A new method for the solution of the radiative transfer equation in expanding spherical media based on the Discrete Ordinate Matrix Exponential (DOME) method is described. The effects of advection and aberration terms on line profiles for scattering dominated shells as observed, e.g., in supernova photospheres are discussed. It is shown that these effects have a large influence on the radiation field in rapidly expanding shells and should therefore be included in model calculations.