ON THE EQUIVALENCE BETWEEN THE DISCRETE ORDINATES AND THE SPHERICAL-HARMONICS METHODS IN RADIATIVE-TRANSFER

In this work concerning steady-state radiative-transfer calculations i n plane-parallel media, the equivalence between the discrete ordinates method and the spherical harmonics method is proved. More specificall y, it is shown that for standard radiative transfer problems without t he imposed restriction of azimuthal symmetry the two methods yield ide ntical results for the radiation intensity when the quadrature scheme for the discrete ordinates method is defined by the zeros of the assoc iated 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 sam e computational effort Finally a justification for using the generaliz ed Mark boundary conditions in the spherical harmonics solution is giv en.