Comprehensive set of analytical solutions for two-dimensional advective-dispersive transport involving flexible boundary inputs, initial distributions and zero-order productions

Abstract:

A comprehensive set of analytical solutions for the two-dimensional advection-dispersion equation in a finite domain involving a wide variety of boundary inputs, initial distributions, and zero-order productions are presented in this study. First, the generalized analytical solution are obtained by successively applying different integral transforms corresponding to the governing equations and its associated initial and boundary conditions. Based on the generalized analytical formulation, a comprehensive set of special-case solutions for some time-dependent boundary distributions and zero-order productions, described by Dirac delta, constant, Heaviside, exponentially-decaying, or periodically sinusoidal functions as well as some position-dependent initial conditions and zero-order productions specified by Dirac delta, constant, Heaviside, or exponentially-decaying functions are derived. Several sample applications, which are rarely noted in the literature, are given based on the comprehensive set of special-case solutions. The solution strategy presented in this study can be applied to more complicated scenarios of solute transport subjected to sequential decay chain reactions.