Robust Solution of Richards' Equation for Non-Uniform Porous Media

. Capillary pressure-saturation-relative permeability relations described using the van Genuchten and Mualem models for non-uniform porous media lead to numerical convergence difficulties when used with Richards' equation for certain auxiliary conditions. These difficulties arise because of discontinuities in the derivative of specific moisture capacity and relative permeability as a function of capillary pressure. Convergence difficulties are illustrated using standard numerical approaches to simulate such problems. Constitutive relations, interblock permeability, and nonlinear algebraic system approximation methods, and two time integration approaches are investigated. An integral permeability approach approximated by Hermite polynomials is recommended and shown to be robust and economical for a set of test problems, which correspond to a sand, a loam, and a clay loam media. 3 1. Introduction Fluid flow in unsaturated porous media is often modeled using Richards' equation (RE) [Ri..