An adaptive time discretization of the classical and the dual porosity model of Richards' equation

  • Authors:
  • Michal Kurá;Petr Mayer;Matj Lepš;Dagmar Trpkošová

  • Affiliations:
  • Czech University of Life Sciences Prague, Faculty of Environmental Sciences, Department of Water Resources and Environmental Modeling, Czech Republic;Czech Technical University in Prague, Faculty of Civil Engineering, Department of Mathematics, Czech Republic;Czech Technical University in Prague, Faculty of Civil Engineering, Department of Mechanics, Czech Republic;Charles University in Prague, Faculty of Science, Institute of Hydrogeology, Engineering Geology and Applied Geophysics, Czech Republic

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2010

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Abstract

This paper presents a numerical solution to the equations describing Darcian flow in a variably saturated porous medium-a classical Richards' equation model Richards (1931) [1] and an extension of it that approximates the flow in media with preferential paths-a dual porosity model Gerke and van Genuchten (1993) [8]. A numerical solver to this problem, the DRUtES computer program, was developed and released during our investigation. A new technique which maintains an adaptive time step, defined here as the Retention Curve Zone Approach, was constructed and tested. The aim was to limit the error of a linear approximation to the time derivative part. Finally, parameter identification was performed in order to compare the behavior of the dual porosity model with data obtained from a non-homogenized fracture and matrix flow simulation experiment.