A Numerical Model for Water Flow and Chemical Transport in Variably Saturated Porous Media

A two‐dimensional numerical model is developed for the simulation of water flow and chemical transport through variably saturated porous media. The nonlinear flow equation is solved using the Calerkin finite‐element technique with either the Picard or the Newton iteration scheme. A continuous velocity field is obtained by separate application of the Galerkin technique to the Darcy's equation. A two‐site adsorption‐desorption model with a first‐order loss term is used to describe the chemical behavior of the reactive solute. The advective part of the transport equation is solved with one‐step backward particle tracking while the dispersive part is solved by the regular Galerkin finite‐element technique. A precondi tioned conjugate gradient‐like method is used for the iterative solution of the systems of linear simultaneous equations to save on computer memory and execution time. The model is applied to a few flow and transport problems, and the numerical results are compared with observed and analytic values. The model is found to duplicate the analytic and observed values quite well, even near very sharp fronts.