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The present article proposes a partitioned Dirichlet-Neumann algorithm, thatallows to address unique challenges arising from a novel mixed-dimensionalcoupling of very slender fibers embedded in fluid flow using a regularizedmortar-type finite element discretization. The fibers are modeled viaone-dimensional (1D) partial differential equations based on geometricallyexact nonlinear beam theory, while the flow is described by thethree-dimensional (3D) incompressible Navier-Stokes equations. The arisingtruly mixed-dimensional 1D-3D coupling scheme constitutes a novel approximatemodel and numerical strategy, that naturally necessitates specifically tailoredsolution schemes to ensure an accurate and efficient computational treatment.In particular, we present a strongly coupled partitioned solution algorithmbased on a Quasi-Newton method for applications involving fibers with highslenderness ratios that usually present a challenge with regard to thewell-known added mass effect. The influence of all employed algorithmic andnumerical parameters, namely the applied acceleration technique, the employedconstraint regularization parameter as well as shape functions, on efficiencyand results of the solution procedure is studied through appropriate examples.Finally, the convergence of the two-way coupled mixed-dimensional problemsolution under uniform mesh refinement is demonstrated, a comparison to a 3Dreference solution is performed, and the method's capabilities in capturingflow phenomena at large geometric scale separation is illustrated by theexample of a submersed vegetation canopy.

A fully coupled regularized mortar-type finite element approach for embedding one-dimensional fibers into three-dimensional fluid flow