Search for minimum residue to determine the shape parameter in the asymmet-ric method (MESHLESS) to simulation of groundwater flow

Abstract

The main objective of this research is the application of the Meshless numerical method in two cases of groundwater flow to simulate the hydraulic head variations on the region. The model uses the Multiquadrics Radial Basis Functions and a new methodology, which uses the residues of the contour and the domain, to determine the shape parameter ‘c’ in the Meshless numerical method. The methodology was applied in two cases: For Case 1 the exact solution was known, therefore it was possible to compare the analytical solution with the solution achieved by using the residue methodology proposed. Case 2 is a real case scenario for which the methodology was applied to simulate groundwater flow in a small region in the Araripe Sedimentary Basin, situated in the state of Ceará-Brazil. In this specific region most public water supply comes from groundwater sources. In case 1, the results indicate that ‘c’ parameter achieved approximate values of the ideal value. In case 2, analyzing the hydraulic head equipotential of the reference point, the percentage of errors was about 5%.

Keywords

• Meshless. Carga hidráulica. Parâmetro de forma e Bacia Sedimentar do Araripe.