Recent Advances in Laplace Transform Analytic Element Method (LT-AEM) Theory and Application to Transient Groundwater Flow

Abstract

Furman and Neuman (2003) proposed a Laplace Transform Analytic Element Method (LT-AEM) for transient groundwater flow. LT-AEM solves the modified Helmholtz equation in Laplace space and back-transforms it to the time domain using a Fourier Series numerical inverse Laplace transform method (de Hoog, et.al., 1982). We have extended the method so it can compute hydraulic head and flow velocity distributions due to any two-dimensional combination and arrangement of point, line and circular area sinks and sources, nested circular regions having different hydraulic parameters, and circular regions with specified head or flux. The strengths of all sinks and sources, and the specified head and flux values, can all vary with time in an independent and arbitrary fashion. Initial conditions may vary from one circular element to another. A solution is obtained by matching heads and normal fluxes inside and outside each circular element. The effect of each circular element on flow is expressed in terms of generalized Fourier series which converge rapidly (<10 terms) in most cases. As there are more matching points than Fourier terms, the matching is accomplished in Laplace space by least-squares. We illustrate the method by calculating head and velocity as well as representative particle flow paths through a distribution of circular inhomogeneities and transient sources and sinks. The results are compared to a MODFLOW simulation. We are presently extending the method to ellipses in two dimensions and spheroids in three dimensions.