At this colloquium, we are happy to welcome:

Stefanie Sonner (Radboud University)

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Iryna Rybak (University Stuttgart)

Coupled free-flow and porous-medium systems: mathematical modelling and numerical methods

Coupled systems of free flow and porous-medium flow appear in a wide range of environmental, industrial and medical settings, e.g. interaction of surface water with groundwater, industrial filtration and drying processes, transport of drugs and nutrients through biological tissues. Such flow problems are usually described by the Stokes equations in the free-flow domain, Darcy’s law in the porous medium and appropriate coupling conditions on the fluid–porous interface.

Classical coupling concepts for free-flow and porous-medium systems based on the Beavers–Joseph condition for the tangential velocity are applicable only for parallel or perpendicular flows to the fluid–porous interface. This limitation severely restricts the variety of applications that can be accurately modelled. Moreover, discretisations of coupled Stokes–Darcy problems lead to large, sparse, ill-conditioned and non-symmetric linear systems. Thus, robust and efficient solution strategies are needed.

In this talk, we present generalised interface conditions for coupled free-flow and porous-medium systems, which are derived using the theory of homogenisation and boundary layer correctors. These conditions are valid for arbitrary flow directions to the fluid–porous interface. All effective model parameters are computed based on the pore-scale geometrical information. We validate the developed conditions numerically by comparison of macroscale simulation results with porescale resolved solutions and demonstrate the advantages of the new conditions over the classical ones. We also prove the well-posedness of the coupled flow model with the newly derived interface conditions and present several robust and efficient numerical algorithms.

T.b.a.

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