Robust solution of Richards' equation for nonuniform porous media

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 bec...

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Bibliographic Details
Published in:Water resources research 1998-10, Vol.34 (10), p.2599-2610
Main Authors: Miller, C.T. (University of North Carolina, Chapel Hill.), Williams, G.A, Kelley, C.T, Tocci, M.D
Format: Article
Language:English
Subjects:
CAPILLARY PRESSURE
DEBIT
FLOW RATE
GASTO
MATEMATICAS
MATHEMATICS
MATHEMATIQUE
MOUVEMENT DE L'EAU DANS LE SOL
MOVIMIENTO DEL AGUA EN EL SUELO
PERMEABILIDAD
PERMEABILITE
PERMEABILITY
SATURATED FLOW
SATURATION
SOIL WATER MOVEMENT
UNSATURATED FLOW
VARIABLY SATURATED FLOW
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Summary: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
ISSN:0043-1397
1944-7973
DOI:10.1029/98WR01673