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.