Analytic Element Method
The analytic element method was developed at the end of the seventies by Otto Strack at the University of Minnesota (Strack and Haitjema, 1981a).
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 focusses 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 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, a few hundred, 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, small lakes or wetlands may be represented by areal sink distributions. 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, such as a partially penetrating well (Haitjema, 1985).
- 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
- Haitjema, H.M. (1995). Analytic Element Modeling of Groundwater Flow.
- Strack, O.D.L. & Haitjema, H.M. (1981a). Modeling double aquifer flow using a comprehensive potenetial and distributed singularities
1. Sloution for homogeneous permeabilities. Water Resour. Res., 17(5):1535-1549.
- Strack, O.D.L. & Haitjema, H.M. (1981b). Modeling double aquifer flow using a comprehensive and potential and distributed singularities
2. Solution for imhomogeneous permabilities. Water Resour. Res., 17(5):1551-1560.
- 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.
- Strack, O.D.L., "Groundwater Mechanics" Prentice Hall, 1989.