Integral and Closed-Form Analytical Solutions to the Transport Contaminant Equation Considering 3D Advection and Dispersion

Abstract

Even though numerical procedures have been tremendously enhanced over the last years, analytical closed-form solutions are of special interest to water resources scientists. In general, these solutions are used to check the consistency and validate numerical routines. Bibliographical research reveals that up-to-date analytical solutions only take into account one-dimensional (1D) advection, even when three-dimensional (3D) dispersion is considered. This assumption creates an axis dependency because the flux is assumed to be parallel to one of the three possible orthogonal directions, which does not apply to all practical situations in which diagonal advection is present. In this work an analytical solution is derived for the 3D advective-dispersive equation (ADE) by means of Fourier and Laplace integral transforms. The solution allows the contaminant plume to move angularly with respect to the coordinate axes.