Abstract
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.
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