Radiative transfer in spherical atmospheres

A method for defining spherical model atmospheres in radiative/convective and hydrostatic equilibrium is presented. A finite difference form is found for the transfer equation and a matrix operator is developed as the discrete space analog (in curvilinear coordinates) of a formal integral in plane geometry. Pressure is treated as a function of temperature. Flux conservation is maintained within the energy equation, although the correct luminosity transport must be assigned for any given level of the atmosphere. A perturbed integral operator is used in a complete linearization of the transfer and constraint equations. Finally, techniques for generating stable solutions in economical computer time are discussed.