Algorithms for the coupling of one-dimensional arterial networks with three-dimensional fluid-structure interaction problems
This work is focused on the development of a geometrical multiscale framework for modeling the human cardiovascular system. This approach is designed to deal with different geometrical and mathematical models at the same time, without any preliminary hypotheses on the layout of the general multiscale problem. This flexibility allows to set up a complete arterial tree model of the circulatory system, assembling first a network of one-dimensional models, described by non-linear hyperbolic equations, and then replacing some elements with more detailed (and expensive) three-dimensional models, where the Navier-Stokes equations are coupled with structural models through fluid-structure interaction algorithms. The coupling between models of different scale and type is addressed imposing the conservation equations in terms of averaged/integrated quantities (i.e., the flow rate and the normal component of the traction vector); in particular, three coupling strategies have been explored for the fluid problem. In all the cases, these strategies lead to small non-linear interface problems, which are solved using classical iterative algorithms.