ASYMPTOTIC ANALYSIS OF THE FINITE MOMENTS TRANSPORT METHOD IN OPTICALLY THICK MEDIA

A theoretical analysis is presented that assesses the accuracy of the finite moments transport method in optically thick, scattering-dominated media. Two algorithms of the method, originally developed for neutronics problems, are considered. One algorithm uses a truncated balance relation, and the other uses a nodal integral relation to close the system of generalized balance equations that arise in the method. The analysis utilizes an asymptotic expansion of the flux with respect to a small parameter, epsilon, which is the ratio of the mean free path of the radiation to a typical dimension of the domain. The behavior of the algorithms is analyzed both in the interior, where the correct solution is that of a diffusion equation, and near the boundary, where the flux should decay exponentially at a rate proportional to 1/epsilon. Relations valid for an arbitrary number of moments, and that contain earlier results for low-order neutronics methods as special cases, are derived for slab geometry. Preliminary conclusions are also drawn on the asymptotic and boundary-layer behaviors of the two finite moments algorithms in (x-y) geometry. Similar results are discussed for the finite moments algorithms to solve the time-dependent Boltzmann equation. The finite moments nodal integral scheme appears to be vastly superior to conventional deterministic schemes and higher order truncated balance schemes in optically thick problems.