Introduction
is a USGS program for flow and solute transport in variably saturated, singlephase flow in porous media. A finitedifference approximation is used in VS2DT to solve the advectiondispersion equation. Simulated regions include onedimensional columns, twodimensional vertical cross sections, and axially symmetric, threedimensional cylinders. VS2DT Program options include backward or centered approximations for both space and time derivatives, firstorder decay, equilibrium adsorption (Freundlich or Langmuir) isotherms, and ion exchange. Nonlinear storage terms are linearized by an implicit NewtonRaphson method. Relative hydraulic conductivity is evaluated in VS2DT at cell boundaries using full upstream weighting, arithmetic mean or geometric mean. Saturated hydraulic conductivities are evaluated in VS2DT at cell boundaries using distanceweighted harmonic means.
VS2DT has been modified to present pertinent data during execution. Five additional utility modules are included with VS2DT. GREEN is the GreenAmpt analytical solution for infiltration. PRESS1D and CONCEN1D produce onedimensional pressure and concentration profiles, respectively. MASSBAL produces mass balance rate component profiles. OBSERV produces volumetric moisture content, saturation and concentration time history data sets at each observation point.
VS2DT includes the source and executable codes, the five utility modules, and technical support.
VS2DT uses a finitedifference approximation to the advectiondispersion equation.
Simulated regions can be:
 Onedimensional columns,
 Twodimensional vertical cross sections, or
 Axiallysymmetric, threedimensional cylinders.
Program options include:
 Backward or centered approximations for both space and time derivatives,
 Firstorder decay,
 Equilibrium adsorption as described by Freundlich or Langmuir isotherms, and
 Ion exchange.
VS2DT is a useful tool in studies of water quality, groundwater contamination, waste disposal, or groundwater recharge. The program is useroriented and easy to use.
VS2DT uses a finitedifference approximation to the advectiondispersion equation as well as the nonlinear waterflow equation (based on total hydraulic head).
VS2DT can simulate problems in one, two (vertical cross section), or three dimensions (axially symmetric). The porous media may be heterogeneous and anisotropic, but principal directions must coincide with the coordinate axes. Nonlinear storage terms are linearized by an implicit NewtonRaphson method. Relative hydraulic conductivity is evaluated at cell boundaries using full upstream weighting, arithmetic mean or geometric mean. Saturated hydraulic conductivities are evaluated at cell boundaries using distanceweighted harmonic means. Moisturecharacteristic curves may be represented by the BrooksCorey, Haverkamp and van Genuchten models or interpolated from tabular data.
Boundary conditions for flow in VS2DT can take the form of fixed pressure heads, infiltration with ponding, evaporation from the soil surface, plant transpiration, or seepage faces.
Boundary conditions for solute transport in VS2DT include fixed solute concentration and fixed mass flux. Solute source/sink terms include firstorder decay, equilibrium partitioning to the solid phase (Langmuir or Freundlich isotherms), and ion exchange.
The design of VS2DT is modular and may be easily modified in order to apply the model to a particular field, laboratory, or hypothetical problems.
VS2DT Solute Transport
The derivation of the equation in VS2DT is based on the conservation of mass and Fick's Law.
Three mechanisms affect the movement of solutes in the VS2DT model under variably saturated conditions:
 Advective transport in which solutes are moving with the flowing water. The second term on the equation represents the divergence of the advective flux. This accounts for changes in solute concentrations due to water moving and carrying solute with it.
 Hydrodynamic dispersion in which molecular diffusion and variability of fluid velocity cause a spreading of solutes about the average direction of water flow. Hydrodynamic dispersion refers to a spreading process whereby molecules of a solute gradually move in directions different from that of the average groundwater flow. Two mechanisms comprise hydrodynamic dispersion. The first is called mechanical dispersion and is caused by variations in the velocity field at the microscopic level. These variations are related to the tortuous nature of flow paths through porous media and the differences in velocity that occur across a single pore. Flow paths are not straight but must follow the pores. Therefore molecules of a solute will also be carried through these paths. The second mechanism is molecular diffusion which results from variations in solute concentrations. Molecules of solute will move from areas of high concentration to areas of low concentrations.
 Sources and sinks include fluid sources, where a water of a specified chemical concentration is introduced to water of a different concentration, and chemical reactions such as radioactive decay or adsorption to the solid phase. Source/sink terms can be divided into two general categories: solute mass introduced to or removed from the domain by fluid sources and sinks, and mass introduced or removed by chemical reactions occurring within the water or between the water and the solid phase.
VS2DT has been modified to present pertinent data (simulation time, iteration number, elapsed time) on the screen during execution.
Five additional utility modules have been developed and are included with the VS2DT package: GREEN, MASSBAL, OBSERV, PRESS1D and CONCEN1D.
 GREEN is the GreenAmpt analytical solution for infiltration. The other four modules read VS2DT output files and produce data files which may be plotted with TECGRAF (not included). XYZ files may also be produced.
 MASSBAL produces mass balance rate component profiles.
 PRESS1D and CONCEN1D produce onedimensional pressure and concentration profiles, respectively.
 OBSERV produces volumetric moisture content, saturation and concentration timehistory data sets at each observation point specified in the VS2DT simulation.
A graphical user interface for VS2DT is now available in the WHI UnSat Suite. The VS2DT model is also included.
