Award Date

August 2019

Degree Type


Degree Name

Master of Science (MS)


Mathematical Sciences

First Committee Member

Angel Muleshkov

Second Committee Member

Monika Neda

Third Committee Member

Pengtao Sun

Fourth Committee Member

David Kreamer

Number of Pages



In this thesis, numerical results using the Boundary Element Method (BEM) for groundwater flow in a domain with a boundary that contains numerous singularities with a phreatic surface are developed. The flow in the domain is modeled using Darcy’s law for a homogeneous isotropic porous medium. The boundary conditions are a combination of Dirichlet and Neumann with the phreatic surface having both boundary conditions. Exact solutions by Conformal Mapping for simplified domains with the same singularity as the original domain allow for modifications to the BEM resulting in an improvement to the numerical solution.

An iterative process is used to determine the location of the phreatic surface and the location of the exit point. The iteration starts with an initial guess for the phreatic surface using the exact solution by conformal mapping for an infinite unconfined domain that preserves the important features of the domain around phreatic surface near the exit point.

Initially, the problem is solved using the conventional BEM as described by Liggett and Liu (1983). It is expected that the singularities and unknown location of the phreatic surface will lead to a failure of the BEM solution especially near the singular points and on the phreatic surface. Then, the modified BEM with the conformal mapping improvements is used to find the solution. The modified and conventional BEM are then compared with an emphasis on accuracy of the numerical solutions. Several tables and figures are produced to illustrate the results.


Boundary Element Method; Conformal Mapping; Free Surface; Phreatic Surface; Seepage; Singularity


Applied Mathematics | Mathematics

File Format


Degree Grantor

University of Nevada, Las Vegas




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