Time-dependent simplified PN approximation to the equations of radiative transfer

Journal of Computational Physics

Volumn 226, Issue 2, 2007, Pages 2289-2305

  Frank, Martin ^a   Klar, Axel ^a   Larsen, Edward W ^b   Yasuda, Shugo ^c  

^a University of Koblenz Landau   (Germany)

^b UNIVERSITY OF MICHIGAN   (United States)

^c KYOTO UNIVERSITY   (Japan)

Author keywords

Asymptotic analysis; Radiative transfer; Simplified PN equations

Indexed keywords

EQUATIONS OF STATE; RADIATIVE TRANSFER;

ASYMPTOTIC DERIVATIONS; EQUATION OF RADIATIVE TRANSFER; NON EQUILIBRIUM; NUMERICAL TESTS; RADIATIVE TRANSPORT EQUATION; SIMPLIFIED PN EQUATION; STEADY STATE; TEST CASE; TIME DEPENDENT; WELLPOSEDNESS;

ASYMPTOTIC ANALYSIS;

EID: 34548691236     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2007.07.009     Document Type: Article

References (14)

1. Amann H. Linear and quasilinear parabolic problems. first ed. (1995), Birkhäuser
2. 3 approximation. Nucl. Sci. Eng. 134 (2000) 1
3. Brunner T.A., and Holloway J.P. Two-dimensional time dependent Riemann solvers for neutron transport. J. Comput. Phys. 210 (2005) 386-399
4. E.M. Gelbard, Applications of Spherical Harmonics Method to Reactor Problems, Tech. Report WAPD-BT-20, Bettis Atomic Power Laboratory, 1960.
5. E.M. Gelbard, Simplified Spherical Harmonics Equations and Their Use in Shielding Problems, Tech. Report WAPD-T-1182, Bettis Atomic Power Laboratory, 1961.
6. E.M. Gelbard, Applications of the Simplified Spherical Harmonics Equations in Spherical Geometry, Tech. Report WAPD-TM-294, Bettis Atomic Power Laboratory, 1962.
7. N equations with anisotropic scattering. Nucl. Sci. Eng. 123 (1996) 328
8. Larsen E.W., Thömmes G., and Klar A. New frequency-averaged approximations to the equations of radiative heat transfer. SIAM J. Appl. Math. 64 (2003) 565-582
9. n approximations to the equations of radiative heat transfer in glass. J. Comput. Phys. 183 (2002) 652-675
10. Marshak R.E. Note on the spherical harmonic method as applied to the Milne problem for a sphere. Phys. Rev. 71 (1947) 443-446
11. R.G. McClarren, J.P. Holloway, T.A. Brunner, An upwind spherical harmonics method for thermal radiation transfer, in: ANS National Meeting, 2006, pp. 879-880.
12. N method. Nucl. Sci. Eng. 123 (1996) 319-327
13. Su B., and Olson G.L. An analytical benchmark for non-equilibrium radiative transfer in an isotropically scattering medium. Ann. Nucl. Energy 24 (1997) 1035-1055
14. 2 approximation. Nucl. Sci. Eng. 122 (1996) 309-325