Stochastic radiative transfer in random media. IV. The impact of dimension in conditions with the radiation coupled to material.

Abstract

We study the impact of dimension on the radiative transfer (i.e., thermal x-ray transport) through the nonscattering random medium within the coupling of radiation to material. To this purpose, our approach is based on the direct numerical simulations (DNSs) combined with developed analytical models. Systematic calculations for 29 different sets of physical parameters show two- and three-dimensional transport results are similar, while a remarkable problem-dependent difference is observed in most cases between one and two dimensions, which are explicitly analyzed by using the dimension compression method. Furthermore, we find a good scaling law with respect to the effective optical thickness, thereby we propose an analytical model to predict the impact of dimension and a good agreement with DNS results is identified. In addition, we develop a simple formula to account for the maximum dimensional effect when the materials' opacity contrast is infinitely large. Our work provides a clear physical picture and predictable analytical models for the influence of dimension on the radiative transfer in the thermally participating random media.