Analytical Solutions For Two-Dimensional Transport Equation with Time-Dependent Dispersion Coefficients
Mustafa M. Aral and Boshu Liao
Multimedia Environmental Simulation Laboratory
School of Civil and Environmental Engineering
Georgia Institute of Technology
Atlanta, Georgia 30332
Abstract
Analytical solutions to advection-dispersion equation are of continuous interest since they present bench mark solutions to problems in hydrogeology, chemical engineering and fluid mechanics. In this paper, we examine solutions to two-dimensional advection-dispersion equation with time dependent dispersion coefficients. Time and space dependent nature of the dispersion coefficient in subsurface contaminant transport problems has been demonstrated in the literature in both field and laboratory scale studies. Analytical solutions given in this paper could be used to model the transport of solute in hydrogeologic systems characterized by dispersion coefficients that may vary as a function of travel time from the input source. In particular, in this paper we develop instantaneous and continuous point source solutions for constant, linear, asymptotic and exponentially varying dispersion coefficients. The relationship between the proposed general solution and the particular solutions which are given in the relevant literature are discussed. Examples are included to demonstrate the effect of time dependent dispersion coefficient on solute transport.