Multiscale mixed finite elements for the Stokes-Brinkman equations

We present a multiscale mixed finite-element method for solving the Stokes-Brinkman equations. This gives a unified and efficient approach to simulating flow in carbonate reservoirs that contain both free-flow and porous regions. The multiscale method uses a standard Darcy model to approximate pressures and fluxes on a coarse grid, but captures fine-scale effects through basis functions determined from local Stokes-Brinkman flow problems on an underlying fine-scale grid. For the special case of Darcy flow in a homogeneous medium, the multiscale elements reduce to the lowest-order Raviart-Thomas elements. We present a few illustrative numerical experiments and discuss various discretizations of the fine-scale problem to enable efficient solution of cases with multi-million cells in 3D.