Advection‐diffusion modelling using the modified QUICK scheme

Abstract

AbstractIn recent years the QUICK finite difference scheme has been increasingly used in solving the advection‐diffusion equation, particularly for water quality modelling studies relating to coastal and estuarine flows. This scheme has the benefits of mass conservation, reasonably high accuracy and computational efficiency in comparison with many other higher‐order‐accurate schemes reported in the recent literature. A von Neumann stability analysis showed that the explicit QUICK scheme has a severe stability constraint which depends upon the diffusion coefficient. It can be proved that this scheme is numerically unstable for the case of pure advection. Various modified forms of the implicit QUICK scheme have been formulated and their numerical stability properties have been studied and analysed. The modified QUICK schemes considered have been tested for transient simulations for the cases of pure advection and of advection and diffusion in an idealized one‐dimensional basin using three different initial boundary conditions: (a) a sharp front concentration gradient, (b) a Gaussian concentration distribution and (c) a plug source. Details of the comparisons between these modified schemes and with other typical second‐order‐accurate difference schemes are given, together with comparisons with the analytical solutions for each case. A two‐dimensional version of the semi‐time‐centred QUICK scheme (ADI‐QUICK), has also been applied to a two‐dimensional test case using the standard ADI technique and has been shown to be attractive in comparison with other comparable second‐order schemes.