<title>About the mathematical model of three-dimensional radiative transfer problems in a turbid medium</title>

Abstract

It is typical for the arbitrary turbid media the local compactness disturbance. It leads to appearing singularities in the solution of the radiative transfer equation for the space-limited sources. Thus the classical solution methods are inefficient. The solution for the point isotropic (PI) source has the singularities not only angular dependence but spatial variable as well. For elimination such effect the solution may be rewritten in the form of sum of the small angle part and the rest is a smooth function. The small angle approximation (SAA) contains all the singularities of the exact solution. The further solution is lead only for the smooth function. It allows using the finite elements method. The system is solved by the iteration method. Using of the discrete ordinates method allows to consider arbitrary boundary conditions. The suggested method considers the scattering photons ways dispersion. It allows estimating the (SAA) application range for the different three-dimensional medium parameters.