Radiative transfer in a rectangular anisotropically scattering medium exposed to diffuse radiation

Linearly anisotropic scattering in a two-dimensional rectangular medium exposed to diffuse radiation is studied using three methods. A standard differential approximation and Olfe's modified differential approximation are presented, and an exact integral formulation in terms of moments of intensity is developed. A collocation method is extended to the solutions of the 2-D integral equations. For the purpose of validating the method, the results of the integral formulation are compared with the existing solutions of 2-D isotropic scattering. We then use the solutions of the integral formulation as a benchmark to examine the accuracy of the two differential approximations. Comparisons of the results derived from the three methods show that both differential approximations work well for radiative transfer in an optically-thick medium, while the modified differential approximation is superior to the standard differential approximation for radiative transfer around the boundaries and for radiative transfer in an optically-thin medium. However, the modified differential approximation understimates the total intensity around the center of a medium. Graphic results are also reported to show the effects of anisotropic scattering, optical sizes and scattering albedos.