Numerical investigations of degenerate equations for fluid flow and reactive transport in clogging porous media

Structural changes of the pore space and clogging phenomena are inherent to many porous media applications. However, numerical investigations of the related flow and transport problem remain challenging due to the degeneration of the hydrodynamic parameter porosity, and in turn of the permeability a...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2022-11, Vol.515 (2), p.126384, Article 126384
Main Authors: Zech, Simon, Ray, Nadja, Schulz, Raphael
Format: Article
Language:English
Subjects:
Clogging
Degenerate PDEs
Error analysis
Mixed finite elements
Porous media
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Summary:Structural changes of the pore space and clogging phenomena are inherent to many porous media applications. However, numerical investigations of the related flow and transport problem remain challenging due to the degeneration of the hydrodynamic parameter porosity, and in turn of the permeability and diffusion tensor. A remedy is to use appropriate scalings of the unknowns velocity, pressure and species' concentration in terms of the porosity. This enables us to conduct numerical simulations for the combined, degenerating flow and transport problem. As discretization method, lowest order mixed finite elements are used and stability of the numerical scheme is shown. Under certain additional regularity assumptions, convergence (with optimal order) can be proven. Our numerical results confirm that optimal convergence is obtained for the transformed variables whereas the non-transformed variables might not converge.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2022.126384