메뉴 건너뛰기




Volumn 109, Issue 9, 2008, Pages 1641-1666

Elliptic PDE formulation and boundary conditions of the spherical harmonics method of arbitrary order for general three-dimensional geometries

Author keywords

High order; Radiative transfer equation; Spherical harmonics; Three dimensional

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; COMPUTATIONAL GEOMETRY; MONTE CARLO METHODS; PARTIAL DIFFERENTIAL EQUATIONS;

EID: 43149089353     PISSN: 00224073     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jqsrt.2007.12.018     Document Type: Article
Times cited : (75)

References (28)
  • 2
    • 0027840903 scopus 로고
    • Ray effect and false scattering in the discrete ordinates method
    • 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
    • (1993) Numer Heat Transfer B , vol.24 , pp. 373-389
    • Chai, J.C.1    Lee, H.S.2    Patankar, S.V.3
  • 3
    • 33750802177 scopus 로고    scopus 로고
    • High-order P-N approximation for radiative transfer in arbitrary geometries
    • Yang J., and Modest M.F. High-order P-N approximation for radiative transfer in arbitrary geometries. JQSRT 104 2 (2007) 217-227
    • (2007) JQSRT , vol.104 , Issue.2 , pp. 217-227
    • Yang, J.1    Modest, M.F.2
  • 4
    • 0001330182 scopus 로고
    • A modification of the differential approximation for radiative transfer
    • Olfe D.B. A modification of the differential approximation for radiative transfer. AIAA Jl 5 4 (1967) 638-643
    • (1967) AIAA Jl , vol.5 , Issue.4 , pp. 638-643
    • Olfe, D.B.1
  • 5
    • 0024706033 scopus 로고
    • The modified differential approximation for radiative transfer in general three-dimensional media
    • Modest M.F. The modified differential approximation for radiative transfer in general three-dimensional media. J Thermoph Heat Transfer 3 3 (1989) 283-288
    • (1989) J Thermoph Heat Transfer , vol.3 , Issue.3 , pp. 283-288
    • Modest, M.F.1
  • 6
    • 33750838406 scopus 로고
    • Complete spherical harmonics solution of the Boltzmann equation for neutron transport in homogeneous media with cylindrical geometry
    • 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
    • (1959) Nucl Sci Eng , vol.6 , pp. 473-486
    • Kofink, W.1
  • 8
    • 85003265765 scopus 로고
    • Radiative heat transfer in emitting-absorbing-scattering spherical media
    • 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
    • (1987) J Thermoph Heat Transfer , vol.1 , Issue.2 , pp. 162-170
    • Tong, T.W.1    Swathi, P.S.2
  • 9
    • 0020751280 scopus 로고
    • Two-dimensional radiation in absorbing-emitting-scattering media using the P-N Approximation
    • Ratzel A.C., and Howell J.R. Two-dimensional radiation in absorbing-emitting-scattering media using the P-N Approximation. J Heat Transfer 105 (1983) 333-340
    • (1983) J Heat Transfer , vol.105 , pp. 333-340
    • Ratzel, A.C.1    Howell, J.R.2
  • 10
    • 0000584672 scopus 로고
    • Radiative transfer in three-dimensional rectangular enclosures containing inhomogeneous, Anisotropically scattering media
    • Mengüç M.P., and Viskanta R. Radiative transfer in three-dimensional rectangular enclosures containing inhomogeneous, Anisotropically scattering media. JQSRT 33 6 (1985) 533-549
    • (1985) JQSRT , vol.33 , Issue.6 , pp. 533-549
    • Mengüç, M.P.1    Viskanta, R.2
  • 12
    • 0002717336 scopus 로고
    • Generalization of the spherical harmonic method to radiative transfer in multi-dimensional space
    • 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
    • (1982) JQSRT , vol.28 , Issue.4 , pp. 271-288
    • Ou, S.C.S.1    Liou, K.N.2
  • 13
    • 43149104491 scopus 로고    scopus 로고
    • FlexPDE software. Antioch: PDE Solutions Inc.
    • FlexPDE software. Antioch: PDE Solutions Inc.
  • 14
    • 43149113332 scopus 로고    scopus 로고
    • FLUENT computational fluid dynamics software, Version 5. New Hampshire: Fluent Corp.; 1998.
    • FLUENT computational fluid dynamics software, Version 5. New Hampshire: Fluent Corp.; 1998.
  • 16
    • 43149086965 scopus 로고    scopus 로고
