TRANSIENT FREE-SURFACE GROUNDWATER-FLOW DUE TO AN ARRAY OF CIRCULAR DRAINAGE DITCHES

The present paper is a numerical study of a transient free-surface flow into an array of circular drainage ditches in a Porous medium. By the boundary integral equation method and a semi-Lagrangian description of motion, the groundwater table is tracked as a function of time. Primarily, we consider the case of atmospheric pressure along the ditch contour. An analytical small-time expansion is presented in an appendix. In contrast to the case of constant flux into a sink (Papatzacos, 1989), there is no cusp formation at the free surface. The flux into a ditch is approximately a linearly decreasing function of time. We also include a second version of the boundary condition at the ditch; parts of its contour are impermeable.