Document Type
Dissertation
Date of Degree
Spring 2011
Degree Name
PhD (Doctor of Philosophy)
Degree In
Applied Mathematical and Computational Sciences
First Advisor
Lihe Wang
First Committee Member
Kendall Atkinson
Second Committee Member
Victor Camillo
Third Committee Member
Palle Jorgensen
Fourth Committee Member
Yi Li
Fifth Committee Member
C. Wei Li
Abstract
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.
Keywords
Finite Difference, Fluid Flow, hydrogeology
Pages
xi, 139 pages
Bibliography
Includes bibliographical references (pages 137-139).
Copyright
Copyright 2011 Ben Galluzzo