Augmented fluid-structure interaction systems for viscoelastic pipelines and blood vessels

In this work, innovative 1D hyperbolic models able to predict the behavior of the fluid-structure interaction mechanism that underlies the dynamics of flows in different compliant ducts are presented. Starting from the study of plastic water pipelines, the proposed tool is then applied to the biomathematical field to reproduce the mechanics of blood flow in both arteries and veins. With this aim, various different viscoelastic models have been applied and extended to obtain augmented fluid-structure interaction systems in which the constitutive equation of the material is directly embedded into the system as partial differential equation. These systems are solved recurring to Finite Volume Methods that take into account the recent evolution in the computational literature of hyperbolic balance laws systems. To avoid the loss of accuracy in the stiff regimes of the proposed systems, asymptotic-preserving Implicit-Explicit Runge-Kutta schemes are considered for the time discretization, which are able to maintain the consistency and the accuracy in the diffusive limit, without restrictions due to the scaling parameters.