  Coupled systems of free flow and porous media arise in a variety of technical
and environmental applications. For laminar flow regimes, such systems are
described by the Stokes equations in the free-flow region and Darcy's law in
the porous medium. An appropriate set of coupling conditions is needed on the
fluid-porous interface. Discretisations of the Stokes-Darcy problems yield
large, sparse, ill-conditioned, and, depending on the interface conditions,
non-symmetric linear systems. Therefore, robust and efficient preconditioners
are needed to accelerate convergence of the applied Krylov method. In this
work, we develop and investigate block diagonal, block triangular and
constraint preconditioners for the coupled Stokes-Darcy problems. We apply two
classical sets of coupling conditions considering the Beavers-Joseph and the
Beavers-Joseph-Saffman condition for the tangential velocity. For the
Beavers-Joseph interface condition, the resulting system is non-symmetric,
therefore GMRES method is used. Spectral and field-of-values bounds independent
of the grid width are derived for the exact versions of the preconditioners.
Furthermore, we develop efficient inexact versions of the preconditioners. We
demonstrate the effectiveness and robustness of the proposed preconditioners in
numerical experiments.
