Unsteady flow in confined aquifers: A comparison of two boundary integral methods

The boundary integral equation method )BIEM( is used for the solution of unsteady flow in confined aquifers. Such flows are described by a diffusion equation. Two approaches are presented. The first method removes the time derivatives with a Laplace transform first and solves an associated equation with the BIEM for several values of the transform parameter. A numerical transform inversion is then used to express the results in physical terms. The second method solves the differential equation directly with the BIEM. Both of these techniques are compared to the exact solutions of two simple problems. The Laplace transform method is found to be superior for general use, although the direct method is simpler and requires less judgment on the part of the analyst.