Transient-State Analytical Solution for Groundwater Recharge in Triangular-Shaped Aquifers Using the Concept of Expanded Domain

The purpose of this work is to present analytical solution for linearized Boussinesq equation in triangular-shaped aquifers in response to transient recharge from an overlaying basin. Four different configurations of hydrogeological boundary conditions (constant-head and no-flow) are considered. At first, the solutions for the rectangular-shaped aquifers are obtained through the well known image well theory. Then, the concept of expanded domain is utilized to arrive at the solution for the intended triangular domain. The resulting point-recharge solution (Green’s function) facilitates treating any arbitrary shaped recharge basin subjected to spatiotemporal varying recharge. Few examples describing the nature of transient recharge in triangular-shaped aquifers are presented. The investigation of equipotential contour lines and velocity vector fields confirms the validity of the method adopted here. The computed mound profiles are in favourably well agreement with the numerical results obtained by finite element method. Stream flow rates due to recharging are also computed for a single case. Overall, the closed form solutions provide an effective tool in order to conduct sensitivity analysis on various hydrogeological parameters that affect the formation of groundwater mound in triangular-shaped aquifers.