Multiscale techniques for the coupling of 3D-1D fsi equations system in compliant vessels

In this paper we present a multiscale model for the analysis of fluid-structure interaction which couples the three-dimensional vessel equations with an appropriate linked mono-dimensional system. This approach allows the study of transient phenomena with remarkable reduction of the computational complexity. This model, when large displacements are taken into account, is of considerable interest for time-dependent simulations of blood flow in components such as large arteries or blood vessels. The computational domain consists of two interacting fluid-structure regions: one described by the multidimensional Navier-Stokes system and the other defined by the structural mechanics equations. Due to the computational cost of fully three-dimensional fluid structure interaction problems and the complexity of the cardiovascular system, this multi dimensional models can only be applied to selected regions of interest. According to this multiscale approach the rest of the blood circuit is represented by a mono dimensional formulation of the Navier-Stokes system. In particular the mono-dimensional model has to describe properly the wave propagation nature of blood flow and, when coupled with the rest of geometry, must act as a proper absorbing and generating device for the exiting waves inside the computational domain. The mono-three dimensional interface and the multi dimensional geometry of components such as heart valves add complexity to the treatment of inflow and outflow boundaries, where one would like to have a correct representation of the traveling waves, without spurious reflections which may compromise the stability of the solution. In this work we study the propagation of fluid waves into a multidimen- sional geometry solving fully coupled fluid-structure problem with multiscale approach and present the results of two different cases