A comparative study of finite-difference methods for radiative transfer problems.

Abstract

We have compared the numerical results of two widely used difference methods for the radiative transfer equation in plane-parallel medium. The Discrete Space theory (DS) is based on the direct first-order differential equation for the specific intensity whereas Auer's Hermitian (AH) method used the second order form for the mean-intensity and flux-like variables. The numerical results of these two methods are compared with analytical solutions under the two-stream approximation in a semi-infinite atmosphere. For the multi-stream case, the numerical errors are estimated using the solution of Chandrasekhar's discrete ordinate method. It is found that DS method is stable with respect to the logarithmic spacing of optical depth and gives less error for the specific intensity at the surface than that of AH method. The maximum relative error for the mean intensity variable is less for AH method. Analytical solution of the difference equation of DS method is studied and it is found that the solution gives the correct surface value and the diffusion limit in a semi-infinite atmosphere.