Falling Water Tables in Horizontal/Sloping Aquifer

Abstract

To describe falling water tables between two drains lying on a horizontal/sloping impermeable barrier, analytical solutions of the Boussinesq equation linearized by Baumann's and Werner's methods and numerical solutions of the nonlinear form of the Boussinesq equation using finite-difference and finite-element methods were obtained. A hybrid finite analytic method, in which the nonlinear Boussinesq equation was locally linearized and solved analytically after approximating the unsteady term by a simple finite-difference formula to approximately preserve the overall nonlinear effect by the assembly of locally analytic solutions, was also used to obtain a solution of the Boussinesq equation. Midpoints of falling water tables between two drains in a horizontal/sloping aquifer as obtained from various solutions were compared with already existing experimental values. Euclidean L2 and Tchebycheff L∞ norms were used to rank the performance of various solutions with respect to experimental data. It was observed that the performance of the hybrid finite analytic solution is the best, followed by finite element, finite difference, analytical with Werner's linearization method, and analytical with Baumann's linearization method, respectively.