This paper is concerned with the numerical simulation of a thermodynamically compatible
viscoelastic shear-thinning fluid model, particularly well suited to describe the
rheological response of blood, under physiological conditions. Numerical simulations are
performed in two idealized three-dimensional geometries, a stenosis and a curved vessel,
to investigate the combined effects of flow inertia, viscosity and viscoelasticity in
these geometries. The aim of this work is to provide new insights into the modeling and
simulation of homogeneous rheological models for blood and a basis for further
developments in modeling and prediction.