The following is the abstract for my PhD Dissertation.
Here is a link to the 15 MB PDF of the document
(Tauxe, 1994) without the code appendix.
POROUS MEDIUM ADVECTION-DISPERSION MODELING
IN A GEOGRAPHIC INFORMATION SYSTEM
John David Tauxe, Ph.D.
The University of Texas at Austin, 1994
Supervisor: Randall J. Charbeneau
Solutions to fundamental groundwater flow and transport equations are
incorporated into a geographic information system (GIS) as map algebra
functions which operate on spatially distributed hydrogeologic data. These
functions include a discrete form of Darcy's law to generate flow field maps and
to assure conservation of mass, two particle tracking procedures to calculate
advection along streamlines, and two gaussian dispersion functions to
determine the distribution of a solute in the porous medium from both
instantaneous and continuous sources. The modular design of the functions
allows for calculation of advection and dispersion of any source which can be
modeled as a collection of one or more point sources. The functions are
applied in the two-dimensional block-centered finite difference raster GIS
environment, using maps of aquifer saturated thickness, porosity, isotropic
transmissivity, and head elevation. Additional values are supplied for location
and strength of the sources, first-order decay coefficient of the solute,
longitudinal and transverse dispersivities, retardation in the porous medium, and
time horizon. From these data are calculated a flow field, advection path, and
map of concentration of the dispersed constituent. Complex simulations
involving transient head fields and multiple transient sources are performed by
superimposing results of single-source solutions. All of these calculations take
place within the native GIS environment.
reference for this paper:
Tauxe, J.D., Porous Medium Advection-Dispersion Modeling
in a Geographic Information System,
Doctoral Dissertation in Civil Engineering,
The University of Texas at Austin,
Austin, Texas, May 1994