Coupled Stokes-Darcy model with Beavers-Joseph interface boundary condition. (English) Zbl 1189.35244

Cao, Yanzhao; Gunzburger, Max; Hua, Fei; Wang, Xiaoming

Commun. Math. Sci. 8, No. 1, 1-25 (2010).

Summary: We investigate the well-posedness of a coupled Stokes-Darcy model with Beavers-Joseph interface boundary conditions. In the steady-state case, the well-posedness is established under the assumption of a small coefficient in the Beavers-Joseph interface boundary condition. In the time-dependent case, the well-posedness is established via an appropriate time discretization of the problem and a novel scaling of the system under an isotropic media assumption. Such coupled systems are crucial to the study of subsurface flow problems, in particular, flows in karst aquifers.

MSC:

35Q35	PDEs in connection with fluid mechanics
65M60	Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
76D07	Stokes and related (Oseen, etc.) flows
76S05	Flows in porous media; filtration; seepage
86A05	Hydrology, hydrography, oceanography

Keywords:

Stokes and Darcy system; fluid and porous media flow; Beavers-Joseph interface boundary condition; well-posedness; time discretization; finite element approximation