A COMPARATIVE-STUDY OF FINITE-DIFFERENCE METHODS FOR RADIATIVE-TRANSFER PROBLEMS

We have compared the numerical results of two widely used difference m ethods for the radiative transfer equation in plane-parallel medium. T he Discrete Space theory (DS) is based on the direct first-order diffe rential equation for the specific intensity whereas Auer's Hermitian ( AH) method used the second order form for the mean-intensity and Aux-l ike variables. The numerical results of these two methods are compared with analytical solutions under the two-stream approximation in a sem i-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 loga rithmic 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. Analytic al solution of the difference equation of DS method is studied and it is found that the solution gives the correct surface value and the dif fusion limit in a semi-infinite atmosphere.