Well-posed Stokes/Brinkman and Stokes/Darcy coupling revisited with new jump interface conditions

• Published in: ESAIM. Mathematical modelling and numerical analysis 2018-09, Vol.52 (5), p.1875-1911
• Main Author: Angot, Philippe
• Format: Article
• Language: English
• Subjects: 35Q30; 35Q35; 65M85; 76D03; 76D05; 76D07; 76S05; Analysis of PDEs; Computational fluid dynamics; Computer Science; Cross flow; Fluid mechanics; Fluid–porous coupled flow; jump interface conditions; Mathematics; Mechanics; Modeling and Simulation; Numerical Analysis; Physics; Pressure jump; Shear stress; Steady flow; Stokes/Brinkman model; Stokes/Darcy model; stress vector jump; tangential velocity jump; Well posed problems
• ISSN: 0764-583X; 1290-3841
• DOI: 10.1051/m2an/2017060

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.