No abstract

No abstract

The classical problem of flow induced by a sudden change of the piezometic head in a semi-infinite aquifer is re-examined. A new analytical solution is derived, by combining an expression describing the water table elevation upstream, obtained by the Adomian's decomposition approach, to an existing polynomial expression (Tolikas et al. in Water Resour Res 20:24-28, 1984), adequate for the downstream region; the parameters of both approximations are computed by matching the two solutions at the inflection point of the water table. Although several analytical solutions are available in the literature, we demonstrate that the expression we have developed in this issue is the most accurate for strong or moderate non-linear flows, where the degree of non-linearity is defined as the ratio of the piezometric head elevation at the origin to the initial water table elevation. For this type of flows the perturbation-series solution of Polubarinova-Kochina, characterized by previous studies as the best available analytical solution provides physically unacceptable results, while the analytical solution of Lockington (J Irrig Drain Eng 123:24-27, 1997), used to check the accuracy of numerical schemes, underestimates the penetration distance of the recharging front.

No abstract

[1] The case of inflow to an aquifer or porous medium inhibited by the presence of a semipervious (clogging) layer is investigated. The flow process is characterized by transient, free surface flow conditions. Here, unlike in previous studies, the nonlinear Boussinesq equation is considered. The influence of the clogging layer is simulated by imposing a nonlinear Robin (third kind) boundary condition at the edge of the aquifer. A semianalytical solution was derived by using the Adomian decomposition method, whose validity was checked by solving the problem by a finite difference method. By adopting a nondimensional analysis, the hydraulic behavior of the investigated problem was presented also in tabular form. Potential application examples are the study of water body-aquifer interactions and the hydraulic processes inside a permeable dam with a semipervious core.