, California, USA
Conference Sponsors:
- Heat Transfer Division
ISBN:
978-0-7918-4356-7
PROCEEDINGS PAPER
An Angular Finite Element Method for the Solution of the Even-Parity Equation
R. Becker,
R. Becker
Universita¨t Karlsruhe, Karlsruhe, Germany
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R. Koch,
R. Koch
Universita¨t Karlsruhe, Karlsruhe, Germany
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M. F. Modest,
M. F. Modest
Universita¨t Karlsruhe, Karlsruhe, Germany
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H.-J. Bauer
H.-J. Bauer
Universita¨t Karlsruhe, Karlsruhe, Germany
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R. Becker
Universita¨t Karlsruhe, Karlsruhe, Germany
R. Koch
Universita¨t Karlsruhe, Karlsruhe, Germany
M. F. Modest
Universita¨t Karlsruhe, Karlsruhe, Germany
H.-J. Bauer
Universita¨t Karlsruhe, Karlsruhe, Germany
Paper No:
HT2009-88505, pp. 371-380; 10 pages
Published Online:
March 12, 2010
Citation
Becker, R, Koch, R, Modest, MF, & Bauer, H. "An Angular Finite Element Method for the Solution of the Even-Parity Equation." Proceedings of the ASME 2009 Heat Transfer Summer Conference collocated with the InterPACK09 and 3rd Energy Sustainability Conferences. Volume 1: Heat Transfer in Energy Systems; Thermophysical Properties; Heat Transfer Equipment; Heat Transfer in Electronic Equipment. San Francisco, California, USA. July 19–23, 2009. pp. 371-380. ASME. https://doi.org/10.1115/HT2009-88505
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