Volume 52, Number 5, September–October 2018
|Page(s)||1875 - 1911|
|Published online||11 December 2018|
Well-posed Stokes/Brinkman and Stokes/Darcy coupling revisited with new jump interface conditions
Aix-Marseille Université, CNRS, Centrale Marseille, Institut de Mathématiques de Marseille (UMR-7373),
Marseille cedex 13, France.
* Corresponding author: email@example.com
Accepted: 24 November 2017
The global well-posedness in time is proved, with no restriction on the size of the data, for the Stokes/Brinkman and Stokes/Darcy coupled flow problems with new jump interface conditions recently derived by Angot et al. [Phys. Rev. E 95 (2017) 063302-1–063302-16] using asymptotic modelling and shown to be physically relevant. These original conditions include jumps of both stress and tangential velocity vectors at the fluid–porous interface. They can be viewed as generalizations for the multi-dimensional flow of Beavers and Joseph’s jump condition of tangential velocity and Ochoa-Tapia and Whitaker’s jump condition of shear stress. Therefore, they are different from those most commonly used in the literature. The case of Saffman’s approximation is also studied, but with a force balance for the cross-flow including the Darcy drag and inducing a law of pressure jump different from the usual one. The proof of these results follows the general framework briefly introduced by Angot [C. R. Math. Acad. Sci. Paris, Ser. I 348 (2010) 697–702; Appl. Math. Lett. 24 (2011) 803–810.] for the steady flow.
Mathematics Subject Classification: 35Q30 / 35Q35 / 65M85 / 76D03 / 76D05 / 76D07 / 76S05
Key words: Fluid–porous coupled flow / Stokes/Brinkman model / Stokes/Darcy model / jump interface conditions / stress vector jump / tangential velocity jump
© EDP Sciences, SMAI 2018
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