  Fluid flows in coupled systems consisting of a free-flow region and the
adjacent porous medium appear in a variety of environmental settings and
industrial applications. In many applications, fluid flow is non-parallel to
the fluid-porous interface that requires a generalisation of the Beavers-Joseph
coupling condition typically used for the Stokes-Darcy problem. Generalised
coupling conditions valid for arbitrary flow directions to the interface are
recently derived using the theory of homogenisation and boundary layers. The
aim of this work is the mathematical analysis of the Stokes-Darcy problem with
these generalised interface conditions. We prove the existence and uniqueness
of the weak solution of the coupled problem. The well-posedness is guaranteed
under a suitable relationship between the permeability and the boundary layer
constants containing geometrical information about the porous medium and the
interface. We numerically study the validity of the obtained results for
realistic problems and provide a benchmark for numerical solution of the
Stokes-Darcy problem with generalised interface conditions.
