Comparing Absorbing Boundary Conditions for a 3D Non Newtonian Fluid-Structure Interaction Model for Blood Flow in Arteries

Abstract

A 3D fluid-structure interaction (FSI) problem in a compliant vessel, consisting of a hyperelastic structure model coupled with a shear-thinning generalized Newtonian fluid, is used to represent the pressure wave propagation that characterizes blood flow in arteries, and several absorbing boundary conditions are analyzed in order to avoid the numerical spurious reflections due to the truncation of the domain. First, the 3D FSI model is coupled to a 1D hyperbolic model that captures very well the pulse propagation nature of blood flow in arteries. This coupling has been shown to be stable at the continuous level, and the 1D model proved to effectively absorb the pressure wave outgoing the 3D domain. Afterward, other absorbing boundary conditions, based on a simple analysis of the characteristics of the 1D hyperbolic model, are imposed directly on the outflow sections of the 3D FSI problem. These conditions, which can be identified with linear resistance models, relate the mean pressure with the volume flow rate at the artificial section at hand. Numerical results comparing the 3D-1D coupling and the different absorbing conditions in both idealized and realistic geometries, reconstructed from medical imaging, are discussed.