A Semidiscrete Model for Water and Solute Movement in Tile‐Drained Soils: 1. Governing Equations and Solution

A finite element model has been developed to simulate solute transport in tile-drained soil-aquifer systems. Water flow in the unsaturated zone and to drains in the saturated zone was assumed to be at steady state. The model considers the transport of nonreactive solutes, as well as of reactive solutes whose behavior can be described by a distribution coefficient. The exact-in-time numerical solution yields explicit expressions for the concentration field at any future point in time without having to compute concentrations at intermediate times. The semidiscrete method involves the determination of an eigensystem of eigenvalues and eigenvectors of the coefficient matrix. The eigensystem may be complex (i.e., it may have imaginary components) due to asymmetry created by the convection term in the governing convection-dispersion equation. The proposed approach facilitates long-term predictions of concentrations in drainage effluents and of salt distributions in soil and groundwater. The accuracy of the model was verified by comparing model results with those based on an analytical solution for two-dimensional solute transport in groundwater.

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