    • Mark JC. The spherical harmonics method, part I. Technical Report Atomic Energy Report No. MT 92, National Research Council of Canada: 1944.
    • Mark JC. The spherical harmonics method, part I. Technical Report Atomic Energy Report No. MT 92, National Research Council of Canada: 1944.
  • 17
    • 43149087203 scopus 로고    scopus 로고
    • Mark JC. The spherical harmonics method, part II. Technical Report Atomic Energy Report No. MT 97, National Research Council of Canada; 1945.
    • Mark JC. The spherical harmonics method, part II. Technical Report Atomic Energy Report No. MT 97, National Research Council of Canada; 1945.
  • 18
    • 0000890680 scopus 로고
    • Note on the spherical harmonics method as applied to the Milne problem for a sphere
    • Marshak R.E. Note on the spherical harmonics method as applied to the Milne problem for a sphere. Phys Rev 71 (1947) 443-446
    • (1947) Phys Rev , vol.71 , pp. 443-446
    • Marshak, R.E.1
  • 20
    • 0347874846 scopus 로고    scopus 로고
    • Evaluation of the rotation matrices in the basis of real spherical harmonics
    • Blanco M.A., Flórez M., and Bermejo M. Evaluation of the rotation matrices in the basis of real spherical harmonics. J Mole Struct (Theochem) 49 (1997) 19-27
    • (1997) J Mole Struct (Theochem) , vol.49 , pp. 19-27
    • Blanco, M.A.1    Flórez, M.2    Bermejo, M.3
  • 21
    • 43149122350 scopus 로고    scopus 로고
    • Sewell G. PDE2D 9.0 〈http://www.pde2d.com/〉.
    • Sewell G. PDE2D 9.0 〈http://www.pde2d.com/〉.
  • 22
    • 43149091992 scopus 로고    scopus 로고
    • Schönauer W. FDEM, (2005), see the "Fuel Cell Report" at 〈http://www.rz.uni-karlsruhe.de/produkte/5336.php〉.
    • Schönauer W. FDEM, (2005), see the "Fuel Cell Report" at 〈http://www.rz.uni-karlsruhe.de/produkte/5336.php〉.
  • 23
    • 49949123360 scopus 로고
    • Application of a modified differential approximation to radiative transfer in a gray medium between concentric sphere and cylinders
    • Olfe D.B. Application of a modified differential approximation to radiative transfer in a gray medium between concentric sphere and cylinders. JQSRT 8 (1968) 899-907
    • (1968) JQSRT , vol.8 , pp. 899-907
    • Olfe, D.B.1
  • 24
    • 0016125477 scopus 로고
    • Two-dimensional radiative equilibrium of a gray medium in a plane layer bounded by gray non-isothermal walls
    • Modest M.F. Two-dimensional radiative equilibrium of a gray medium in a plane layer bounded by gray non-isothermal walls. J Heat Transfer 96C (1974) 483-488
    • (1974) J Heat Transfer , vol.96 C , pp. 483-488
    • Modest, M.F.1
  • 25
    • 0000906824 scopus 로고
    • Radiative equilibrium in a rectangular enclosure bounded by gray non-isothermal walls
    • Modest M.F. Radiative equilibrium in a rectangular enclosure bounded by gray non-isothermal walls. JQSRT 15 (1975) 445-461
    • (1975) JQSRT , vol.15 , pp. 445-461
    • Modest, M.F.1
  • 26
    • 0024903136 scopus 로고    scopus 로고
    • Modest MF. The improved differential approximation for radiative transfer in general three-dimensional media. In: Heat transfer phenomena in radiation, combustion and fires, vol. HTD-106. ASME; 1989. p. 213-20.
    • Modest MF. The improved differential approximation for radiative transfer in general three-dimensional media. In: Heat transfer phenomena in radiation, combustion and fires, vol. HTD-106. ASME; 1989. p. 213-20.
  • 27
    • 0025468409 scopus 로고
    • The improved differential approximation for radiative transfer in multi-dimensional media
    • Modest M.F. The improved differential approximation for radiative transfer in multi-dimensional media. J Heat Transfer 112 (1990) 819-821
    • (1990) J Heat Transfer , vol.112 , pp. 819-821
    • Modest, M.F.1
  • 28
    • 0242660875 scopus 로고    scopus 로고
    • Mitigation of ray effects in the discrete ordinates method
    • 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
    • (2003) Numer Heat Transfer B , vol.43 , Issue.5 , pp. 445-466
    • Li, H.S.1    Flamant, G.2    Lu, J.D.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.