Green element simulations of multiaquifer flows with a time-dependent Green's function

Abstract

A new formulation of the Green element method (GEM), based on the transient Green's function of the diffusion differential operator, is herein used to solve the problem of transient flow in multiply layered aquifers that are separated by aquitards (leaky strata) which provide hydraulic interactions between them. By adopting the commonly used hydraulic flow approximation, flow in the aquifers is considered to take place in two lateral dimensions and in one vertical direction in the aquitards. As with an earlier GE multiaquifer model, the current model solves the one-dimensional flow in the aquitards by the formulation of [Appl. Math. Model. 22 (1998) 687] but uses the transient Green's function of the diffusion operator to solve the two-dimensional aquifer flow instead of the logarithmic Green's function formulation of [Water Resour. Res. 36 (2000) 3631]. In essence, the current formulation uses the same form of Green's functions for both flows in the aquifers and aquitards. While this can be viewed as an advantage of the current formulation over the previous one, the former presents other computational challenges and intricacies that are discussed in this paper. Applying the current formulation, and incorporating a Picard-type iterative algorithm, solutions are provided for regional flows in heterogeneous multiaquifer systems of arbitrary geometries that are subjected to point and distributed recharge of arbitrary strengths.