Abstract
The advantages of using the Algorithm of Pattern Extraction (ALOPEX) stochastic optimization technique in combination with both analytical models as well as 3D numerical simulators have been recently studied in detail in [23]–[25]. In this work, we present some preliminary results from the coupling of the Collocation method and the FEniCS open source modules to the ALOPEX algorithm as an effective pumping management process of 2D aquifer approximation models. The results refer to a test case of a homogeneous rectangular aquifer that approximates the freshwater coastal aquifer at Vathi area in the Greek island of Kalymnos. The objective is, on the one hand, to provide an optimal pumping management plan for the aquifer that would maximumize the total freshwater volume pumped from the aquifer and, on the other, to keep all pumping active locations safe from saltwater intrusion. For this we adapt and use the ALOPEX parameter configuration and the efficient penalty system introduced in [25] with guard points around the pumping locations. Our numerical simulations indicate that our pumping management results using the Collocation and FEniCS methods strongly compete the results obtained by using the analytical representation of the flow potential, known for this type of aquifers. Therefore, both Collocation and FEniCS methods can be effectively used to investigate the problem of optimal pumping management in heterogeneous aquifers with complex geometry boundaries and in general, aquifers where the analytical representation of the flow potential is unavailable.