Mosquito: An efficient finite difference scheme for numerical simulation of 2D advection

An explicit finite difference method for the treatment of the advective ter ms in the 2D equation of unsteady scalar transport is presented. The scheme is a conditionally stable extension to two dimensions of the popular QUICK EST scheme. It is deduced imposing the vanishing of selected components of the truncation error for the case of steady uniform flow. The method is the n extended to solve the conservative form of the depth-averaged transport e quation. Details of the accuracy and stability analysis of the numerical sc heme with test case results are given, together with a comparison with othe r existing schemes suitable for the long-term computations needed in enviro nmental modelling. Although with a truncation error of formal order 0(Delta x Delta t,Delta y Delta t,Delta t(2)), the present scheme is shown actuall y to be of an accuracy comparable with schemes of third-order in space, whi le requiring a smaller computational effort and/or having better stability properties. In principle, the method can be easily extended to the 3D case. Copyright (C) 1999 John Wiley & Sons, Ltd.