A Staggered-Grid Scheme for the Advection-Dispersion Equation

A higher-order accurate numerical scheme is developed to solve the advection-dispersion equation. A staggered-grid system is introduced with the first-order spatial derivatives being approximated by the fourth-order accurate finite-difference scheme, thus keeping all truncation errors to a smaller order of magnitude than that of the dispersion term. The dispersion term, a second-order spatial derivative, is discretized by the second-order accurate finite-difference scheme. For the time derivative, the fourth-order accurate Adams predictor-corrector method is used. The numerical method is validated against available analytical solutions for a one-dimensional problem. The stability analysis is carried out using the Van Neumann method. It is shown that the proposed algorithm has a good stability property and there is no need to add a numerical dispersion term. As a result, the model can provide more accurate and stable results for long-term simulation. The model is demonstrated to be a useful and accurate modeling tool for a wide range of transport problems.