Confined aquifer flow modeling whithout temporary discretization
DOI:
https://doi.org/10.21701/bolgeomin.119.2.006Keywords:
confined aquifer, flow model, groundwater, Laplace transform, StehfestAbstract
A interactive program for flow modeling in confined homogeneous or heterogeneous aquifer is presented (MGAC). The equation from which the program has been elaborated is the one obtained by applying the Laplace transform to the differential flow equation on the two directions of the plane. The models spatially discretize the aquifer in square cells and pose the system of transformed equations in the form of finite differences, the time variable not being present. The SOR method is used to solve the system. The solution obtained is numerically inverted to obtain the values of the drawdown, si, instead of their transform, s̄i, and to recover the time variable instead of the inversion parameter p. The inversion method used is that of Stehfest (1970). The application of time is performed once and in its totality, so that the models do not need time discretization. The use of the Stehfest method entails an error for small values of Tt/r2S. The validity of the method for homogeneous confined aquifer is approximated by comparing the values obtained with the inversion of the transformed analytic Theis equation and the own Theis expression. The analytical results are also compared with those obtained for a generical model. The truncation errors and the limitations originated by the lack of precision in the initial potentials or in the fixed real potentials in transient flow are reviewed. The required memory and the computer times for different examples are shown.
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