Countless applications in science and engineering involve incompressible flows and their interaction with elastic bodies. As a prime example from the biomedical context, complex clinical applications in the cardiovascular system continue to challenge numerical methods and well-established algorithms. However, there is vast potential for computer methods to assist in clinic, e.g., in training medical personnel or evaluating treatment options in-silico.
To this end, we devise stabilised coupled and split-step schemes for generalised Newtonian fluid flow, capturing blood’s rheology. Targeting the haemodynamic regime, the split-step flow solver is coupled to hyperelastic tissue models in an added-mass stable, partitioned fashion. Combining Robin transmission conditions and interface quasi-Newton methods, we tackle real-world applications such as blood flow in an iliac bifurcation or a patient-specific aortic dissection. The proposed flow and fluid–structure interaction schemes are carefully investigated with respect to their accuracy, robustness and reliability while bridging the gap to real-world problems, considering state-of-the-art modelling aspects, physiological parameters and showcasing the framework’s versatility.