Modeling groundwater flow : an honors thesis (HONRS 499)

Abstract

The purpose of this thesis is to use basic ideas of Mathematics and Physics, such as Darcy's Law and the Law of Conservation of Mass to derive a differential equation to model the flow of groundwater. This equation will then be solved analytically for the two-dimensional groundwater flow equation, which will be a function that describes the head height of groundwater at a certain point at any given time. The differential equation will also be solved by a numerical method, using basic laws of Calculus. The two methods — analytical and numerical — will then be compared by applying each one to an example problem, and another possible method for solving the example problem will arise from the comparison.