Elliptic PDE formulation of general, three-dimensional high-order PN-approximations for radiative transfer

Journal of Quantitative Spectroscopy and Radiative Transfer

Volumn 104, Issue 2, 2007, Pages 217-227

  Yang, Jun ^a   Modest, Michael F ^a  

^a The Pennsylvania State University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; GEOMETRICAL OPTICS; HARMONIC ANALYSIS; PARTIAL DIFFERENTIAL EQUATIONS; TENSORS;

ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS; RADIATIVE TRANSFER EQUATION; SPHERICAL HARMONICS METHOD;

HEAT RADIATION;

COMPUTER SIMULATION; EQUATION; NUMERICAL METHOD; RADIATIVE TRANSFER; SPHERICAL HARMONICS;

EID: 33750802177     PISSN: 00224073     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jqsrt.2006.07.017     Document Type: Article

References (20)

1. Modest M.F. Radiative heat transfer. 2nd ed. (2003), Academic Press, New York
2. Chai J.C., Lee H.S., and Patankar S.V. Ray effect and false scattering in the discrete ordinates method. Numer Heat Transfer B 24 (1993) 373-389
3. Kofink W. Complete spherical harmonics solution of the Boltzmann equation for neutron transport in homogeneous media with cylindrical geometry. Nucl Sci Eng 6 (1959) 473-486
4. 3 approximation. AIAA J 17 (1979) 424-431
5. Tong T.W., and Swathi P.S. Radiative heat transfer in emitting-absorbing-scattering spherical media. J Thermoph Heat Transfer 1 2 (1987) 162-170
6. Ratzel A.C., and Howell J.R. Two-dimensional radiation in absorbing-emitting-scattering media using the P-N approximation. ASME J Heat Transfer 105 (1983) 333-340
7. Mengüç M.P., and Viskanta R. Radiative transfer in three-dimensional rectangular enclosures containing inhomogeneous. Anisotropically scattering media. JQSRT 33 6 (1985) 533-549
8. Davison B. Neutron transport theory (1958), Oxford University Press, London
9. Ou S.C.S., and Liou K.N. Generalization of the spherical harmonic method to radiative transfer in multi-dimensional space. JQSRT 28 4 (1982) 271-288
10. MacRobert T.M. Spherical harmonics. 3rd ed. (1967), Pergamon Press, New York
11. Mark JC. The spherical harmonics method, part I. Technical report, Atomic energy report No. MT 92, National Research Council of Canada; 1944.
12. Mark JC. The spherical harmonics method, part II. Technical report, Atomic energy report No. MT 97, National Research Council of Canada; 1945.
13. Marshak R.E. Note on the spherical harmonics method as applied to the Milne problem for a sphere. Phys Rev 71 (1947) 443-446
14. Rose ME. Elementary theory of angular momentum. New York: Dover; 1995.
15. FlexPDE software. Sunol, CA: PDE Solutions Inc.
16. Chai J.C., Lee H.S., and Patankar S.V. Finite volume method for radiation heat transfer. J Thermoph Heat Transfer 8 3 (1994) 419-425
17. Li H.S., Flamant G., and Lu J.D. Mitigation of ray effects in the discrete ordinates method. Numer Heat Transfer B 43 5 (2003) 445-466
18. El Wakil N, Sacadura J-F. Some improvements of the discrete ordinates method for the solution of the radiative transport equation in multidimensional anisotropically scattering media. In: Developments in radiative heat transfer HTD-203. New York: ASME; 1992. p. 119-27.
19. Fiveland WA. The selection of discrete ordinate quadrature sets for anisotropic scattering. In: Fundamentals of radiation heat transfer HTD-160. New York: ASME; 1991. p. 89-96.
20. Cheong K.B., and Song T.H. An alternative discrete ordinates method with interpolation and source differencing for two-dimensional radiative transfer problems. Numer Heat Transfer B 32 (1997) 107-125