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The coupled Darcy-Stokes problem is widely used for modeling fluid transportin physical systems consisting of a porous part and a free part. In this workwe consider preconditioners for monolitic solution algorithms of the coupledDarcy-Stokes problem, where the Darcy problem is in primal form. We employ theoperator preconditioning framework and utilize a fractional solver at theinterface between the problems to obtain order optimal schemes that are robustwith respect to the material parameters, i.e. the permeability, viscosity andBeavers-Joseph-Saffman parameter. Our approach is similar to our earlier work,but since the Darcy problem is in primal form, the mass conservation at theinterface introduces some challenges. These challenges will be specificallyaddressed in this paper. Numerical experiments illustrating the performance areprovided. The preconditioner is posed in non-standard Sobolev spaces which maybe perceived as an obstacle for its use in applications. However, we detail theimplementational aspects and show that the preconditioner is quite feasible torealize in practice.

Robust preconditioning for coupled Stokes-Darcy problems with the Darcy problem in primal form