Steady Unsaturated Flow in Random Porous Media: Using an Analytical Perturbation Solution as Initial Guess to a Numerical Model

Effects of soil heterogeneity have been the focus of both field and theoretical research for the past decade (e.g., Hills et al., 1991; Hopmans et al., 1988; Mantoglou and Gelhar, 1987; McCord et al., 1991, Russo, 1991; Ünlü et al., 1990; Wierenga et al., 1991; Yeh et al., 1985a,b; Yeh et al., 1986). Analytical models are essential tools for investigating the effect of heterogeneity on flow and transport in the unsaturated zone. However, the nonlinearity of the governing flow equation, the degree of nonlinearity, and the spatial variability in the unsaturated hydraulic properties make the development of analytical solutions difficult. Analytical solutions are only available for some special cases, such as one-dimensional steady-state and transient infiltration in layered soil with Gardner type unsaturated properties (Yeh, 1989; Warrick and Yeh, 1990; Srivastava and Yeh, 1991). For more general problems one often relies on numerical techniques such as finite difference and finite element methods (c.f. Fletcher, 1988; Anderson and Woessner, 1992). The finite element or finite difference equations for unsaturated media are commonly written in form of a linearized matrix equation such as: