Monotonicity Considerations for Saturated--Unsaturated Subsurface Flow

It is demonstrated that monotonicity is a sufficient condition to ensure that no new nonphysical local maxima and minima can be produced in the discrete nonlinear unsaturated flow equation. Monotonicity conditions are derived for various types of weighting for the mobility term. The basic discretization is of finite element type, but the results can be extended to finite volume discretizations. Central weightings are only conditionally monotone, while upstream weightings are unconditionally monotone. Sample computations are given for highly heterogeneous problems.