Some thoughts on solving the radiative transfer equation in stochastic media using polynomial chaos and Wick products as applied to radiative equilibrium

The solution of the stochastic radiative transfer equation is described from the point of view of polynomial chaos and Wick products. Polynomial chaos is best suited for properties that are random fields. When the properties are characterized by white noise, this method can become computationally infeasible because of the need to solve coupled differential equations. When the radiative processes are Gaussian, then the expense is tolerable. For white noise the Wick product approach offers a reasonable level of computational expense in determining a strong solution. The method is demonstrated by computing the effect of an absorption coefficient corrupted by white noise. The method yields reasonable estimates of the standard deviations of the radiative behavior with less cost than the usual Monte Carlo approach. A substantial amount of further research is needed before the method can be applied to coupled radiative/conduction problems.