Coupled Stokes-Darcy model with Beavers-Joseph interface boundary condition

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.

Keywords

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

2010 Mathematics Subject Classification

35Q35, 65M60, 76D07, 76S05, 86A05

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Published 1 January 2010