Consistent treatment of boundary conditions for blood flow modeling in networks of viscoelastic vessels

This work regards a numerical model for the simulation of blood flow in networks of viscoelastic vessels. The viscoelasticity of the vessels wall is treated with a Standard Linear Solid Model, from which a tube law in the form of a partial differential equation is derived and added to the system of governing equations. The innovative aspect consists in the congruent numerical treatment of the viscoelastic contribution in all boundary sections of the networks, namely inlet or outlet sections and junctions. For this purpose, a Riemann problem valid for these sections has been defined, which relies on an additional Riemann Invariant relating blood pressure and vessel lumen, besides the typical ones that relate blood velocity and pulse wave celerity.