Implicit coupling of one-dimensional and three-dimensional blood flow models with compliant vessels

Simulating arterial trees in the cardiovascular system can be made by the help of different models, depending on the outputs of interest and the desired degree of accuracy. In particular, one-dimensional fluid-structure interaction models for arteries are very effective in reproducing the physiological pressure wave propagation and in providing quantities like pressure and velocity, averaged on the cross section of the arterial lumen. In locations where one-dimensional models cannot capture the complete flow dynamics, e.g., in presence of stenoses and aneurysms, three-dimensional coupled fluid-structure interaction models are necessary to evaluate, for instance, critical factors responsible for pathologies which are associated to hemodynamics. In this work we formalize and investigate the geometrical multiscale problem, where heterogeneous fluid-structure interaction models for arteries are implicitly coupled. We introduce new coupling algorithms, describe their implementation and investigate on simple geometries the numerical reflections that occur at the interface between the heterogeneous models. We also simulate on a supercomputer a three-dimensional abdominal aorta under physiological conditions, coupled with up to six one-dimensional models representing the surrounding arterial branches. Finally, we compare CPU times and number of coupling iterations for different algorithms and time discretizations.