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Computation of Inter-Nodal Permeabilities for Richards Equation

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Modelling Water Flow in Unsaturated Porous Media

Part of the book series: GeoPlanet: Earth and Planetary Sciences ((GEPS))

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Abstract

An important part of all finite difference and many finite volume discretization schemes developed for multiphase flow equations is the approximation of the average permeability value between two neighbouring nodes. Various averaging techniques are presented in this chapter, with particular focus on the case of one-dimensional unsaturated flow in a homogeneous medium, for which accurate inter-nodal permeability estimations based on steady flow analysis are available. It is shown that the relation between capillary and gravity forces at the scale of a single grid cell has key importance for the choice of the averaging scheme. An averaging method developed by the author for one-dimensional flow is presented in detail, and its extensions to heterogeneous materials and multidimensional problems are discussed. Implications for two-phase flow modelling are also considered.

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Authors and Affiliations

  1. Faculty of Civil and Environmental Engineering, Gdansk University of Technology, Narutowicza 11/12, 80-233, Gdansk, Poland

    Adam Szymkiewicz

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  1. Adam Szymkiewicz
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Correspondence to Adam Szymkiewicz .

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Szymkiewicz, A. (2013). Computation of Inter-Nodal Permeabilities for Richards Equation. In: Modelling Water Flow in Unsaturated Porous Media. GeoPlanet: Earth and Planetary Sciences. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23559-7_4

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