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

Abstract

Arterial 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 design. Consequently, any reliable model of such physical processes must consider the coupling of fluids and solids. However, complexity increases for non-Newtonian fluids, such as blood or polymer melts. In these fluids, subtle differences in the local shear-rate can have a drastic impact on the flow. Existing numerical solution strategies devised for Newtonian fluids are either not applicable or ineffective in such scenarios. 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 a realistic setting of blood flow through an abdominal aortic aneurysm.