Some analytical solutions for the advection-dispersion equation
In this paper the parallel plate and cylindrical geometry are considered to model contaminant transport in a main fracture surrounded by a two-dimensional rock matrix. The transformation group theoretical approach is applied to present some new analytical solutions for the advection-dispersion equation governing these models. The application of this approach reduces the number of independent variables, and consequently the governing equation is reduced to ordinary differential equations. The general analysis developed in this study corresponds to the case of parabolic manner of the velocity within the main fracture.