Gray and multigroup radiation transport models for two-dimensional binary stochastic media using effective opacities

•Gray and multigroup radiation transport is done through 2D stochastic media.•Approximate models for the mean radiation field are found for all test problems.•Effective opacities are adjusted to fit the means of stochastic media transport.•Test problems include temperature dependent opacities and heat capacities•Transport solutions are done with angle orders n=1 and 5.

One-dimensional models for the transport of radiation through binary stochastic media do not work in multi-dimensions. Authors have attempted to modify or extend the 1D models to work in multidimensions without success. Analytic one-dimensional models are successful in 1D only when assuming greatly simplified physics. State of the art theories for stochastic media radiation transport do not address multi-dimensions and temperature-dependent physics coefficients. Here, the concept of effective opacities and effective heat capacities is found to well represent the ensemble averaged transport solutions in cases with gray or multigroup temperature-dependent opacities and constant or temperature-dependent heat capacities. In every case analyzed here, effective physics coefficients fit the transport solutions over a useful range of parameter space. The transport equation is solved with the spherical harmonics method with angle orders of n=1 and 5. Although the details depend on what order of solution is used, the general results are similar, independent of angular order.