A numerical model for transient-hysteretic flow and solute transport in unsaturated porous media

A two-dimensional flow and transport model was developed for simulating transient water flow and nonreactive solute transport in heterogeneous, unsaturated porous media containing air and water. The model is composed of a unique combination of robust and accurate numerical algorithms for solving the Richardsʹ, Darcy flux, and advection–dispersion equations. The mixed form of Richardsʹ equation is solved using a finite-element formulation and a modified Picard iteration scheme. Mass lumping is employed to improve solution convergence and stability behavior. The flow algorithm accounts for hysteresis in the pressure head–water content relationship. Darcy fluxes are approximated with a Galerkin and Petrov–Galerkin finite-element method developed for random heterogeneous porous media. The transport equation is solved using an Eulerian–Lagrangian method. A multi-step, fourth-order Runge–Kutta, reverse particle tracking technique and a quadratic–linear interpolation scheme are shown to be superior for determining the advective concentration. A Galerkin finite-element method is used for approximating the dispersive flux. The unsaturated flow and transport model was applied to a variety of rigorous problems and was found to produce accurate, mass-conserving solutions when compared to analytical solutions and published numerical results.