An adaptive time discretization of the classical and the dual porosity model of Richards’ equation |
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Authors: | Michal Kurá ?,Petr Mayer,Dagmar Trpko&scaron ová |
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Affiliation: | a Czech University of Life Sciences Prague, Faculty of Environmental Sciences, Department of Water Resources and Environmental Modeling, Czech Republic b Czech Technical University in Prague, Faculty of Civil Engineering, Department of Mathematics, Czech Republic c Czech Technical University in Prague, Faculty of Civil Engineering, Department of Mechanics, Czech Republic d Charles University in Prague, Faculty of Science, Institute of Hydrogeology, Engineering Geology and Applied Geophysics, Czech Republic |
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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. |
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Keywords: | Darcy&rsquo s law Variable saturation Retention curve Mass balance Adaptive time discretization Preferential flow Homogenization Parameter identification Multi-objective evolutionary algorithm |
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