Water Resources Applications Software
Summary of VS2DI - Version 1.1
VS2DI - A Graphical Software Package for Simulating Fluid
Flow and Solute or Energy Transport in Variably Saturated
VS2DI is a graphical software package for simulating flow and
transport in variably saturated porous media. This software
package consists of three components:
- VS2DTI, for simulating fluid flow and solute transport,
- VS2DHI, for simulating fluid flow and energy (heat) transport,
- a standalone postprocessor, for viewing results saved from
previous simulation runs.
Both VS2DTI and VS2DHI combine a graphical user interface with a
numerical model to create an integrated, window-based modeling
environment. Users can easily specify or change the model domain,
hydraulic and transport properties, initial and boundary conditions,
grid spacing, and other model parameters. Simulation results can
be displayed as contours of pressure head, moisture content,
saturation, concentration or temperature, and velocity or flux for
each time step, thus creating a simple animation.
The numerical models used for flow and transport calculations are
the U.S. Geological Survey’s computer models VS2DT (for solute
transport) and VS2DH (for energy transport). VS2DT is a
finite-difference model that solves Richard’s equation for fluid flow,
and the advection-dispersion equation for solute transport.
The model can analyze problems in one or two dimensions using either
cartesian or radial coordinate systems. Relations between pressure
head, moisture content, and relative hydraulic conductivity may be
represented by functions developed by van Genuchten, Brooks and Corey,
Haverkamp and others, or by data points. Initial hydraulic condition
can be specified as static equilibrium, specified pressure head, or
specified moisture content. Boundary conditions include specified
pressure or total head, specified flux, infiltration with ponding,
evaporation, plant transpiration, and seepage faces. Solute transport
processes include advection, dispersion, first-order decay, adsorption,
and ion exchange. VS2DH is a version of VS2DT that has been modified
to simulate energy transport instead of solute transport. Both VS2DT
and VS2DH are written in Fortran 77. Although these models are
integrated into the graphical software package, their source codes
are maintained as individual Fortran programs that can be compiled and
run separately from the graphical user interface.
For the flow equation, spatial derivatives are approximated by
central differences written about grid-block boundaries. Time
derivatives are approximated by a fully implicit backward scheme.
Nonlinear conductance terms, boundary conditions, and sink terms are
linearized implicitly. Relative hydraulic conductivity is evaluated
at cell boundaries by using full upstream weighting, the arithmetic
mean, or the geometric mean of values from adjacent cells.
Saturated hydraulic conductivities are evaluated at cell boundaries
by using distance-weighted harmonic means. Nonlinear conductance
and storage terms can be represented by algebraic equations or by
For the advection-dispersion equation, either central or backward
differences may be selected for the spatial and time derivatives.
In VS2DT, equilibrium adsorption can be described by either Freundlich or
Langmuir isotherms; four types of ion exchange can also be simulated.
In VS2DH, thermal conductivity is assumed to vary linearly with
moisture content. The matrix equations produced for the flow and transport
equations are solved sequentially using the strongly implicit
Version 1.1 2000/02/09 - extended to work with VS2DH; improved
post processing capabilities. This release contains
revised versions 3.0 of VS2DT and VS2DH,
which allow run time selection of hydraulic function
and adsorption type. The VS2DI postprocessor has the
capability to run on input files created with earlier
versions of VS2DT and VS2DH.
Version 1.0 1999/07/28 - Initial release
A conceptual model of the geometry and boundaries of the region to
be simulated is of prime importance. Initial conditions in terms of
pressure heads or moisture contents for flow simulations and
concentrations or temperatures for transport simulations are needed.
Hydraulic and transport properties of the porous media are also required.
These values can be different for different sediments. Flow simulations
require values for saturated hydraulic conductivity and for relative
hydraulic conductivity and moisture content as functions of pressure
head. Solute transport simulations require values for dispersivity and
molecular diffusion. Energy transport simulations require values for
heat capacities of water and soil and thermal conductivity. Other
information may be needed, depending on the program options that are selected.
