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Robust solution of Richards' equation for nonuniform porous media
Author(s) -
Miller Cass T.,
Williams Glenn A.,
Kelley C. T.,
Tocci Michael D.
Publication year - 1998
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/98wr01673
Subject(s) - richards equation , capillary pressure , porous medium , loam , classification of discontinuities , mathematics , permeability (electromagnetism) , saturation (graph theory) , nonlinear system , relative permeability , geotechnical engineering , discontinuity (linguistics) , capillary action , algebraic number , mathematical analysis , porosity , water content , soil science , materials science , geology , soil water , physics , composite material , genetics , combinatorics , quantum mechanics , membrane , biology
Capillary pressure–saturation‐relative permeability relations described using the van Genuchten [1980] and Mualem [1976] models for nonuniform 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. We investigate constitutive relations, interblock permeability, nonlinear algebraic system approximation methods, and two time integration approaches. 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 sand, loam, and clay loam media.