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.