The Darcy problem with porosity depending exponentially on the pressure

We consider the flow of a viscous incompressible fluid through a porous medium. We allow the permeability of the medium to depend exponentially on the pressure and provide an analysis for this model. We study a splitting formulation where a convection diffusion problem is used to define the permeabi...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2021-12, Vol.398, p.113642, Article 113642
Main Authors: Birhanu, Zerihun Kinfe, Mengesha, Tadele, Salgado, Abner J.
Format: Article
Language:English
Subjects:
Darcy equations
Finite elements
Porous media flow
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Summary:We consider the flow of a viscous incompressible fluid through a porous medium. We allow the permeability of the medium to depend exponentially on the pressure and provide an analysis for this model. We study a splitting formulation where a convection diffusion problem is used to define the permeability, which is then used in a linear Darcy equation. We also study a discretization of this problem, and provide an error analysis for it.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2021.113642