Abstract
An explicit finite difference method for the treatment of the advective terms in the 2D equation of unsteady scalar transport is presented. The scheme is a conditionally stable extension to two dimensions of the popular QUICKEST scheme. It is deduced imposing the vanishing of selected components of the truncation error for the case of steady uniform flow. The method is then extended to solve the conservative form of the depth-averaged transport equation. Details of the accuracy and stability analysis of the numerical scheme with test case results are given, together with a comparison with other existing schemes suitable for the long-term computations needed in environmental modelling. Although with a truncation error of formal order 0(ΔxΔt, ΔyΔt, Δt2), the present scheme is shown actually to be of an accuracy comparable with schemes of third-order in space, while requiring a smaller computational effort and/or having better stability properties. In principle, the method can be easily extended to the 3D case. Copyright © 1999 John Wiley & Sons, Ltd.
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