On numerical modeling of the contaminant transport equations of the wetland hydrology and water quality model WETSAND

Abstract

The reliability of the MacCormack finite difference method for solving the contaminant transport equations of wetland model WETSAND is investigated. WETSAND solves the coupled advection-dispersion-reaction equations for the nitrogen cycle, total nitrogen and total phosphorus concentrations by using the implicit finite difference method. In addition to the implicit scheme, the MacCormack algorithm is implemented within WETSAND. Then, the results obtained by using the MacCormack algorithm are compared with the results obtained by using the implicit finite difference method for both synthetic examples and real data which is collected at the restored wetland site of Duke University at Sandy Creek watershed. Results show that the numerical methods are in good agreement. While the MacCormack scheme may be computationally more efficient for small velocities and dispersion coefficients (as is commonly the case for wetlands and lakes), much longer computational times are needed for the cases with high velocity and dispersion coefficient values (e.g., streams) since the magnitude of the time step has to be selected according to the CFL stability condition.