AN ACCURATE AND NUMERICALLY STABLE MODEL FOR ONE-DIMENSIONAL SOLUTE TRANSPORT IN SOILS

Most numerical calculation schemes are either unstable or fairly complicated to solve and program when used for calculating water and solute transport in unsaturated soils. A solute transport model that is both numerically stable and easy to program will represent a useful alternative to existing models. We present an accurate and easily programmed numerical model for one-dimensional transport of solutes in unsaturated or saturated soils at steady or transient water flow. The new approach is based on the classical convection-dispersion concept of solute transport. The model is labeled the moving concentration slope (MCS) model because it uses the slope of the curve representing the natural log of the solute concentration (c) times the ratio of the hydrodynamic dispersion (D) to the water flux (v) plotted versus the convective solute flux (vc) as a governing, time-dependent parameter. The MCS model is a modification of the recently presented moving mean slope (MMS) water flow model and was developed using the mathematical equivalence between the basic flux and continuity equations for water and solute transport. In the MCS model, an integrated version of the solute flux equation is used together with a simple, forward-time discretization of the continuity equation to calculate solute transport. In case of a depth increment larger than 1 cm and a ratio of D to the pore water velocity (u) smaller than 2, it is necessary to correct the MCS model for numerical errors of second order (numerical dispersion), but the corrections are easy to make. Analytical equations for the second and third order numerical errors inherent in the MCS model were derived using Taylor series and validated using method of moments analysis. The magnitude of numerical errors inherent in the MCS model is generally small compared to explicit finite difference (FD) models. Also, the MCS model is very simple to program compared to finite element (FE) and implicit FD models. The MCS model was validated against analytical solutions in the case of steady water flow and against FE models in the case of transient water flow. The MCS solute transport model used together with the MMS water flow model represents a convenient tool for easy and accurate modeling of one-dimensional transport of water and solutes in soils.