HR: 1340h
AN: H13B-1254    [Abstracts]
TI: An exact solution to a line-sink in a leaky aquifer
AU: * Gusyev, M A
EM: mgusyev@indiana.edu
AF: School of Public and Environmental Affairs, 1315 East Tenth Street Room 439, Bloomington, IN 47405, United States
AU: Haitjema, H M
EM: haitjema@indiana.edu
AF: School of Public and Environmental Affairs, 1315 East Tenth Street Room 439, Bloomington, IN 47405, United States
AB: By use of Wirtinger calculus we obtained an exact solution for a line-sink in a leaky aquifer by integrating the potential for a well in a leaky aquifer. The potential for a well in a leaky aquifer is the modified Bessel function of the second kind and zero order K₀, which can be represented by an infinite series. Theoretically, this series expansion for the well is exact, although numerical evaluation will only give exact results within some finite distance from the well, depending on machine accuracy. For a double precision machine this distance is about to 18λ, whereby λ is the "leakage factor" or "characteristic leakage length" which depends on the aquifer properties. Earlier solutions that were based on an approximation to the function K₀ limited the domain of validity even more; from 2λ to 8λ away from the well. As a result, these earlier (approximate) solutions for a well in a leaky aquifer limited the length of the line-sink along which it could be integrated to approximately λ. It appears that our use of the infinite series (exact representation of K₀), makes it possible to formulate a solution for a line-sink of any length, thus avoiding to need to break up line-sinks into smaller sections as has been done to date. Formulating our solution in terms of the complex variable z and its conjugate \bar{z}, using Wirtinger calculus, also allows us to calculate the exact integrated steady-state flow induced by the line-sink across an arbitrarily placed line element. This feature is often necessary in the context of the analytic element method in order to satisfy boundary conditions in terms of integrated fluxes, such as no-flow boundaries or leaky walls. The capability to accurately calculate such integrated fluxes across line elements is also important in order to obtain the integrated leakage over a domain by applying water balance rather than (numerically) integrating the leakage directly. The new solution is particularly suitable for use in analytic element models of leaky aquifer systems.
DE: 1829 Groundwater hydrology
SC: Hydrology [H]
MN: 2007 Fall Meeting