Método livre de malha usando solução fundamental aplicado na simulação do fluxo de água subterrâneo

Abstract

The Fundamental Solutions Method (MSF) is a mesh-free numerical method used to estimate functional values ​​of systems governed by Partial Differential Equations in a domain from a set of boundary conditions of a problem as well defined. According to this methodology, the Fundamental Solution of the differential operator is applied contour points related to points on a fictitious border. Besides not needing the building a mesh of nodes or elements, the MSF has convergence and stability with respect to the variation of a fictitious boundary that geometrically contains the domain analyzed and that makes up one of its main characteristics. The choice of the location of this fictitious border places an uncertainty in the application of method. Therefore, in this work, the influence of this location on the application of the MSF to determine the piezometric level of points in a sedimentary aquifer under adoption of the Dupuit-Forchheimer hypotheses, incompressibility of water, homogeneity of aquifer and flow in a permanent regime, since these hypotheses allow to apply the Laplacian operator to describe the underground water flow. MSF was implemented in programming language Java and SciLAB, the model obtained was applied to a real aquifer and compared with MODFLOW, which implements the Finite Difference Method. Were data from observation wells in the region of the Environmental Protection Area of ​​the stream do Guariroba, which has an area of ​​approximately 360 km², located in the municipality of Campo Grande in the State of Mato Grosso do Sul. These data were obtained in the work of Cavazzana, Lastoria and Gabas (2019) and correspond to data from a single day of sampling. When applying distances of up to 200 km and up to 10,000 km to the fictitious border, in different stages of analysis, it was observed that errors related to field measurements showed stability. The results showed the convergence of the load equipotentials obtained through the two methods and that the location of the fictitious border that provided the smallest errors between numerical and field values ​​was associated with a distance of 1.7 times the radius of the circumference of the same area of ​​the analyzed region. That result shows that MSF is efficient to approximate piezometric levels in aquifers sediments adopted the previous hypotheses.