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## Section: New Results

### Numerical methods for multi-physics problems

Participants : Miguel Ángel Fernández Varela, Fannie Gerosa.

In [24] we introduce a mixed dimensional Stokes-Darcy coupling where a d-dimensional Stokes' flow is coupled to a Darcy model on the $d-1$ dimensional boundary of the domain. The porous layer introduces tangential creeping flow along the boundary and allows for the modelling of boundary flow due to surface roughness. This leads to a new model of flow in fracture networks with reservoirs in an impenetrable bulk matrix. Exploiting this modelling capability, we then formulate a fluid-structure interaction method with contact, where the porous layer allows for mechanically consistent contact and release. Physical seepage in the contact zone due to rough surfaces is modelled by the porous layer. Some numerical examples are reported, both on the Stokes-Darcy coupling alone and on the fluid-structure interaction with contact in the porous boundary layer.

Unfitted mesh finite element approximations of immersed incompressible fluid-structure interaction problems which efficiently avoid strong coupling without compromising stability and accuracy are rare in the literature. Moreover, most of the existing approaches introduce additional unknowns or are limited by penalty terms which yield ill conditioning issues. In [28], we introduce a new unfitted mesh semi-implicit coupling scheme which avoids these issues. To this purpose, we provide a consistent generalization of the projection based semi-implicit coupling paradigm of [Int. J. Num. Meth. Engrg.,69(4):794-821, 2007] to the unfitted mesh Nitsche-XFEM framework.