A Fourier-Laplace transform finite element method (FLTFEM) for the analysis of contaminant transport in porous media

Abstract

In many practical situations, a simplified two-dimensional model is often sufficiently accurate for practical purposes, however on some occasions it is still necessary to consider the full three-dimensional situation. Conventional numerical techniques such as the finite difference and finite element methods are able to deal with contaminant transport under 3D conditions, however the computational effort involved in using them is often very large. Under some circumstances it is possible to perform 3D analyses more efficiently. A particular case is when the geometry is 2D but the problem is actually 3D. In such cases the analysis can be simplified by application of a Fourier transform. In this paper, the dimensions of the contaminant transport problem will be reduced by one and the transient mass transport equation will be transformed into a time-independent mass transport equation through the use of a combination of integral transforms (Laplace and Fourier transforms) and a finite element technique. The mathematical model developed here is called Fourier–Laplace transform finite element method (FLTFEM). By using the FLTFEM a three-dimensional transient problem can be analysed as a two-dimensional time-independent problem and the computational cost will thus greatly be reduced. Copyright © 1999 John Wiley & Sons, Ltd.