Gray radiation transport models for two-dimensional binary stochastic media with material temperature coupling using spherical harmonics

- Radiation transport is done though 2D stochastic media using spherical harmonics.
- The standard closure does not work well on any of the three test problems.
- Approximate models for the mean radiation field are found for all test problems.
- Test problems include temperature dependent opacities and heat capacities.
- Solutions with angle order n=5 are consistent with previous n=1 solutions.

Due to the high computational cost of time-dependent radiation transport calculations, most multi-dimensional simulations of stochastic media have used the lowest angle order approximation, the P1 approximation. Here spherical harmonics of order n=5 are used to solve the transport equation in two-dimensional binary stochastic media. The results are consistent with earlier P1 simulations. Transport solutions using constant and temperature-dependent opacities and heat capacities are shown and analyzed. The standard closure poorly approximates the mean radiation field in these test problems. For one physical case, a less common closure is better. To best fit the most general cases, a new procedure is presented. In all cases, the approximate transport solutions work best in dilute systems where one material comprises less than about 10% of the total. The conclusions reached here should be independent of the transport solution method whether one uses spherical harmonics or discrete ordinates.