Understanding Groundwater Flow, Tóth, and Laplace's Equation
I wrote this paper with two classmates for my differential equations class, exploring the mathematics behind groundwater flow.
Background
We based our understanding on J. Tóth’s seminal work “A Theoretical Analysis of Groundwater Flow in Small Drainage Basins” (1962), which established foundational principles for understanding subsurface water movement.
Project Content
Part 1: Theoretical Foundation
The first half of our paper explores:
- Tóth’s equations and findings
- The application of Laplace’s equation to groundwater systems
- Mathematical derivations of flow patterns
Part 2: Numerical Simulations
In the second half, we created MATLAB visualizations showing:
- How groundwater flows around different obstacles
- Flow patterns into and out of various locations
- Different scenarios with varying boundary conditions
Sample Visualizations
