CLOSED-FORM SOLUTIONS FOR UNSATURATED FLOW UNDER VARIABLE FLUX BOUNDARY-CONDITIONS

It is shown that from any solution of the linear diffusion equation, w e may construct a solution of a realistic form of the Richards equatio n for unsaturated flow. Compared to the usual direct linearization met hod, our inverse approach involves a quite different sequence of trans formations. This opens the possibility of exact solutions with a wider variety of continuously varying flux boundary conditions. Closed-form solutions are presented for two examples. In these, the varying water flux boundary conditions resemble (i) the passage of a peaking storm and (ii) the continuous opening of a valve preceding a steady water su pply. Unlike earlier more systematic approaches to this problem, our m ethod does not require the numerical solution of an integral equation. Copyright (C) 1996 Elsevier Science Limited