Iterative and direct Chebyshev collocation spectral methods for one-dimensional radiative heat transfer

International Journal of Heat and Mass Transfer

Volumn 51, Issue 25-26, 2008, Pages 5887-5894

  Li, Ben Wen ^a   Sun, Ya Song ^a   Yu, Yang ^a  

^a NORTHEASTERN UNIVERSITY   (China)

Author keywords

Chebyshev collocation spectral methods; Discrete ordinates method; Radiative transfer

Indexed keywords

ASTROPHYSICS; CYLINDERS (SHAPES); ELECTROMAGNETIC WAVES; HEAT EXCHANGERS; HEAT RADIATION; HEAT TRANSFER; HEATING EQUIPMENT; RADIATIVE TRANSFER; SPECTRUM ANALYSIS; THERMOANALYSIS;

CHEBYSHEV COLLOCATION SPECTRAL METHODS; CHEBYSHEV COLLOCATIONS; COMPETITIVE ABILITIES; COMPLEX PROBLEMS; DIRECT SOLVERS; DISCRETE-ORDINATES METHOD; EXPONENTIAL CONVERGENCES; HIGH ACCURACIES; NUMERICAL RESULTS; PARTICIPATING MEDIAS; RADIATIVE HEAT TRANSFER EQUATIONS; RADIATIVE HEAT TRANSFERS;

NUMERICAL METHODS;

EID: 55549108351     PISSN: 00179310     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijheatmasstransfer.2008.04.048     Document Type: Article

References (36)

1. Carlson B.G., and Lathrop K.D. Transport theory: the method of discrete ordinates. In: Greenspan H., Kelber C.N., and Okrent D. (Eds). Computing Methods in Reactor Physics (1968), Gordon & Breach, New York
2. Fiveland W.A. Discrete-ordinates solutions of the radiative transport equation for rectangular enclosures. J. Heat Transfer 106 (1984) 699-706
3. Fiveland W.A. Discrete ordinates methods for radiative heat transfer in isotropically and anisotropically scattering media. J. Heat Transfer 109 (1987) 809-812
4. Fiveland W.A. Three-dimensional radiative heat-transfer solutions by the discrete-ordinates method. J. Thermophys. Heat Transfer 2 (1988) 309-316
5. Siegel R., and Howell J.R. Thermal Radiation Heat Transfer. fourth ed. (2002), Taylor and Francis, New York
6. Modest M.F. Radiative Heat Transfer. second ed. (2003), Academic Press, San Diego
7. Gritzo L.A., and Strickland J.H. A gridless solution of the radiative transfer equation for fire and combustion calculations. Combust. Theory Modell. 3 (1999) 159-175
8. Liu L.H., and Tan J.Y. Meshless local Petrov-Galerkin approach for coupled radiative and conductive heat transfer. Int. J. Thermal Sci. 46 (2007) 672-681
9. Liu L.H., and Tan J.Y. Least-squares collocation meshless approach for radiative heat transfer in absorbing and scattering media. JQSRT 103 (2007) 545-557
10. Wu Y., Modest M.F., and Haworth D.C. A high-order photon Monte Carlo method for radiative transfer in direct numerical simulation. J. Comput. Phys. 223 (2007) 898-922
11. Pontaza J.P., and Reddy J.N. Least-squares finite element formulations for one-dimensional radiative transfer. JQSRT 95 (2005) 387-406
12. Frank M., Dubroca B., and Klar A. Partial moment entropy approximation to radiative heat transfer. J. Comput. Phys. 218 (2006) 1-18
13. Chang B. A deterministic photon free method to solve radiation transfer equations. J. Comput. Phys. 222 (2007) 71-85
14. Vargas R.F., Segatto C.F., and Vilhena M.T. Solution of the radiative heat transfer equation with internal energy sources in a slab by the LTSN method. JQSRT 105 (2007) 1-7
15. Gottlieb D., and Orszag S.A. Numerical analysis of spectral methods: theory and applications. Regional Conference Series in Applied Mathematics vol. 28 (1977), SIAM, Philadelphia
16. Canuto C., Hussaini M.Y., Quarteroni A., and Zang T.A. Spectral Methods in Fluid Dynamics (1989), Springer-Verlag, Berlin
17. Peyret R. Spectral Methods for Incompressible Viscous Flow (2002), Springer, New York
18. Belgacem F.B., and Grundmann M. Approximation of the wave and electromagnetic diffusion equations by spectral methods. SIAM J. Sci. Comput. 20 (1998) 13-32
19. Shan X.W., Montgomery D., and Chen H.D. Nonlinear magnetohydrodynamics by Galerkin-method computation. Phys. Rev. A 44 (1991) 6800-6818
20. Shan X.W. Magnetohydrodynamic stabilization through rotation. Phys. Rev. Lett. 73 (1994) 1623-1627
21. Zhao J.M., and Liu L.H. Least-squares spectral element method for radiative heat transfer in semitransparent media. Numer. Heat Transfer B 50 5 (2006) 473-489
22. Burke R., Pieter G.D., and Dennis B. Use of fast-Fourier-transform computational methods in radiation transport. Phys. Rev. E 56 (1997) 2217-2227
23. Arnold D.K., and Akira I. A Chebyshev spectral method for radiative transfer equations applied to electromagnetic wave propagation and scattering in a discrete random medium. J. Comput. Phys. 152 (1999) 264-280
24. Arnold D.K., and Miguel M. Chebyshev spectral methods for radiative transfer. SIAM J. Sci. Comput. 23 (2002) 2075-2095
25. Aouled-Dlala N., Sghaier T., and Seddiki E. Numerical solution of radiative and conductive heat transfer in concentric spherical and cylindrical media. JQSRT 107 (2007) 443-457
26. Boyd J.P. Chebyshev & Fourier Spectral Methods. second ed. (2001), Dover, New York
27. Fornberg B. A Practical Guide to Pseudospectral Methods (1996), Cambridge University Press, Cambridge
28. Liu L.H. Least-squares finite element method for radiation heat transfer in graded index medium. JQSRT 103 (2007) 536-544
29. Cengel Y.A., and Özişk M.N. Radiation transfer in an anisotropically scattering plane-parallel medium with spacedependent albedo ω(x). JQSRT 34 (1985) 263-270
30. Braverman E., Israeli M., Averbuch A., and Vozovoi L. A fast 3D Poisson solver of arbitrary order accuracy. J. Comput. Phys. 144 (1998) 109-136
31. -1) time step restriction. J. Comput. Phys. 104 (1993) 457-469
32. 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
33. Li B.W., Tao W.Q., and Liu R.X. Ray effect in ray tracing method for radiative heat transfer. Int. J. Heat Mass Transfer 40 (1997) 3419-3426
34. Cumber P.S. Ray effect mitigation in jet fire radiation modelling. Int. J. Heat Mass Transfer 43 (2000) 935-943
35. Li B.W., Yao Q., Cao X.Y., and Cen K.F. A new discrete ordinates quadrature scheme for three-dimensional radiative heat transfer. J. Heat Transfer 120 (1998) 514-518
36. Lu X., and Hsu P.F. Parallel computing of an integral formulation of transient radiation transport. J. Thermophys. Heat Transfer 17 (2003) 425-433