A flux‐correct green element model of quasi three‐dimensional multiaquifer flow

Abstract

Transient flow in multiply layered aquifers, separated by connecting layers of aquitards which provide hydraulic interactions between the aquifers, is solved by the Green element method (GEM) in a manner that reveals one of its strengths of being able to correctly model the leakage flux without resorting to adjusting the grid representing the one‐dimensional (1‐D) flow in the aquitards, as done in the finite element method (FEM). The hydraulic approach of approximating the flow is adopted so that flow in the aquifer takes place in two dimensions and that in the aquitards takes place in the one‐dimensional vertical direction. The 1‐D Green element (GE) model earlier developed for transient diffusion and referred to as the transient GE (TGE) formulation [Taigbenu and Onyejekwe, 1999] is used in modeling the flow in the aquitards, while the 2‐D GE model developed for linear and nonlinear transient diffusion [Taigbenu and Onyejekwe, 1998] is used for calculating the flows in the confined and unconfined aquifers. Both models are coupled to solve regional flow problems in multiaquifer systems of arbitrary geometry which receive point and distributed recharge of arbitrary strengths. The solution procedure, which is iterative, provides information on the hydraulic heads and fluxes in the aquifers and aquitards at various specified times. Because GEM is founded on the singular integral theory, singularities that arise from water abstractions at wells (point recharge) are naturally captured in the singular Green's function, thereby making it possible to use a more coarse grid for problems in which there exist active wells. Furthermore, the implementation procedure of GEM achieves sparsity of the coefficient matrix so that less amount of computing resources is required for its decomposition. The superiority of the current approach over FEM in predicting the leakage flux through the aquitards and achieving comparable accuracy for well problems with coarser grid is demonstrated.