  This paper presents a numerical method for the simulation of fluid-structure
interaction specifically tailored to interactions between Newtonian fluids and
a large number of slender viscoelastic Cosserat rods. Because of their high
flexibility and low weight the rods considered here exhibit large deflections,
even under moderate fluid loads. Their motion, in turn, modifies the flow so
that fluid and structures are strongly coupled to each other which is
numerically very challenging. The paper proposes a new coupling approach based
on an immersed boundary method which improves upon existing methods for this
problem. It is numerically stable and exempt from any global iteration between
the fluid part and the structure part, thus yielding high stability and low
computational cost of the coupling scheme. The contribution presents the
underlying methodology and its algorithmic realization, including an assessment
of accuracy and convergence by systematic studies. Various validation cases
illustrate performance and versatility of the proposed method.
