Comparison between Kim, Wiscombe and least squares scattering phase function renormalization methods

A numerical code is made allowing the simulation, in two-dimensional geometry, of the radiative transfer within a semi-transparent medium (STM), gray, absorbing, emitting and anisotropically scattering. The solution method is provided by a new formulation of the modified discrete transfer (MDT) method. A bilinear interpolation of the temperature as well as of the scattered radiation intensity within a grid mesh proved to be necessary in order to cure the occurring problem of negative radiation intensities when one calls upon the linear profile of Cumber with a first fine netting. When analysing the effect of the renormalization methods of the scattering phase function of Kim, of Wiscombe and of least squares on the global modeling of radiative transfer in an anisotropic scattering STM, we have shown that the method of Kim is easy to implement and present the same accuracy degree than the one of Wiscombe. However, the technique of least squares offers real prospects since it stands out by the absence of unrealistic values on the diagonal of the matrix associated to the renormalized phase function and the renormalization of the scattering phase function with the desired precision.