Percolation in gently sloping beaches. (English) Zbl 0536.76085

Considering the two-dimensional Darcy flows through a homogeneous dam, the authors are interested in the case when the free boundary, the seepage face and the upper surface of the dam are nearly in the same horizontal line. They present the asymptotic formulation of this problem in the steady case. For a class of particular flows the problem is reformulated heuristically, as an obstacle problem, using results from the theory of variational inequalities. Then the relevant minimization problem is solved numerically using a finite-element approximation. Finally, the unsteady problem is studied using an evolutionary variational inequality. The model seems to be valid away from certain singular points.
Reviewer: D.Polisevski


76S05 Flows in porous media; filtration; seepage
86A05 Hydrology, hydrography, oceanography
Full Text: DOI