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

Zech, Simon; Ray, Nadja; Schulz, Raphael

doi:10.1016/j.jmaa.2022.126384

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2022

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“…Finally, a numerical realisation of scenarios with vanishing porosity and a related thorough numerical analysis as presented in [3,4] for the situation of a degenerate flow problem are of interest. First results in this direction for the coupled flow and transport problem are found in [30].…”

Section: Discussionmentioning

confidence: 99%

Existence and uniqueness of solutions to a flow and transport problem with degenerating coefficients

Ray¹,

Schulz²

2022

Eur. J. Appl. Math

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Structural changes of the pore space and clogging phenomena are inherent to many porous media applications. However, related analytical investigations remain challenging due to potentially vanishing coefficients in the respective systems of partial differential equations. In this research, we apply an appropriate scaling of the unknowns and work with porosity-weighted function spaces. This enables us to prove existence, uniqueness and non-negativity of weak solutions to a combined flow and transport problem with vanishing, but prescribed porosity field, permeability and diffusion.

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Section: Discussionmentioning

confidence: 99%