Traveling waves and shocks in a contaminant transport model

Abstract

Contaminant transport modeling plays a great role in environmental science to understand how chemical or biological contaminants are transported through subsurface aquifer systems. This thesis introduces a simple mathematical model for the transport of contaminants carried by water through a porous medium, such as soil. Moreover, we briefly introduce important mathematical concepts in the study of partial differential equations: traveling waves and shock formation. By examining the behavior of traveling waves and shock formation within our model, we describe the solution’s behavior and compare this description with the numerical solution of the model. Keywords. Mathematics, Partial Differential Equations, Contaminant transport, Groundwater, Mathematical modeling, Conservation laws, Reaction-Advection-Dispersion Equations, Numerical methods, Simulation