# Mathematical modeling to simulate the movement of contaminants in groundwater

Kamel Al-Khaled, Mohamed Ali Hajji

Research output: Contribution to journalArticle

### Abstract

The objectives of this paper are twofold. Firstly, we formulate a system of partial differential equations that models the contamination of groundwater due to migration of dissolved contaminants through unsaturated to saturated zone. A closed form solution using the singular perturbation techniques for the flow and solute transport equations in the unsaturated zone is obtained. Indeed, the solution can be used as a tool to verify the accuracy of numerical models of water flow and solute transport. The second part of this paper, deals with how the water level in a water reserve drops due to pumping water out of a well that is some distance away.

Original language English 156-170 15 Journal of Applied Analysis and Computation 6 1 https://doi.org/10.11948/2016013 Published - 2016

### Fingerprint

Ground Water
Mathematical Modeling
Solute Transport
Water
Perturbation Technique
Systems of Partial Differential Equations
Singular Perturbation
Contamination
Closed-form Solution
Transport Equation
Migration
Verify
Movement
Model

### Keywords

• Approximate solutions
• Bromwich contour
• Inverse Laplace transform
• Laplace transform
• Singular perturbation method
• Solute transport
• Talbot’s algorithm

### ASJC Scopus subject areas

• Mathematics(all)

### Cite this

Mathematical modeling to simulate the movement of contaminants in groundwater. / Al-Khaled, Kamel; Hajji, Mohamed Ali.

In: Journal of Applied Analysis and Computation, Vol. 6, No. 1, 2016, p. 156-170.

Research output: Contribution to journalArticle

Al-Khaled, Kamel ; Hajji, Mohamed Ali. / Mathematical modeling to simulate the movement of contaminants in groundwater. In: Journal of Applied Analysis and Computation. 2016 ; Vol. 6, No. 1. pp. 156-170.
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