DISCRETE ORDINATES AND FINITE VOLUME METHODS
Following from: Radiation transfer theory and the computational methods
Leading to: Mathematical formulation; Spatial discretization schemes; Angular discretization methods; Boundary conditions; Solution algorithm; Alternative formulations; Ray effects and false scattering; Modified discrete ordinates and finite volume methods; Application to nongray media; Variable refractive index media; Transient problems; Parallel implementation
The discrete ordinates method (DOM) was originally developed in the astrophysics community to study radiation transfer in stellar and planetary atmospheres (Chandrasekhar, 1950). Later on, it was employed in nuclear engineering to study neutron transport (Lee, 1962; Lathrop, 1966; Carlson and Lathrop, 1968). Despite a few early works on 1D heat transfer problems published between 1965 and 19 ...
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- Carlson, B. G. and Lathrop, K. D., Transport Theory–The Method of Discrete Ordinates, Computing Methods in Reactor Physics, H. Greenspan, C. N. Kelber, and D. Okrent, Eds., New York: Gordon & Breach, 1968.
- Chai, J. C., Lee, H. S., and Patankar, S. V., Finite Volume Method for Radiation Heat Transfer, J. Thermophys. Heat Transfer, vol. 8, no. 3, pp. 419−425, 1994.
- Chai, J. C., Parthasarathy, G., Lee, H. S., and Patankar, S. V., Finite Volume Radiative Heat Transfer Procedure for Irregular Geometries, J. Thermophys. Heat Transfer, vol. 9, no. 3, pp. 410−415, 1995.
- Chandrasekhar, S., Radiative Transfer, London: Oxford University Press, 1950.
- Chui, E. H., Hughes, P. M. J., and Raithby, G. D., Implementation of the Finite Volume Method for Calculating Radiative Transfer in a Pulverized Fuel Flame, Combust. Sci. Technol., vol. 92, pp. 225−242, 1993.
- Chui, E. H. and Raithby, G. D., Implicit Solution Scheme to Improve Convergence Rate in Radiative Transfer Problems, Numer. Heat Transfer, Part B, vol. 22, pp. 251−272, 1992.
- Chui, E. H. and Raithby, G. D., Computation of Radiant Heat Transfer on a Nonorthogomal Mesh Using the Finite-Volume Method, Numer. Heat Transfer, Part B, vol. 23, pp. 269−288, 1993.
- Chui, E. H., Raithby, G. D., and Hughes, P. M. J., Prediction of Radiative Transfer in Cylindrical Enclosures with the Finite Volume Method, J. Thermophys. Heat Transfer, vol. 6, no. 4, pp. 605−611, 1992.
- Fiveland, W. A., A Discrete Ordinates Method for Predicting Radiative Heat Transfer in Axisymmetric Enclosures, ASME Paper No. 82−HT−20, 1982.
- Fiveland, W. A., Discrete-Ordinates Solutions of the Radiative Transport Equation for Rectangular Enclosures, J. Heat Transfer, vol. 106, pp. 699−706, 1984.
- Fiveland, W. A., Discrete Ordinate Methods for Radiative Heat Transfer in Isotropically and Anisotropically Scattering Media, J. Heat Transfer, vol. 109, pp. 809−812, 1987.
- Fiveland, W. A., Three-Dimensional Radiative Heat-Transfer Solutions by the Discrete-Ordinates Method, J. Thermophys. Heat Transfer, vol. 2, no. 4, pp. 309−316, 1988.
- Hyde, D. J. and Truelove, J. S., The Discrete Ordinates Approximation for Multidimensional Radiant Heat Transfer in Furnaces, UKAEA Report No. AERE−R8502, AERE Harwell, Oxfordshire, 1977.
- Jamaluddin, A. S. and Smith, P. J., Predicting Radiative Transfer in Rectangular Enclosures Using the Discrete Ordinates Method, Combust. Sci. Technol., vol. 59, pp. 321−340, 1988a.
- Jamaluddin, A. S. and Smith, P. J., Predicting Radiative Transfer in Axisymmetric Cylindrical Enclosures Using the Discrete Ordinates Method, Combust. Sci. Technol., vol. 62, pp. 173−186, 1988b.
- Lathrop, K. D., Use of Discrete-Ordinate Methods for Solution of Photon Transport Problems, Nucl. Sci. Eng., vol. 24, pp. 381−388, 1966.
- Lee, C. E., The Discrete Sn Approximation to Transport Theory, Technical Information Series Report No. LA 2595, Lawrence Livermore Laboratory, 1962.
- Liu, J., Shang, H. M., Chen, Y. S., and Wang, T. S., Prediction of Radiative Transfer in General Body-Fitted Coordinates, Numer. Heat Transfer, Part B, vol. 31, pp. 423−439, 1997.
- Modest, M. F., Radiative Heat Transfer, New York: Academic Press, 2003.
- Patankar, S. V., Numerical Heat Transfer and Fluid Flow, New York: McGraw-Hill, 1980.
- Raithby, G. D. and Chui, E. H., A Finite Volume Method for Predicting a Radiant Heat Transfer in Enclosures with Participating Media, J. Heat Transfer, vol. 112, pp. 415−423, 1990.
- Sakami, M., Charrete, A., and Le Dez, V., Radiative Heat Transfer in Three-Dimensional Enclosures of Complex Geometry by Using the Discrete-Ordinates Method, J. Quant. Spectrosc. Radiat. Transfer, vol. 59, pp. 117−136, 1998.
- Truelove, J. S., Discrete-Ordinates Solutions of the Radiation Transport Equation, J. Heat Transfer, vol. 109, pp. 1048−1051, 1987.
- Truelove, J. S., Three-Dimensional Radiation in Absorbing-Emitting-Scattering Media Using the Discrete-Ordinates Method, J. Quant. Spectrosc. Radiat. Transfer, vol. 39, no. 1, pp. 27−31, 1988.