Radiation Transport in Stochastic Media

The need to investigate numerical methods for the transport of radiation (thermal photons, light, neutrons, gammas) in random mixtures of immiscible materials arises in numerous applications, including inertial confinement fusion, turbid media (e.g., skin tissue), stellar atmospheres, clouds, and pebble bed nuclear reactors. Stochastic geometry techniques enable rendering of realizations of such random media and deterministic finite difference/finite element as well as Monte Carlo techniques are used to numerically simulate radiation transport on a large ensemble of realizations. The results are then averaged to obtain statistical moments of the radiation intensity, in particular the mean and variance, to assess the effect of random mixing on the radiation field. These approaches are computationally expensive but serve as valuable benchmarks for approximate, homogenized or reduced-order models such as obtained by ensemble averaging the random transport equation directly and invoking closures. In this work we consider a binary mixture with Markovian mixing statistics in 1D planar geometry and compare simulated average radiation intensities obtained from numerical solution of the so-called Levermore-Pomraning (LP) model against exact solutions obtained by realization averaging. The range of key physics and mixing parameters for which the LP-closure is valid are identified and an improved closure demonstrated. Finally, results from the numerical experiments are used to investigate higher order statistics, such as probability density distribution of functionals of the radiation intensity, which the closure models are incapable of providing