P1 approximation,MDA and IDA for the simulation of radiative transfer in a 3D geometry for an absorbing scattering medium

A numerical study has been conducted using the differential approximation and two modified versions of this method, known as MDA and IDA. The methods have been applied on a 3D geometry containing a participating, absorbing, emitting and anisotropically scattering medium. Comparisons have been carried out with some cases of the literature. It has been observed that the IDA can significantly improve the solution, where the classical P1 approximation is not able to reproduce accurately the actual flux or flux divergence in some of studied configurations. The MDA does not really improve the solution in the purely absorbing cases and when radiation is mainly coming from the medium. In other situations (scattering media, relevant influence of the boundaries), the MDA is more accurate than the P1 but the IDA still performs better, with uncertainties around a few percents for the literature cases studied in the present work.