Two-Dimensional QUICKEST Solution of the Depth-Averaged Transport-Dispersion Equation

摘要

This study details the derivation of a third-order accurate, explicit, finite-difference scheme (QUICKEST) for the solution of the depth-averaged transport-dispersion equation and compares its performance to an existing third-order accurate Lagrangian algorithm (12-POINT). Test comparisons included both one- and two-dimensional transient transport. Performance criteria examined included numerical diffusion/amplitude, phase, and mass conservation errors. Results presented show that both schemes possess favorable amplitude and phase characteristics. However, unlike QUICKEST, which is mass conservative, the 12-POINT scheme exhibits mass conservation errors that are directly attributable to the time step employed. Neglect of the cross-derivation terms in the QUICKEST formulation results in increased diffusion/amplitude errors as grid density decreases or time step increases. The work presented herein is preliminary to the development of a general purpose, depth-integrated water quality model. Of the two third-order finite schemes examined, QUICKEST is far superior for engineering applications where practical grid spacing and time steps are essential. Keywords include: Finite element method; Quickest; Water Quality--Measurement--Mathematical Models; Diffusion--Mathematical Models.