Solvability of the variable-viscosity fluid-porous flows coupled with an optimal stress jump interface condition
Abstract
In this study, we prove the well-posedness of both the variable-viscosity Stokes/Darcy-Brinkman and Stokes/Darcy coupled problems governing the viscous flow in fluid-porous systems. The coupling is made by a recent optimal stress jump interface condition associated to velocity continuity at the bottom surface of a transition layer inside the porous region. Indeed, this original condition has been shown to be physically relevant for multi-directional flows and optimal by minimizing the loss of flow rate in the viscous boundary layer. Besides, its inherent tensorial form ensures to handle arbitrary flow directions with anisotropic effects of the microstructure. The analysis of the transmission problem is carried out by introducing a unified mixed variational framework with no Lagrange multiplier at the interface. Moreover, the analysis of variable-viscosity fluid-porous flows seems new in the literature.
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