Solution of the unsaturated soil moisture equation using repeated transforms

An alternative method of solution for the linearized 'theta-based' form of the Richards equation of unsaturated flow is developed in two spatial dimen sions. The Laplace and Fourier transformations are employed to reduce the R ichards equation to an ordinary differential equation in terms of a transfo rmed moisture content and the transform variables, s and xi. Separate analy tic solutions to the transformed equation are developed for initial states which are either in equilibrium or dis-equilibrium. The solutions are assem bled into a finite layer formulation satisfying continuity of soil suction, thereby facilitating the analysis of horizontally stratified soil profiles . Solution techniques are outlined for various boundary conditions includin g prescribed constant moisture content, prescribed constant flux and flux a s a function of moisture change. Example solutions are compared with linear ized finite element solutions. The agreement is found to be good. An adapta tion of the method for treating the quasilinearized Richards equation with variable diffusivity is also described. Comparisons of quasilinear solution s with some earlier semi-analytical, finite element and finite difference r esults are also favourable. Copyright (C) 2001 John Wiley & Sons, Ltd.