  Mathematical models and numerical simulations are widely used in the field of
hemodynamics, representing a valuable resource to better understand
physiological and pathological processes. The theory behind the phenomenon is
closely related to the study of incompressible flow through compliant
thin-walled tubes. The mechanical interaction between blood flow and vessel
wall must be properly described by the model. Recent works show the benefits of
characterizing the rheology of the vessel wall through a viscoelastic law.
Considering the viscous contribution of the wall material and not simply the
elastic one leads to a more realistic representation of the vessel behavior,
which manifests not only an instantaneous elastic strain but also a viscous
damping effect on pulse pressure waves, coupled to energy losses. The aim of
this work is to propose an easily extensible 1D mathematical model able to
accurately capture the FSI. The originality lies in the introduction of a
viscoelastic tube law in PDE form, valid for both arterial and venous networks,
leading to an augmented FSI system. In contrast to well established
mathematical models, the proposed one is natively hyperbolic. The model is
solved with a 2nd-order numerical scheme based on an IMEX RK scheme conceived
for applications to hyperbolic systems with stiff relaxation terms. The
validation of the model is performed on different tests. Results obtained in
Riemann problems, adopting a simple elastic tube law for the characterization
of the vessel wall, are compared with available exact solutions. To validate
the contribution given by the viscoelastic term, the Method of Manufactured
Solutions is applied. Specific tests are designed to verify the well-balancing
and the AP property of the scheme. A specific test with an inlet pulse pressure
wave is designed to assess the effects of viscoelasticity.

Fluid Dynamics;Numerical Analysis;Analysis of PDEs;Numerical Analysis