Abstract
A higher‐order accurate numerical scheme is developed to solve the two‐dimensional advection–diffusion equation in a staggered‐grid system. The first‐order spatial derivatives are approximated by the fourth‐order accurate finite‐difference scheme, thus all truncation errors are kept to a smaller order of magnitude than those of the diffusion terms. Therefore, there is no need to add an artificial diffusion term to balance the unwanted numerical diffusion. For the time derivative, the fourth‐order accurate Adams–Bashforth predictor–corrector method is applied. The stability analysis of the proposed scheme is carried out using the Von Neumann method. It is shown that the proposed algorithm has good stability. This method also shows much less spurious oscillations than current lower‐order
accurate numerical schemes. As a result, the proposed numerical scheme can provide more accurate results for long‐time simulations. The proposed numerical scheme is validated against available analytical and numerical solutions for one‐ and two‐dimensional transport problems. One‐ and two‐dimensional numerical examples are presented in this paper to demonstrate the accuracy and conservative properties of the proposed algorithm by comparing with other numerical schemes. The proposed method is demonstrated to be a useful and accurate modelling tool for a wide range of transport problems. Copyright © 2007 John Wiley & Sons, Ltd.