Numerical methods for reactive transport on rectangular and streamline-oriented grids

Abstract

Coupling advection-dominated transport to reactive processes leads to additional requirements and limitations for numerical simulation beyond those for non-reactive transport. Particularly, both monotonicity avoiding the occurence of negative concentrations, and high-order accuracy suppressing artificial diffusion, are necessary to study accurately the reactive interactions of compounds transported in groundwater. These requirements are met by non-linear Eulerian methods. Two cell-centered Finite Volume schemes are presented for the simulation of advection-dominated reactive transport. The first scheme is based on rectangular grids, whereas the second scheme requires streamline-oriented grids the generation of which is explained in an accompanying paper. Although excellent results for conservative transport are obtained by the scheme for rectangular grids, some artificial transverse mixing occurs in the case of multi-component transport. This may lead to erroneous reaction rates if the compounds interact. The transport scheme for streamline-oriented grids, on the other hand, avoids artificial transverse mixing. A quantitative comparison is given by two test cases. A conservative tracer simulation for a five-spot configuration in a heterogeneous aquifer shows a high coincidence of the breakthrough curves obtained for the two methods, whereas a test case of two reacting compounds shows significant differences. In this test case, a rate of convergence with respect to the overall reaction rates lower than first-order is calculated for the rectangular grid.