The Asymptotic Diffusion Limit of Discretized Transport Problems

A well-known asymptotic analysis describes the transition of transport theory to diffusion theory in the limit of optically thick systems with small absorption and sources. Recently, this analysis has been applied to discretized transport algorithms. The results of this analysis, which provide information on accuracy and iteration efficiency, cannot be obtained from standard truncation error analyses because in the asymptotic limit, the optical thickness of a spatial cell generally tends to infinity. The ideas underlying this analysis are described, the main results are reviewed, and some open questions are discussed.