  Blood flow, dam or ship construction and numerous other problems in
biomedical and general engineering involve incompressible flows interacting
with elastic structures. Such interactions heavily influence the deformation
and stress states which, in turn, affect the engineering design process.
Therefore, any reliable model of such physical processes must consider the
coupling of fluids and solids. However, complexity increases for non-Newtonian
fluid models, as used, e.g., for blood or polymer flows. In these fluids,
subtle differences in the local shear rate can have a drastic impact on the
flow and hence on the coupled problem. There, existing (semi-)implicit solution
strategies based on split-step or projection schemes for Newtonian fluids are
not applicable, while extensions to non-Newtonian fluids can lead to
substantial numerical overhead depending on the chosen fluid solver. To address
these shortcomings, we present here a higher-order accurate, added-mass-stable
fluid-structure interaction scheme centered around a split-step fluid solver.
We compare several implicit and semi-implicit variants of the algorithm and
verify convergence in space and time. Numerical examples show good performance
in both benchmarks and an idealised setting of blood flow through an abdominal
aortic aneurysm considering physiological parameters.
