Abstract
ABSTRACT In this paper we consider a groundwater flow problem in a semi-infinite vertical region bounded on top by a sloping sinusoidal curve dealt with by Shivakumar et al. (Shivakumar, P.N.; Williams, J.J.; Qiang Ye.; Chuanxiang, Ji. An Analysis of Groundwater Flow in an Infinite Region with Sinusoidal Top. Numer. Funct. Anal. and Optimiz. 2000, 21(1&2), 263–271). We first extend the analysis to the more realistic case of a finite region Ω. The problem is described by an elliptic equation for the hydraulic head under given boundary conditions. The obtained results are in good agreement with a classical result (Toth, J. A Theoretical Analysis of Groundwater Flow in Small Drainage Basins. J. Geophys. Res. 1963, 67, 4795–4812). We extend the problem further by allowing Dirichlet-type boundary conditions on the lower boundary. Our first goal is to obtain a semi-analytical solution. The problem is reduced to an infinite system of linear equations by using a suitable Fourier expansion method, transforming low...
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