  The present article proposes a partitioned Dirichlet-Neumann algorithm, that
allows to address unique challenges arising from a novel mixed-dimensional
coupling of very slender fibers embedded in fluid flow using a regularized
mortar-type finite element discretization. The fibers are modeled via
one-dimensional (1D) partial differential equations based on geometrically
exact nonlinear beam theory, while the flow is described by the
three-dimensional (3D) incompressible Navier-Stokes equations. The arising
truly mixed-dimensional 1D-3D coupling scheme constitutes a novel approximate
model and numerical strategy, that naturally necessitates specifically tailored
solution schemes to ensure an accurate and efficient computational treatment.
In particular, we present a strongly coupled partitioned solution algorithm
based on a Quasi-Newton method for applications involving fibers with high
slenderness ratios that usually present a challenge with regard to the
well-known added mass effect. The influence of all employed algorithmic and
numerical parameters, namely the applied acceleration technique, the employed
constraint regularization parameter as well as shape functions, on efficiency
and results of the solution procedure is studied through appropriate examples.
Finally, the convergence of the two-way coupled mixed-dimensional problem
solution under uniform mesh refinement is demonstrated, a comparison to a 3D
reference solution is performed, and the method's capabilities in capturing
flow phenomena at large geometric scale separation is illustrated by the
example of a submersed vegetation canopy.
