P. Broadbridge et al., CLOSED-FORM SOLUTIONS FOR UNSATURATED FLOW UNDER VARIABLE FLUX BOUNDARY-CONDITIONS, Advances in water resources, 19(4), 1996, pp. 207-213
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