HR: 1340h
AN: H13B-1250    [Abstracts]
TI: Analytic element formulations for flow in leaky aquifers and for transient flow, with discontinuous aquifer parameters.
AU: * Strack, O D
EM: strac001@umn.edu
AB: Analytic elements are functions that satisfy a given differential equation, mostly applicable to groundwater flow, and have properties that make it possible to meet a variety of boundary conditions; the solution to the flow problem is obtained by superposition of suitable analytic elements. Analytic elements are similar to boundary elements, but differ from these in two respects. First, they need not be obtained by integration, and second, and more important, analytic elements are defined throughout the infinite domain, even for cases where properties are discontinuous. In the analytic element formulation presented here all analytic elements are defined throughout the infinite domain, and special analytic elements are added to meet the conditions along the boundaries of inhomogeneities in properties. This is in contrast with boundary element and boundary integral formulations, where the domain is subdivided, with each element defined in its own sub domain, and with boundary elements used to stitch the sub domains together. For the case of problems governed by the Poisson equation, discontinuities in properties imply that the potential function representing the mathematical solution to the problem is discontinuous along with the component of flow tangential to the discontinuity boundary, but the differential equation itself is not affected. Such discontinuities can be dealt with conveniently by the use of the appropriate discontinuous function. If we consider, however, more general cases of flow, such as leaky aquifer flow and transient flow, then the coefficients that appear in the differential equation itself are discontinuous across the discontinuity line, which makes not obvious that the analytic elements can be defined throughout the domain, the discontinuities notwithstanding, and that correcting discontinuous functions can be constructed to include the discontinuities correctly in the solution obtained by superposition. We demonstrate in this presentation, however, that this is possible both for the case of leaky aquifer flow, governed by the modified Helmholz equation, and for transient flow, governed by the heat equation.
DE: 1828 Groundwater hydraulics
SC: Hydrology [H]
MN: 2007 Fall Meeting