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Description
Fluid flow in coupled systems, which consist of a free-flow region and an adjacent porous medium occurs in a variety of environmental and industrial applications, such as soil–water interactions and industrial filtration. In this work, we investigate the mathematical formulation of these systems, which are modeled by a coupled Stokes-Darcy system with interface conditions governed by the Beavers-Joseph-Saffman law. Specifically, we address the case where porosity in the Darcy region vanishes, representing pore clogging phenomena. To handle this degeneracy, we rescale both the pressure and velocity in the Darcy region with respect to the vanishing porosity, following the framework introduced by Arbogast and Taicher (SIAM J. Numer. Anal., 2016). This approach leads to a transformed Stokes-Darcy system with appropriately rescaled interface conditions. We then establish the existence and uniqueness of solutions to the transformed system using the theory of mixed variational problems, adapted to account for the degenerating porosity and weighted function spaces. Moreover, we supplement our theoretical findings for the scaled Stokes-Darcy problem with numerical results.
Key words. coupled porous media and fluid flow, Beavers-Joseph-Saffman law, Stokes and Darcy equations, degenerate elliptic, weak solutions, convergence rates
| References | [1] T. Arbogast, A. Taicher (2016): A linear degenerate elliptic equation arising from two-phase mixtures. SIAM J. Numer. Anal. Vol.54, No. 5, p. 3105-3122. [2] W. Layton, F. Schieweck, I.Yotov (2003): Coupling fluid flow with porous media flow. SIAM J. Numer. Anal. Vol.40, No. 6, p. 2195-2218. |
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| Country | Germany |
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