A Nitsche-based cut finite element method for the coupling of incompressible fluid flow with poroelasticity

Abstract

The focus of this contribution is the numerical treatment of interface coupled problems concerning the interaction of incompressible fluid flow and permeable, elastic structures. The main emphasis is on extending the range of applicability of available formulations on especially three aspects. These aspects are the incorporation of a more general poroelasticity formulation, the use of the cut finite element method (CutFEM) to allow for large interface motion and topological changes of the fluid domain, and the application of a novel Nitsche-based approach to incorporate the Beavers–Joseph(–Saffmann) tangential interface condition. This last aspect allows one to extend the practicable range of applicability of the proposed formulation down to very low porosities and permeabilities which is important in several examples in application. Different aspects of the presented formulation are analyzed in a numerical example including spatial convergence, the sensitivity of the solution to the Nitsche penalty parameters, varying porosities and permeabilities, and a varying Beavers–Joseph interface model constant. Finally, a numerical example analyzing the fluid induced bending of a poroelastic beam provides evidence of the general applicability of the presented approach.