A Complementary Solution to the Dam Problem

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Abstract
This paper is concerned with the solution of the porous dam problem, as an example of an elliptic free boundary problem. We outline the main methods of solving this problem, together with their drawbacks and then present a new method, a complementary energy approach based on a stream function formulation. This provides a more satisfactory calculation of the unknown point of contact of the free boundary with the dam wall and also a direct estimate of the “discharge” of the dam. Numerical results illustrating the accuracy of the method are given for homogeneous and inhomogeneous rectangular dams and an axisymmetric case.

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