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

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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. © 2009 Elsevier B.V. All rights reserved.

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Kuráž, M., Mayer, P., Lepš, M., & Trpkošová, D. (2010). An adaptive time discretization of the classical and the dual porosity model of Richards’ equation. Journal of Computational and Applied Mathematics, 233(12), 3167–3177. https://doi.org/10.1016/j.cam.2009.11.056

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