Holistic discretisation of shear dispersion in a two-dimensional channel

(14 January 2003) Consider the spread of a contaminant along a 2D channel or river. We directly derive the 1D discrete numerical model from the 2D advective and diffusive dynamics for the evolu-tion of the contaminant. The holistic discretisation of the 2D advection-diffusion equation is placed within the purview of centre manifold theory by dividing the physical domain into rectangular 2D elements through introducing artificial in-sulating boundaries which are later removed. The resulting holistic discretisation is consistent with the 1D Taylor model for shear dispersion in the channel. This new technique ac-curately models the subgrid scale processes and provides a direct link between the 1D numerical discretisation and th