Boundary integral equation solution to axisymmetric potential flows: 2. Recharge and well problems in porous media

The boundary integral equation method (BIEM) is employed to solve both steady and transient axisymmetric flow problems in porous media. The problems analyzed here are governed by Laplace's equation; however, the unsteady and nonlinear behavior result from the presence of a free surface. Both finite and infinite domains are easily handled with the BIEM. Results are presented for a variety of well and recharge problems. Comparisons of BIEM results to a linearized theory show excellent agreement for recharge problems where the linearized theory is valid. In addition, results were obtained for cases where the linearized theory cannot be used. The BIEM solutions for steady state well problems are in excellent agreement with solutions obtained by a finite element method, as well as the analytic solution using the Dupuit assumption. Finally, the BIEM yields solutions to a variety of transient well problems. It is concluded that the BIEM is both an accurate and efficient method for solving well and recharge problems.