In this paper, one considers the coupling of a Brinkman model and Stokes equations with jump embedded transmission conditions. In this model, one assumes that the viscosity in the porous region is very small. Then we derive a Wentzel–Kramers–Brillouin (WKB) expansion in power series of the square root of this small parameter for the velocity and the pressure which are solution of the transmission problem. This WKB expansion is justified rigorously by proving uniform errors estimates.
P.Angot, A fictitious domain model for the Stokes/Brinkman problem with jump embedded boundary conditions, C. R. Math. Acad. Sci. Paris348(11,12) (2010), 697–702.
2.
P.Angot, On the well-posed coupling between free fluid and porous viscous flows, Appl. Math. Lett.24(6) (2011), 803–810.
3.
F.Boyer and P.Fabrie, Eléments D’analyse Pour L’étude de Quelques Modèles D’écoulements de Fluides Visqueux Incompressibles, Vol. 52, Springer, 2005.
4.
C.-H.Bruneau and I.Mortazavi, Contrôle passif d’écoulements incompressibles autour d’obstacles à l’aide de milieux poreux, Comptes Rendus de l’Académie des Sciences – Series IIB – Mechanics329(7) (2001), 517–521.
5.
G.Carbou, Penalization method for viscous incompressible flow around a porous thin layer, Nonlinear Anal. Real World Appl.5(5) (2004), 815–855.
6.
G.Carbou, Brinkmann model and double penalization method for the flow around a porous thin layer, J. Math. Fluid Mech.10(1) (2008), 126–158.
7.
G.Carbou and P.Fabrie, Boundary layer for a penalization method for viscous incompressible flow, Adv. Differential Equations8(12) (2003), 1453–1480.
8.
N.Chen, M.Gunzburger and X.Wang, Asymptotic analysis of the differences between the Stokes–Darcy system with different interface conditions and the Stokes–Brinkman system, J. Math. Anal. Appl.368(2) (2010), 658–676.
