Axisymmetric free surface seepage

Summary Seepage through porous media in most instances is not a two-dimensional flow phenomenon. One such situation which is investigated herein is the flow from a pond with a bottom formed by the rotation of a curve consisting of a small segment being horizontal and the remainder being an arbitrary convex shaped curve. The approach used to solve this free surface axisymmetric seepage problem is an alternating iteration scheme in conjunction with the Baiocchi transformation and method. The problem is split into two overlapping regions, one in which the free surface is treated and the other in which the singularity is treated. This approach does not require moving meshes and allows a very general prescribed shape for the pond boundary. The numerical approach to the reformulated seepage problem is presented along with several numerical results and comparisons. Also presented is a proof of uniqueness of the solution for such problems provided we make a certain smoothness assumption for the free surface.The alternating iteration scheme is proved to converge provided existence and certain smoothness for the iterates and for their free surfaces are assumed. The iterates involved are solutions of certain complementarity systems. The existence and regularity of these solutions is not investigated in this paper.