Mathematical modeling of groundwater flow with the effects of dispersion and advection in a medium

Abstract

Groundwater is one of the most important fresh water resources in our earth. This dissertation presents the mathematical model of groundwater flow with with the effect of advection and dispersion in a porous medium. The purpose of this dissertation is to review in detail the one-dimentional advection-dispersion (ADE) for two different groundwater problems that is continuous injection and instantaneous injection. In this study, we are formulating a one dimensional mathematical model of a groundwater flow with only the effect of advection and dispersion. We are using Laplace transform to solve the advection dispersion equation for both cases but in a different way. Foe continuous injection we introduce dependent variable,C(x,t) = r(x,t)exp(ux/2d - u2t/4d) and apply the Duhamel's theorem. While for instantaneous injection, after transform the general equation into Laplace form we change it into characteristic for and solve it using by applied the boundary condition. Lastly, we solved the continuous injection problem used numerical method via Mathematica programming. Results of the advection dispersion model of this problem are presented by the graphical figures.