Simulation results can be displayed as contours of pressure head,
moisture content, saturation, concentration or temperature, and
velocity or flux for each time step, thus creating a simple animation.
The graphical displays may be printed or saved as bitmap files.
Text (or ASCII) output can be obtained for pressure head, total head,
volumetric moisture content, saturations, velocities, and solute
concentrations or temperatures. Time histories and spatial profiles
of the data can be obtained. In addition, the user may opt to view time
histories of up to 72 mass balance parameters.
The VS2DI software package is developed using a combination of Java, C,
and Fortran programming languages. This software has run successfully
on the following operating systems: Microsoft Windows 95, 98, and NT 4.0,
Silicon Graphics Irix 6.3, 6.4, and 6.5, and Sun Solaris 2.6. For other
computer platforms, the usability of VS2DI depends on the availability
of a Java Development Kit for that platform, and the ability to compile
Fortran and C programs into dynamic or shared libraries that can be used
by the Java program. Additional information on computer requirements can
be found in the README file distributed with the software.
The numerical models VS2DT and VS2DH may be compiled and run separately
from the graphical user interface. These two models are written in
Fortran 77 with the extension of using variable names longer than 6
characters. They have been used on UNIX, DOS, and Windows-based computers.
Healy, R.W., 1990, Simulation of solute transport in variably
saturated porous media with supplemental information on
modifications to the U.S. Geological Survey's Computer Program
VS2D: U.S. Geological Survey Water-Resources Investigations
Report 90-4025, 125 p.
Healy, R.W., and Ronan, A.D., 1996, Documentation of computer program
VS2DH for simulation of energy transport in variably saturated
porous media -- modification of the U.S. Geological Survey's
computer program VS2DT: U.S. Geological Survey Water-Resources
Investigations Report 96-4230, 36 p.
Hsieh, P.A., Wingle, William, and Healy, R.W., 1999, VS2DI-
a graphical software package for simulating fluid flow and solute or
energy transport in variably saturated porous media: U.S. geological
Survey Water-Resources Investigations Report 99-4130, 16 p.
Lappala, E.G., Healy, R.W., and Weeks, E.P., 1987, Documentation of
computer program VS2D to solve the equations of fluid flow in
variably saturated porous media: U.S. Geological Survey Water-
Resources Investigations Report 83-4099, 184 p.
Healy, R.W., 1987, Simulation of trickle irrigation, an extension to
the U.S. Geological Survey's Computer Program VS2D: U.S.
Geological Survey Water-Resources Investigations Report 87-4086,
VS2DT and VS2DH have been used by scientists at the USGS and at various
universities and consulting companies.
Example applications are described in:
Bartolino, J.R., and Niswonger, R.G., 1999, Numerical simulation of
vertical ground-water flux of the Rio Grande from ground-water
temperature profiles, central New Mexico: U.S. Geological Survey
Water-Resources Investigations Report 99-4212, 34p.
Mills, P.C., and Healy, R.W., 1993, Water and tritium movement
through the unsaturated zone at a low-level radioactive-waste
disposal site near Sheffield, Illinois, 1981-85: U.S. Geological
Survey Water-Supply Paper 2386, 72 p.
Halford, K.J., 1997, Effects of the unsaturated zone on aquifer test
analysis in a shallow-aquifer system: Ground Water, v. 35, no.3,
McCord, J.T., Gotway, C.A., and Conrad, S.H., 1997, Impact of geologic
heterogeneity on recharge estimation using environmental tracers:
Numerical modeling investigation: Water Resources Research, v. 33,
no. 6, p. 1229-1240.
Operation and Distribution:
U.S. Geological Survey
Hydrologic Analysis Software Support Program
437 National Center
Reston, VA 20192
Official versions of U.S. Geological Survey water-resources analysis
software are available for electronic retrieval via the World Wide
Web (WWW) at:
and via anonymous File Transfer Protocol (FTP) from:
water.usgs.gov (path: /pub/software).
The WWW page and anonymous FTP directory from which the VS2DI
software can be retrieved are, respectively:
See http://water.usgs.gov/software/ordering_documentation.html for
information on ordering printed copies of USGS publications.