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MODIFIED DISCRETE ORDINATES AND FINITE VOLUME METHODS

Following from: Discrete ordinates and finite volume methods

The discrete ordinates method (DOM) and the finite volume method (FVM) suffer from ray effects, as discussed in the article “Ray Effects and False Scattering”. Ray effects may be successfully reduced by increasing the number of discrete directions in the DOM or the number of control angles in the FVM. However, ray effects decrease slowly with the refinement of the angular quadrature. The modified discrete ordinates method, MDOM (Ramankutty and Crosbie, 1997), based on the modified differential approximation (Olfe, 1970, Modest, 1989), proved to significantly mitigate ray effects originated from discontinuities or abrupt changes of the wall temperature. The model was originally developed for two-dimensional enclosures with black walls and homogeneous, isotropi ...

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References

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  2. Baek, S. W., Byun, D. Y., and Kang, S. J., The Combined Monte-Carlo and Finite-Volume Method for Radiation in a Two-Dimensional Irregular Geometry, Int. J. Heat Mass Transfer, vol. 43, pp. 2337−2344, 2000.
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  4. Coelho, P. J., A Modified Version of the Discrete Ordinates Method for Radiative Heat Transfer Modelling, Computational Mech., vol. 33, no. 5, pp. 375−388, 2004.
  5. Crosbie, A. L. and Schrenker, R. G., Radiative Transfer in a Two-Dimensional Rectangular Medium Exposed to Diffuse Radiation, J. Quantitative Spectroscopy and Radiative Transfer, vol. 31, pp. 339−372, 1984.
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  7. Kim, T. -K. and Lee, H. S., Modified δ-M Scaling Results for Mie-Anisotropic Scattering Media, J. Heat Transfer, vol. 112, pp. 988−994, 1990b.
  8. Olfe, D. B., Radiative Equilibrium of a Gray Medium Bounded by Nonisothermal Walls, Progress in Astronautics and Aeronautics, vol. 23, pp. 295−317, 1970.
  9. Modest, M. F., The Modified Differential Approximation for Radiative Transfer in Three-Dimensional Media, J. Thermophysics and Heat Transfer, vol. 3, pp. 283−288, 1989.
  10. Ramankutty, M. A. and Crosbie, A. L., Modified Discrete Ordinates Solution of Radiative Transfer in Two-Dimensional Rectangular Enclosures, J. Quantitative Spectroscopy Radiative Transfer, vol. 57, pp. 107−140, 1997.
  11. Ramankutty, M. A., and Crosbie, A. L., Modified Discrete Ordinates Solution of Radiative Transfer in Three-Dimensional Rectangular, J. Quantitative Spectroscopy Radiative Transfer, vol. 60, pp. 103−134, 1998.
  12. Sakami, M. and Charette, A., Application of a Modified Discrete Ordinates Method to Two-dimensional Enclosures of Irregular Geometry, J. Quantitative Spectroscopy Radiative Transfer, vol. 64, pp. 275−298, 2000.
  13. Sakami, M., El Kasmi, A., and Charette, A., Analysis of Radiative Heat Transfer in Complex Two-dimensional Enclosures with Obstacles Using the Modified Discrete Ordinates Method, J. Heat Transfer, vol. 123, pp. 892−900, 2001.
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