Some exact solutions of interface problems by means of the hodograph method
Jacob Bear, Gédéon Dagan · Journal of Geophysical Research Atmospheres · 1964
The hodograph method is used to study the shape and position of the interface between two immiscible liquids of different densities when the heavier liquid is at rest. The principles of the method are briefly reviewed. Four cases are presented: (a) An interface in a confined aquifer, (b) upconing toward a sink in an unbounded aquifer, (c) upconing toward a sink in a confined aquifer of infinite thickness, and (d) a drain above the interface in an aquifer of infinite depth. The shape of the interface in each case is presented in the form of an equation and graphs. It is shown that in cases (a) and (c) the approximate solution based on the Dupuit assumption is, under certain conditions, sufficiently accurate.