Robust Solution of Richards ' Equation for Non - Uniform PorousMediaCass
نویسندگان
چکیده
Capillary pressure-saturation-relative permeability relations described using the van Genuchten and Mualem models for non-uniform porous media lead to numerical convergence diiculties when used with Richards' equation for certain auxiliary conditions. These diiculties arise because of discontinuities in the derivative of speciic moisture capacity and relative permeability as a function of capillary pressure. Convergence diiculties 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
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