Foreword: Ground Water Flow Modeling with the Analytic Element Method

At the time this issue goes to press, it will be 28 years ago that the first analytic element code was written. Otto Strack, Department of Civil Engineering at the University of Minnesota, developed the original idea in the fall of 1977. At that time, it was called ‘‘distributed singularities’’ but would later become the ‘‘Analytic Element Method. ’’ Although it solves the same differential equation and satisfies the same type of boundary conditions as existing grid-based numerical (finite-difference, finiteelement) methods, the analytic element method does so by combining the efficiency of classical analytic solution techniques with the power of digital computers. Although the first application of the analytic element method succeeded in solving a problem where previous numerical modeling attempts had failed, the introduction of analytic element techniques into the field of quantitative ground water hydrology was met with some skepticism. Analytic solutions to ground water flow, while perhaps elegant and efficient, are understood to be very limiting. Basic analytic solutions, as found in most textbooks, concern only one-dimensional or radial flow. Analytic solutions to more complicated flow systems either require cumbersome conformal mapping techniques or tricks, such as the method of images. Why would anyone in their right mind go back to these obsolete analytic techniques if ever more powerful finite-difference and finite-element models run on computers that double in speed every year and can readily solve complex ground water flow problems? What do analytic solutions have to offer over numerical models that already incorporate three-dimensional, transient, multiaquifer, and conjunctive surface water and ground water flow, as well as other capabilities? Seen in this light, the analytic element method appears to be dead even before it can grow up. In this theme issue on analytic element modeling, however, we find a very different picture. During the last quarter of a century, the analytic element method found its own niche in the field of ground water modeling, providing a unique tool for many innovative modeling applications. For instance, analytic element models are rather straightforward to apply, having no model grid or element mesh, which makes them ideal for educational purposes. The absence of a computational grid or element network also results in other advantages. As described by de Lange, what is likely one of the world’s largest multiaquifer ground water flow models, a national model of the ground water flow system in the Netherlands, is an analytic element model. The gridless design inherent to the method facilitated flexibility for adding features; expanding, contracting, and connecting model domains; and coupling local flow near streams, canals, and lakes to the larger-scale flow in the supraregional model. Analytic element models can often be constructed rather quickly, which makes them ideal as screening models for more encompassing numerical modeling efforts. The ease of setting up a basic analytic element flow model has made the method popular for capture-zone delineation, both in the context of aquifer remediation and EPA’s Wellhead Protection Program. The method is also well suited for accurate computer modeling experiments on dispersion and has been used to simulate both twoand three-dimensional flow in a highly heterogeneous aquifer with tens to hundreds of thousands of inclusions that, in turn, can provide information about aquifer properties (Jankovic et al.). Viewed in this light, the analytic element method is far from dead. There remain important limitations to the current generation of analytic element models. Since the method employs superposition of analytic solutions, the governing differential equation must be linear in terms of the discharge potentials. This requirement complicates, although does not prevent, the incorporation of transient flow and continuous variations in fluid and aquifer properties. For example, changes in aquifer properties are routinely included in piecewise-constant zones of differing 1Indiana University, SPEA 439, Bloomington, IN 47405; Haitjema@indiana.edu 2U.S. Geological Survey Water Resources Discipline, 8505 Research Way, Middleton, WI 53562; rjhunt@usgs.gov 3SUNY-Buffalo, 231 Jarvis Hall, Buffalo, NY 14260-4300; ijankovic@eng.buffalo. edu 4RIZA, Zuiderwagenplein 2, 8200 AA Lelystad, The Netherlands; w.dlange@riza.minvenw. nl Copyright a 2006 The Author(s) Journal compilationa 2006National GroundWater Association. doi: 10.1111/j.1745-6584.2005. 00144.x