AN INTEGRAL-EQUATION FORMULATION FOR THE UNCONFINED FLOW OF GROUNDWATER WITH VARIABLE INLET CONDITIONS

We combine an integral equation formulation with a hodograph transform ation to solve self-similar problems describing the unconfined flow of groundwater with variable inlet conditions. A class of new semi-analy tical solutions is obtained for both rectilinear and radial flow geome tries. The solutions are in general agreement with those derived by Ba renblatt, although there are some discrepancies for the case of radial flow. The formulation presented provides additional analytical insigh t, and for computational purposes is simpler than Barenblatt's. In add ition, the method proposed can be successfully used for the solution o f a host of other nonlinear problems that admit self-similarity.