Overlapping Control Volume Method for Solute Transport

In this paper, an overlapping control volume method is presented for the numerical solution of transient 2D solute transport problems in ground water. The method is applicable for nonorthogonal grids and uses an isoparametric formulation for computing the dispersion and for second-order upwinding. Time integration is performed using an implicit approach. Three test cases are considered for comparing the numerical with analytical solutions. The scheme is second order in space and, when combined with Crank-Nicholson, is also second order in time. The results using Crank-Nicholson and full implicit (first-order) time integration methods are compared for problems with a variety of boundary conditions. For diffusion-dominated flows (P(delta) <= 2) Crank-Nicholson works well, but for convection-dominated flows it produces spurious oscillations due to numerical dispersion errors. These oscillations are controlled by a flux limiter but only for Courant numbers below unity. It is shown that for high Courant and Péclet numbers a slight weighting of the time stepping toward fully implicit is effective against spurious oscillations and offers an optimum compromise between numerical dissipation and dispersion errors for a wide range of Courant and Péclet numbers. The scheme is shown to work on mildly nonorthogonal grids.