Due to potential applications in the inertial confinement fusion (ICF), radiation transport in material mixing regions consisting of high-Z material randomly admixed into the low-Z background material has received great attention. In this contribution, we concentrate on the impact of dimension on radiation flows in mixtures within the coupling of radiation to material. For this purpose, we have developed the direct numerical simulation (DNSs) code RAREBIT. 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. Interestingly, we find a good scaling law with respect to the effective optical thickness, thereby an analytical model to predict the impact of dimension has been proposed, and a good agreement with DNS results is identified. Moreover, 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 flows in the thermally mixtures.

radiation flow; mixture; dimensional effect