Percolation in gently sloping beaches. (English) Zbl 0536.76085

Aitchison, J. M.; Elliott, C. M.; Ockendon, J. R.

IMA J. Appl. Math. 30, 269-287 (1983).

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

MSC:

76S05	Flows in porous media; filtration; seepage
86A05	Hydrology, hydrography, oceanography

Keywords:

percolation; minimization; asymptotic formulation in steady case; two- dimensional Darcy flows; homogeneous dam; free boundary; seepage face; obstacle problem; variational inequalities; finite-element approximation; unsteady problem