Solution of the advective-dispersive groundwater mass transport equation using Fourier transforms and the finite analytical method.

Abstract

!The advective-dispersive equation is used extensively in studying and analyzing the transport of contaminants through groundwater systems. In this dissertation, the development and evaluation of a new numerical scheme for an efficient solution of groundwater solute transport problems is presented. The scheme, which is named the Finite Analytical/Fourier Transform Method (FAFM) is based on taking the Fourier transform of the transient equation in the physical domain. The transformed equation resembles a steady-state advective-dispersive equation with a first-order decay term. The FAFM approach for solving the advective-dispersive problem consists of decomposing the spatial domain into a number of fine homogeneous finite elements within each of which a local analytical solution to the solute transport equation can be obtained. The Finite Analytical method uses the local analytical solution to form a set of algebraic equations for the concentration in the frequency domain. Initial conditions in the time and frequency domains must match one another. If they do not, adjustments in the boundary conditions in the time domain for t < 0 have to be made. Time-domain solutions are then recovered from the frequency domain by using an efficient inverse Fourier transform algorithm. The results obtained indicate that the FAFM performs well over a very wide range of Peclet numbers. A comparison with the exact solutions for a number of simple cases reveals the accuracy of the FAFM technique. It is expected that the method will provide good solutions for the problems in which such exact analytical solutions do not exist.