Modelling contaminant transport in rivers and estuaries

Abstract

This study investigates mathematical and numerical methods suitable for modelling contaminant transport in rivers and estuaries. The equations governing contaminant transport in rivers and estuaries are reviewed, and the mathematical representation of diffusion and dispersion processes is discussed with reference to both three-dimensional and two-dimensional depth-averaged flows. A comprehensive survey is carried out of methods for the numerical solution of the transport equation in rivers and estuaries. Theoretical considerations indicate that Eulerian-Lagrangian methods, particularly the Lagrange-Galerkin finite-element method, show the most promise for these problems, having very high accuracy (low numerical diffusion) and no limitations on time-step size. The implementation of the Lagrange-Galerkin method in a new two dimensional transport simulator is described. The simulator combines the high accuracy of the Lagrange-Galerkin method with the flexibility needed for modelling realistic transport problems in rivers and estuaries. Details are given of the algorithms developed for the simulator for tracking particles through complex flows. A new Lagrangian technique for modeUing source terms, including the effects of fluid inflow, is described and implemented. A series of numerical tests is carried out, the results of which demonstrate the high accuracy of the new simulator. Stability and mass conservation properties of the simulator under realistic test conditions are similarly shown to be very satisfactory, and the advantages of the new Lagrangian technique for source-term handling are clearly demonstrated. The new simulator is applied to modelling contamination problems in the Manukau harbour, using a new finite-element grid and hydrodynamic model constructed as part of this study. Preliminary results are given from modelling contamination from the sewage effluent outfall, which indicate the possibility of numerical diffusion in the results of previous models of the harbor. The simulations of Manukau harbour also serve to demonstrate the full flexibility of the new simulator, and its potential as a useful tool in aiding resource management decisions concerning rivers and estuaries.