Direct solution of the equation of transfer using frequency- and angle-averaged photon-escape probabilities for spherical and cylindrical geometries

A previously developed technique for solving the transfer equation directly by using frequency-and angle-averaged escape probabilities in a planar, Doppler-broadened medium is generalized to encompass spherical and cylindrical geometries, as well as a Lorentz opacity profile. Two key elements permit this generalization to be made. The first is a reciprocity theorem relating the coupling constant from cell i to cell j to that from cell j to cell i. The second is the use of a universal but accurate mean angle of diffusivity.