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http://hdl.handle.net/1942/30984
Title: | Formal upscaling and numerical validation of unsaturated flow models in fractured porous media | Authors: | Kumar, Kundan LIST, Florian POP, Sorin Radu, Florin |
Issue Date: | 2020 | Publisher: | ACADEMIC PRESS INC ELSEVIER SCIENCE | Source: | JOURNAL OF COMPUTATIONAL PHYSICS, 407 (Art N° 109138) | Abstract: | In this work, we consider a mathematical model for describing flow in an unsaturated porous medium containing a fracture. Both the flow in the fracture as well as in the matrix blocks are governed by Richards' equation coupled by natural transmission conditions. Using formal asymptotics, we derive upscaled models as the limit of vanishing ε, the ratio of the width and length of the fracture. Our results show that the ratio of porosities and permeabilities in the fracture to matrix determine, to the leading order of approximation, the appropriate effective model. In these models the fracture is a lower dimensional object for which different transversally averaged models are derived depending on the ratio of the porosities and permeabilities of the fracture and respective matrix blocks. We obtain a catalogue of effective models which are validated by numerical computations. | Keywords: | Richards' equation;Fractured porous media;Upscaling;Unsaturated flow in porous media | Document URI: | http://hdl.handle.net/1942/30984 | ISSN: | 0021-9991 | e-ISSN: | 1090-2716 | DOI: | 10.1016/j.jcp.2019.109138 | ISI #: | 000519535500021 | Rights: | 2019 Published by Elsevier Inc. | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2021 |
Appears in Collections: | Research publications |
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JCP_List.pdf Restricted Access | Published version | 2.44 MB | Adobe PDF | View/Open Request a copy |
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