NAME
modfe - Modular finite-element model for areal and axisymmetric
ground-water flow problems
ABSTRACT
This MODular, Finite-Element digital-computer program (MODFE) was
developed to provide solutions to ground-water-flow problems based
on the governing equations that describe two-dimensional and
axisymmetric-radial flow in porous media. The documentation is
divided into three parts.
Part 1 (Torak, L.J., 1993a) is the user's manual that describes
hydrologic features and simulation capabilities of MODFE.
Descriptions are given for preparing hydrologic data to characterize
aquifer properties and boundary conditions by zone. Examples of
data input and model output are provided to demonstrate the
different types of ground-water problems that are solved by using
the simulation capabilities of MODFE. Guidelines for designing the
finite-element mesh and for node numbering and determining
bandwidths are given to instruct users in the appropriate
application of MODFE to ground-water problems of their choosing.
Part 2 (Cooley, R.L., 1992) derives the finite-element equations by
minimizing a function of the difference between the true and
approximate hydraulic head, which produces equations that are
equivalent to those obtained by either classical variational or
Galerkin techniques. Spatial finite elements are triangular with
linear basis functions, and temporal finite elements are one
dimensional with linear basis functions. Comparison of finite-
element solutions with analytical solutions is given for five
example problems.
Part 3 (Torak, L.J., 1993b) contains descriptions of subroutines,
programming details, and program structure diagrams. Descriptions
of subroutines that execute the computational steps of the modular-
program structure are given in tables that cross reference the
subroutines with particular versions of MODFE. Programming details
of linear and nonlinear hydrologic terms are provided. Structure
diagrams for the main programs show the order in which subroutines
are executed for each version and illustrate some of the linear and
nonlinear versions of MODFE that are possible. Computational
aspects of changing stresses and boundary conditions with time and
of mass balance and error terms are given for each hydrologic
feature. Program variables are listed and defined according to
their occurrence in the main programs and in subroutines. Listings
of the main programs and subroutines are given.
METHOD
Aquifer geometry, flow boundaries, and variations in hydraulic
properties are represented by triangular elements or element sides
in a finite-element mesh. Time variations in hydraulic properties
are represented by one-dimensional elements. Linear coordinate
functions are used to approximate variations in hydraulic properties
within elements. The finite-element matrix equations are solved by
using either a direct symmetric-Doolittle method of triangular
decomposition or an iterative method that uses the modified,
incomplete-Cholesky, conjugate-gradient method. The direct method
can be efficient for small- to medium-sized problems (less than
about 500 nodes), and the iterative method is generally more
efficient for larger-sized problems.
Simulation capabilities and uses of MODFE are: transient or steady-
state conditions; nonhomogeneous and anisotropic flow where
directions of anisotropy change within the model region; vertical
leakage from a semiconfining layer that contains laterally
nonhomogeneous properties and elastic storage effects; point and
areally distributed sources and sinks, specified head (Dirichlet);
specified flow (Neumann); and head-dependent (Cauchy-type) boundary
conditions; vertical cross-section and axisymmetric cylindrical
flow; confined and unconfined (water-table) conditions; partial
drying and resaturation of a water-table aquifer; conversion between
confined- and unconfined-aquifer conditions; and nonlinear head-
dependent fluxes (for simulating line, point, or areally distributed
sources and sinks). Aquifer stresses and boundary conditions can be
changed on a time-step basis, a stress-period basis, or both.
Hydraulic properties and boundary conditions can be input by zone.
HISTORY
Documentation for MODFE was developed on the basis of material
presented within the period 1982-92 by the authors in the course
held at the USGS National Training Center (see TRAINING).
DATA REQUIREMENTS
Aquifer and confining-bed characteristics, two-dimensional space
coordinates in Cartesian or radial (r-z) system, and time-step sizes
(see DOCUMENTATION).
OUTPUT OPTIONS
Hydraulic head and water-balance summary information of each time
step (not an option), suppression of input data, and output of nodal
flow rates from vertical leakage and boundary condition zones.
SYSTEM REQUIREMENTS
MODFE is written in Fortran 77. Generally, the program is easily
adapted to most computer systems. The code has been used on UNIX-
based computers.
APPLICATIONS
Buxton, H.T., and Modica, E., 1992, Patterns and rates of ground-
water flow on Long Island, New York: Ground Water, v. 30, no. 6,
p. 857-866. (Solutions of stream and potential functions, cross-
section simulations, flow-net analysis)
Czarnecki, J.B., and Waddell, R.K., 1984, Finite-element simulation
of ground-water flow in the vicinity of Yucca Mountain, Nevada-
California: U.S. Geological Survey Water-Resources Investigations
Report 84-4349, 38 p. (Spring flow, water-table conditions,
recharge)
Iverson, R.M., and Reid, M.E., 1992, Gravity-driven groundwater flow
and slope failure potential, 1. Elastic effective-stress model:
Water Resources Research, v. 28, no. 3, p. 925-938. (Ground-
water-flow field, total-body-force field, and effective-stress
field generated in cross section showing that ground-water flow
can influence shear stresses as well as effective-normal stress
on hill slopes)
Lowther, R.A., and Kuniansky, E.L., 1992, Documentation of finite-
element mesh generation programs using a geographic information
system: U.S. Geological Survey Water-Resources Investigations
Report 92-4155, 187 p. (GIS applications programs written in
ARC5)
Reid, M.E., and Iverson, R.M., 1992, Gravity-driven groundwater flow
and slope failure potential, 2. Effects of slope morphology,
material properties, and hydraulic heterogeneity: Water
Resources Research, v. 28, no. 3, p. 939-950. (Sensitivity
analysis of hydraulic conductivity contrasts and their effects on
ground-water seepage forces, effective stresses, and slope-
failure potentials)
Torak, L.J., Davis, G.S., Herndon, J.G., and Strain, G.A., 1992,
Geohydrology and evaluation of water-resource potential of the
upper Floridan aquifer in the Albany area, southwestern Georgia:
U.S. Geological Survey Water-Supply Paper 2391, 59 p. (Model
application to well-field development, calibration, sensitivity
analysis, flow-vector analysis)
Torak, L.J., Davis, G.S., Strain, G.A., and Herndon, J.G., 1996,
Geohydrology and Evaluation of Stream-Aquifer Relations in the
Apalachicola-Chattahoochee-Flint River Basin, Southeastern
Alabama, Northwestern Florida, and Southwestern Georgia: U.S.
