Published 2019-07-29
Keywords
- porous media,
- curved interfaces,
- Darcy-Stokes system,
- Darcy- Brinkman system
How to Cite
Abstract
We present the asymptotic analysis of a Darcy-Stokes coupled
system, modeling the fluid exchange between a narrow channel (Stokes flow) and a porous medium (Darcy flow), coupled through a C2 curved interface. The channel is a cylindrical domain between the interface (Τ) and a parallel translation of itself (Τ + ε eN, ε> 0). The introduction of a change variable (to fix the domain geometry) and the introduction of two systems of coordinates: the Cartesian and a local one (consistent with the geometry of the surface), permit to find the limiting form of the system when the width of the channel tends to zero (ε → 0). The limit problem is a coupled system with Darcy flow in the porous medium and Brinkman flow on the curved interface (Τ).
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References
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