ANALYTICAL AND NUMERICAL SOLUTION OF INTERFACE PROBLEMS

Problems of two-dimensional flow of groundwater in a vertical plane to a drain above an interface in a system of fresh and salt groundwater may be solved by analytic or numerical methods.

Analytical solutions for the steady flow of fresh groundwater separated from a body of stationary salt groundwater can be constructed using the analyic element method (Strack, 1972; 1989). For non-steady flow problems solution methods have been developed using the finite element method (Bear & Verruijt, 1987; Verruijt, 1996). It is shown in this paper that the finite element results approach the analytical steady state solution for sufficiently large values of time. Because instabilities in the shape of the interface may occur, particular attention should be paid to the magnitude of the time steps in the numerical method.

The finite element method can be generalized to a system of three fluids (fresh, brackish and salt groundwater), separated by two sharp interfaces. For the problem of a drain operating in the fresh water the two interfaces move as a function of time, but the lowest interface eventually will return to its original horizontal position, provided that the interface with the brackish water remains below the drain. The shape of the steady state solution is in agreement with a theoretical prediction by Maas (1999).

References:

J. Bear and A. Verruijt, Modeling Groundwater Flow and Pollution, Reidel, Dordrecht, 1987.

C. Maas, Hatsi-kD, Stromingen, 5, 62-63, 1999.

O.D.L. Strack, Some cases of interface flow towards drains, J. Engng. Math., 6, 175-1991, 1972.

O.D.L. Strack, Groundwater Mechanics, Prentice-Hall, Engelowood Cliffs, N.J., 1989.

A. Verruijt, Displacements of an interface between fesh and salt groundwater, ERCOFTAC Bulletin, 28, 28-31, 1996.