A complete model of shear dispersion in pipes (Q1343502)

High order models of the longitudinal dispersion of a passive contaminant in Poiseuille pipe flow are derived and their validity discussed. The derivation is done using centre manifold theory which provides a systematic and consistent approach to calculating each successive approximation. A stable, nonnegative finite difference scheme is formulated which matches the evolution equation to a predetermined order. An example of an exponentially varying pipe is considered, and the differences between this approach and the classical Taylor theory are examined.