Geological Survey Water-Supply Paper 2460, 95 p.
Torak, L.J., and McDowell, R.J., 1996, Ground-Water Resources of the
Lower Apalachicola-Chattahoochee-Flint River Basin in Parts of
Alabama, Florida, and Georgia--Subarea 4 of the Apalachicola-
Chattahoochee-Flint and Alabama-Coosa-Tallapoosa River Basins:
U.S. Geological Survey Open-File Report 95-321, 145 p.
Reports in review:
Maslia, M.L., Prowell, D.C., and Jones, L.E., Effect of faults on
fluid flow and chloride contamination in the Floridan aquifer
system, Brunswick, Glynn County area, Georgia: interpretation of
field data, conceptual model development, and numerical
simulation: U.S. Geological Survey Water-Supply Paper in
colleague review.
Torak, L.J., Computational Extensions of a MODular Finite-Element
Model (MODFE) for Confined Multilayer Ground-Water-Flow Problems:
U.S. Geological Survey Open-File Report in colleague review.
Torak, L.J., Davis, G.S., Herndon, J.G., and Strain, G.A., 1996,
Geohydrology and evaluation of stream-aquifer relations in the
lower Apalachicola-Chattahoochee-Flint River Basin, southeastern
Alabama, northwestern Florida, and southwestern Georgia: U.S.
Geological Survey Water-Supply Paper 2460, 94 p.
DOCUMENTATION
Cooley, R.L., 1992, A MODular Finite-Element model (MODFE) for areal
and axisymmetric ground-water-flow problems, part 2--derivation
of finite-element equations and comparisons with analytical
solutions: U.S. Geological Survey Techniques of Water-Resources
Investigations, book 6, chap. A4.
Torak, L.J., 1993a, A MODular Finite-Element model (MODFE) for areal
and axisymmetric ground-water-flow problems, part 1--model
description and user's manual: U.S. Geological Survey Techniques
of Water-Resources Investigations, book 6, chap. A3.
Torak, L.J., 1993b, A MODular Finite-Element model (MODFE) for areal
and axisymmetric ground-water-flow problems, part 3--design
philosophy and programming details: U.S. Geological Survey
Techniques of Water-Resources Investigations, book 6, chap. A5.
RELATED DOCUMENTATION
Torak, L.J., 1992a, A MODular Finite-Element model (MODFE) for areal
and axisymmetric ground-water-flow problems, part 1--model
description and user's manual: U.S. Geological Survey Open-File
Report 90-194, 153 p.
Torak, L.J., 1992b, A MODular Finite-Element model (MODFE) for areal
and axisymmetric ground-water-flow problems, part 3--design
philosophy and programming details: U.S. Geological Survey Open-
File Report 91-471, 261 p.
REFERENCES
Torak, L.J., Davis, G.S., Strain, G.A., and Herndon, J.G., 1991,
Geohydrology and evaluation of water-resource potential of the
upper Floridan aquifer in the Albany area, southwestern Georgia:
U.S. Geological Survey Open-File Report 91-52, 86 p. AND U.S.
Geological Survey Water-Supply Paper 2391.
TRAINING
Finite-Element Modeling of Ground-Water Flow (GW2097TC), offered
annually at the USGS National Training Center.
CONTACTS
Operation and Distribution:
U.S. Geological Survey
Hydrologic Analysis Software Support Program
437 National Center
Reston, VA 20192
h2osoft@usgs.gov
Official versions of U.S. Geological Survey water-resources analysis
software are available for electronic retrieval via the World Wide
Web (WWW) at:
http://water.usgs.gov/software/
and via anonymous File Transfer Protocol (FTP) from:
water.usgs.gov (path: /pub/software).
The WWW page and anonymous FTP directory from which the MODFE
software can be retrieved are, respectively:
http://water.usgs.gov/software/modfe.html
--and--
/pub/software/ground_water/modfe
See http://water.usgs.gov/software/ordering_documentation.html for
information on ordering printed copies of USGS publications.
SEE ALSO
moc(1) - Two-dimensional method-of-characteristics
ground-water flow and transport model
modflow(1) - Modular three-dimensional ground-water flow
model
Modflowp(1) - Parameter-estimation version of the modular model
sutra(1) - Saturated and (or) unsaturated, constant or
variable-density fluid flow, and solute or energy
transport (2-dimensional finite-element code)
vs2di(1) - A graphical software package for simulating fluid flow
and solute or energy transport in variably saturated
porous media