Abstract
ABSTRACT We investigated the influence of fictitious boundary distance, a parameter of MFS, to determine piezometric levels of two unconfined sedimentary aquifers assuming Dupuit-Forchheimer and steady-state flow hypothesis. Two study areas were modelled: Guariroba’s Environmental Protection Area, in Mato Grosso do Sul State, Brazil, and Juazeiro do Norte City, in Ceará State, Brazil. It was observed that in order to use the MFS as a numerical method in modeling groundwater flow, it is necessary to determine the best distance value of the fictitious boundary. This value can be chosen from the use of field data within the analyzed domain, where the relative error is a parameter to be minimized. Applying this methodology and comparing with the results of the MODFLOW application for the same set of initial data, we concluded that the MSF allows to estimate the piezometric level values within the analyzed domains and that the results of the statistical comparison between them point to the need to investigate the representativeness of both methods to determine which one is most appropriate for modelling the groundwater flow in each region.
Highlights
After development of digital computers, traditional finite difference method (FDM) and finite element method (FEM) became popular among researches and were applied to approximate functional values to discretized systems in some manifold physical problems (McDonald & Harbaugh, 2003)
The Method of Fundamental Solutions (MFS) was developed in 1960s (Chen et al, 2008), its implementation was mostly oriented to theoretical analysis and other areas than groundwater flow, mainly because the difficult to implement time-dependent problems and, transient states, as well as the implementation of collocation points inside the domain (Wang & Zheng, 2016)
These results show that the choice of an off-set distance in those study areas does not follow the general idea of how the MFS behaves in theoretical analysis
Summary
After development of digital computers, traditional finite difference method (FDM) and finite element method (FEM) became popular among researches and were applied to approximate functional values to discretized systems in some manifold physical problems (McDonald & Harbaugh, 2003). The Method of Fundamental Solutions (MFS) was analyzed under its particularities, such the needing of a fictitious boundary, the conditioning of matrixes, location of external points and alternatives to improve its limitations, providing an excellent background to its application in different physical phenomena (Gu et al, 2019; Oh et al, 2019; Liu & Sarler, 2013; Liu, 2012; Barrero-Gil, 2012; Chen & Wang, 2010; Young et al, 2008; Alves & Chen, 2005; Golberg et al, 1999; Golberg & Chen, 1998; Bogomolny, 1985). The MFS was developed in 1960s (Chen et al, 2008), its implementation was mostly oriented to theoretical analysis and other areas than groundwater flow, mainly because the difficult to implement time-dependent problems and, transient states, as well as the implementation of collocation points inside the domain (Wang & Zheng, 2016)
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