Stochastic radiative transfer in random media. III. Effective opacity.

Abstract

Homogenization of random media is a practical approach to efficiently simulate stochastic radiative transfer, which requires establishing a reliable effective opacity model. In this work, a new effective opacity model is developed by considering the two-point spatial correlations of the opacity fluctuation, which is further simplified by introducing the analytically empirical function of the optical depth. Our new model has been extensively verified by comparing with direct numerical simulations (DNSs) of stochastic radiative transfer in participating random media in two dimensions. A systematic comparison with existing effective opacity models in the literature is made. For more than 50 different sets of physical parameters of random media, including constant and temperature-dependent opacities, it shows that our new model is the most accurate, which can reproduce the DNS transport results within a relative error of 5% in most cases. In contrast, the performance of existing models is problem-dependent, and it yields considerable errors spanning over three orders of magnitude. The reasons why the newly developed model works well and why existing models fail are also discussed. For more realistic problems, radiative transfer in the aluminum-foam mixture is investigated, where our new model shows the best performance among analytical effective opacity models. In addition, the newly developed model's limitations are briefly analyzed.