Figure:
Groundwater pathlines (red) in the 10-year time of travel capture zone for a well field near the East Fork of White River south of Columbus, Indiana. The line-thickness of the streams is proportional to the streamflow. The conjunctive surface water and groundwater solution is obtained with the analytic element model GFLOW 2000.

The analytic element method was developed at the end of the seventies by Otto Strack at the University of Minnesota (Strack and Haitjema, 1981). There are two books about the analytic element method. "Groundwater Mechanics" by O. D. L. Strack, Prentice Hall, 1989, contains detailed mathematical descriptions of the analytic elements and their numerical implementation. "Analytic Element Modeling of Groundwater Flow" by H. M. Haitjema, Academic Press, 1995, provides the basic theoretical framework for the analytic element method and describes on its use.

This new method avoids the discretization of a groundwater flow domain by grids or element networks. Instead, only the surface water features in the domain are discretized, broken up in sections, and entered into the model as input data. Each of these stream sections or lake boundary sections are represented by closed form analytic solutions: the analytic elements. The comprehensive solution to a complex, regional groundwater flow problem is obtained by superposition of all, several hundreds, analytic elements in the model.

Traditionally, superposition of analytic functions was considered to be limited to homogeneous aquifers of constant transmissivity. However, by formulating the groundwater flow problem in terms of appropriately chosen discharge potentials, rather than piezometric heads, the analytic element method becomes applicable to both confined and unconfined flow conditions as well as to heterogeneous aquifers (Strack and Haitjema, 1981b).

The analytic elements are chosen to best represent certain hydrologic features. For instance, stream sections and lake boundaries are represented by line-sinks. Areal recharge is modeled by areal source distributions (areal sinks with a negative strength). Streams and lakes that are not fully connected to the aquifer are modeled by line-sinks or area sinks with a bottom resistance. Discontinuities in aquifer thickness or hydraulic conductivity are modeled by use of line doublets (double layers). Specialized analytic elements may be used for special features, such as drains, cracks, slurry walls, etc. Locally, three-dimensional solutions may be added e.g. a partially penetrating well (Haitjema, 1985).

Refrences:
1. Haitjema, H.M. (1985). Modeling three-dimensional flow in confined aquifers by superstion of both two- and three-dimensional analytic funtions. Water Resour. Res., 21(10):1557-1556
2. Haitjema, H.M. (1995). Analytic Element Modeling of Groundwater Flow. Academic Press, Inc.
3. Strack, O.D.L. & Haitjema, H.M. (1981a). Modeling double aquifer flow using a comprehensive potential and distributed singularities 1. Solution for homogeneous permeabilities. Water Resour. Res., 17(5):1535-1549.
4. Strack, O.D.L. & Haitjema, H.M. (1981b). Modeling double aquifer flow using a comprehensive potential and distributed singularities 2. Solution for inhomogeneous permabilities. Water Resour. Res., 17(5):1551-1560.
5. Ward, D.S., Buss, D.R., Mercer, J.W., & Hughes, S.S. (1987). Evaluation of a groundwater corrective action at the Chem-Dyne hazardous waste site using a telescopic mesh refinement modeling approach. Water Resourc. Res., 23(4):603-617.
6. Strack, O.D.L., "Groundwater Mechanics" Prentice Hall, 1989.