GNGTS 2016 - Atti del 35° Convegno Nazionale

GNGTS 2016 S essione 3.3 611 respectively. The term (in Am −3 ) represents the volumetric source current density. The proposed Matlab program employs the FEM to calculate a numerical solution which approximates the exact solution to the two-dimensional Poisson problem: where W is a “weighting function” and Ω represents the domain in which the condition is enforced. The first term is related to the boundary conditions of the problem while the second and third ones indicate, respectively, the stiffness matrix and the source term. For the implementation, the problem is discretised using the standard Galerkin method; the integrals on Ω for the discretized domain become: where n represents a generic element and N is the number of elements in the solution domain. Cases study analysis. The algorithm is validated by case studies presented by other authors. We show a comparison of the results obtained from the same dataset with the developed numerical code and other software programs. The first case study discussed concerns a pumping test in an unconfined aquifer. The model of the test site and details of the experiment modelled were described by Titov et al. (2005). For the hydraulic modelling, MAxSym, a MATLAB tool which is designed specifically to simulate axisymmetric flow (Louwyck et al. , 2012), was utilized. Taken into account that we used the parameters determined on the basis of the Theis solution (Theis, 1935), we considered the aquifer confined in the course of the pumping test (with the initial head at 48 m above the datum). Supposing the aquifer was homogeneous and of infinite lateral extent with fully penetrating well, drawdown s was calculated analytically using the solution given by Butler (1988). Then, we modeled SP signals on the basis of the material properties reported in Titov et al. (2005) (Fig. 1).We used the no-flow condition on the ground surface, and the condition of zero electrical potential on the other sides. The right boundary of the model was located far away from the pumping well in order to ensure that the boundary conditions have no influence on the computation of the SP. The potentials were calculated relative to infinite point. We obtained a radial SP distribution in the vicinity of the pumping well at the end of the pumping phase in accordance with the results reported from the authors. As is shown in Fig.1, the positive electrical source is centred on the pumping well, while negative sources are located far away under transient regime of the groundwater flow. Furthermore, to test our Fig. 1 – Cross-section of the synthetic SP distribution along the model at the end of the pumping phase.