Stochastic Averaging of Cross Section Uncertainty in Radiation Transport

Radiation transport in a one dimensional random medium is considered. The Karhunen-Loève spectral expansion method is shown to provide an efficient representation of the total cross section that is a continuous random process in space. Numerical results for an exponential covariance function show that a low order truncation suffices to capture the dominant components of the random process for reasonable choices of physical parameters. For Gaussian statistics, Gauss-Hermite quadrature is used to compute the mean scalar flux, with acceptable convergence to the exact result possible with relatively low expansion and quadrature orders. For scattering dominated optically thick, large fluctuation problems, the numerical results show that the random transport equation is accurately approximated by a nonrandom diffusion equation with a diffusion equation determined solely by the mean cross section.