Speaker
Description
In this paper, we derive a new effective interface condition governing the transition between porous and free flow regions of a fluid domain via asymptotic analysis. The proposed non-standard condition represents a Darcy-type law acting across the imaginary interface, asserting that the trace of the free-flow velocity is proportional to the difference in stresses on both sides of the interface. Higher- order asymptotics reveals that the leading-order approximation corresponds to a no-slip condition, the first-order to a non-penetration condition with tangential slip, whereas the second-order approximation acknowledges the leaking across the interface. This hierarchical behaviour is particularly relevant in modelling blood flow in the arteries, where the arterial wall behaves as a porous medium, allowing slow blood seepage relative to the main flow. Our result generalises and improves the usual Beavers-Joseph condition as well as some other conditions used in practice. For instance the continuity of the normal velocities and stresses.
Coupled weak formulation of the obtained problem is given in appropriate setting and it is shown that it is very natural from mathematical and physical point of view. The well-posedness for the obtained problem is proved. The model is justified by rigorous asymptotic analysis confirmed via an error estimate. Corresponding interior-layer problems are studied in more details and the analysis of the effective coefficients in the effective law is given.
| References | Marusic-Paloka, E., Pazanin, I., Fluid flow through a porous membrane and the Darcy interface condition, submitted (2025). |
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| Country | Croatia |
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