Document Type


Date of Degree

Spring 2011

Degree Name

PhD (Doctor of Philosophy)

Degree In

Applied Mathematical and Computational Sciences

First Advisor

Wang, Lihe

First Committee Member

Atkinson, Kendall

Second Committee Member

Camillo, Victor

Third Committee Member

Jorgensen, Palle

Fourth Committee Member

Li, Yi

Fifth Committee Member

Li, C Wei


In this thesis, we examine the equation describing fluid flow through saturated porous medium in order to develop a new method for approximating hydraulic head values in the subsurface. In particular, we show that under reasonable assumptions, the local explicit equation (LEE) method, an accurate, finite-difference based method that is highly sensitive to changes in the assumed location of hydraulic flow parameters, can be used to approximate hydraulic head values throughout a subsurface domain of interest. This forward solution of the fluid flow equation is solved using an altered finite difference scheme, designed to account for discontinuous jumps often encountered between subsurface material types. While the method is able to handle complicated discontinuities arising from the intermingling of various underground materials, the method determines values at nodes on an easy-to-use uniform Cartesian grid and only requires information from immediately adjacent points. The results of this research directly support the development of more accurate subsurface fluid flow models for use in a wide variety of real-world situations in areas such as water management, contaminant remediation and waste storage. Furthermore, the general development of the LEE method allows it to be used as an approximation technique for any equation where the media of interest encounters a jump.


Finite Difference, Fluid Flow, hydrogeology


xi, 139 pages


Includes bibliographical references (pages 137-139).


Copyright 2011 Ben Galluzzo