Implementation of Quadratic Upstream Interpolation Schemes and Monotonic Maintenance for Evaluating Reactive Solute Transport in HYDRUS-1D and HP1.

Numerical solution of advection-dispersion equation, used to evaluate transport of solutes in porous media, requires discretization schemes for space and time stepping. We examine use of quadratic upstream interpolation schemes proposed by Leonard (1979, 1991), QUICK, QUICKEST and the total variation diminution scheme ULTIMATE, and compare these with UPSTREAM and CENTRAL schemes in the HYDRUS-1D model. Results for purely convective transport show that quadratic schemes can reduce the oscillations compared to the central scheme and numerical dispersion compared to the UPSTREAM scheme. When dispersion is introduced all schemes give similar results when Pe < 2. All schemes showed similar behavior for non uniform grids when grids become finer in the direction of flow. When grids becomes coarser in the direction of flow, some schemes produced considerable oscillations, with all schemes showing significant clipping of the peak, but quadratic schemes extended the range of stability by tenfold to Pe < 20. Similar results were also obtained for transport of a nonlinear retarded solute transport (except QUICK scheme) and for reactive transport (except UPSTREAM scheme). Analysis of transient solute transport showed, all schemes produce similar results for the position of the infiltration front for Pe = 2. When Pe = 10 CENTRAL scheme produced significant oscillations near the infiltration front, compared to only minor oscillations for QUICKEST and no oscillations for ULTIMATE scheme.  These comparisons show quadratic schemes have promise for extending the range of stability in numerical solutions of reactive solute transport in porous media and hence allowing coarser grids and more efficient calculations.