The interface between fresh and salt groundwater in heterogeneous aquifers: a numerical approach

In this paper we study the behavior of a sharp interface between fresh and salt groundwater, in horizontally extended heterogeneous aquifers. The heterogeneities considered are discontinuities in intrinsic permeability. Each fluid has a constant, but different specific weight, while the viscosities are equal. The difference in specific weight induces fluid movement, which in turn causes motion of the interface. We are especially interested in the behavior of interfaces crossing discontinuities in permeability. The governing equations are an elliptic equation for the stream function, coupled with an interface motion equation for the time evolution of the interface. A finite element method is used to solve the equation for the stream function and a front tracking scheme to compute the time evolution of the (discrete) interface movement. We compare numerical results with some (semi-)analytical results of simplified interface problems in both homogeneous and heterogeneous aquifers. Some attention is given to hydrodynamically instable situations, i.e. when a heavier fluid is on top of a lighter fluid.