Transient analytic elements for periodic Dupuit–Forchheimer flow

A new analytic element formulation is presented for the simulation of transient, periodic Dupuit–Forchheimer flow. Equations are presented for the discharge potential of periodic wells, line-sinks, and circular area-sinks; all discharge potentials are written in separated form as the product of a function of space and a periodic function of time. Boundary conditions are represented with Fourier series consisting of an arbitrary number of terms. The obtained solution is analytic; water levels in streams are met at collocation points along the stream exactly and continuously through time. Equations are derived for ‘influence factors’, which represent characteristic lengths over which the periodic change of a well or line-sink has a significant influence on the head variation in the aquifer. Possible applications of the proposed method include the modeling of seasonal fluctuations in head and baseflow, and the estimation of aquifer properties from measured head variations. A hypothetical example is presented and the variation of the head in the aquifer and the inflow along a stream branch are evaluated.