Area sinks in the analytic element method for transient groundwater flow

In the analytic element method, regional groundwater flow is modeled by superposition of particular solutions to the governing differential equation. The domain of the solutions is the x, y plane with the possible exception of isolated points. The solutions are referred to as analytic elements and represent a feature of flow in the aquifer, such as a well or the leakage through an aquitard. The analytic element method was originally developed for regional steady groundwater flow. In this paper the method is extended to transient flow. Several transient analytic elements and a method of determining a transient solution are presented. The governing differential equation that is used is the heat equation in two spatial dimensions with a sink term. Solutions for a transient well and a transient line sink are available in the literature. Both have a discharge that is equal to zero before the starting time and has a constant value after the starting time. A solution for a transient area sink is presented that also has a constant strength after the starting time. The area sink is a polygon with an extraction inside that is constant in space. A validation of the approach presented here is obtained by comparison with an exact solution for a case of one‐dimensional transient groundwater flow. The domain is semi‐infinite with a prescribed head at one side. Initially, the water is at rest, and then the head is suddenly raised at the boundary. The use of the transient analytic element method is illustrated by an example model with analytic elements both for steady and for transient flow. The former elements represent the initial steady state. The transient elements simulate variations of the groundwater flow due to seasonal variations in recharge and pumping.