On the equivalence between the discrete ordinates and the spherical harmonics methods in radiative transfer

Journal Article · Tue Sep 01 04:00:00 EDT 1998 · Nuclear Science and Engineering

OSTI ID:653462

Barichello, L B ^[1]; Siewert, C E ^[2]

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1. Univ. Federal do Rio Grande do Sul, Porto Alegre, Rio Grande do Sul (Brazil). Inst. de Matematica
2. North Carolina State Univ., Raleigh, NC (United States). Mathematics Dept.

In this work concerning steady-state radiative-transfer calculations in plane-parallel media, the equivalence between the discrete ordinates method and the spherical harmonics method is proved. More specifically, it is shown that for standard radiative-transfer problems without the imposed restriction of azimuthal symmetry the two methods yield identical results for the radiation intensity when the quadrature scheme for the discrete ordinates method is defined by the zeros of the associated Legendre functions and when generalized Mark boundary conditions are used to define the spherical harmonics solution. It is also shown that, with these choices for a quadrature scheme and for the boundary conditions, the two methods can be formulated so as to require the same computational effort. Finally a justification for using the generalized Mark boundary conditions in the spherical harmonics solution is given.

• OSTI ID: 653462
• Journal Information: Nuclear Science and Engineering, Journal Name: Nuclear Science and Engineering Journal Issue: 1 Vol. 130; ISSN NSENAO; ISSN 0029-5639
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
BOUNDARY CONDITIONS
DISCRETE ORDINATE METHOD
LEGENDRE POLYNOMIALS
QUADRATURES
RADIATION TRANSPORT
SPHERICAL HARMONICS METHOD