Determination of groundwater flownets, fluxes, velocities, and travel times using the complex variable boundary element method

The complex variable boundary element method, CVBEM, employs the Cauchy integral with any complex variable (e.g., complex potential, complex flux, or complex velocity) to solve boundary value problems. The CVBEM formulation is consistent with the primal and dual solutions of the boundary integral equation, as well as the analytic element method. The resulting problem is overdetermined because two boundary conditions can be specified at each node. Ordinary least squares provides a unique solution that minimizes boundary specification errors. Flownets are obtained by noting that the position of fluid–stream potential intersections can be found by exchanging potential and position in the Cauchy integral, which enhances the determination of travel times along streamlines. Three regional groundwater flow problems are used to illustrate the CVBEM approach, the original problem as defined by Tóth, plus two related problems as described by Domenico and Paliauskas, and by Nawalany.