Efficient split-step schemes for fluid-structure interaction involving incompressible generalised Newtonian flows

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.