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

[EN] 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.Bertaglia, G. (2022). Augmented fluid-structure interaction systems for viscoelastic pipelines and blood vessels. En Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference. Editorial Universitat Politècnica de València. 431-438. https://doi.org/10.4995/YIC2021.2021.13450OCS43143

Augmented resolution of linear hyperbolic systems under nonconservative form

Hyperbolic systems under nonconservative form arise in numerous applications modeling physical processes, for example from the relaxation of more general equations (e.g. with dissipative terms). This paper reviews an existing class of augmented Roe schemes and discusses their application to linear nonconservative hyperbolic systems with source terms. We extend existing augmented methods by redefining them within a common framework which uses a geometric reinterpretation of source terms. This results in intrinsically well-balanced numerical discretizations. We discuss two equivalent formulations: (1) a nonconservative approach and (2) a conservative reformulation of the problem. The equilibrium properties of the schemes are examined and the conditions for the preservation of the well-balanced property are provided. Transient and steady state test cases for linear acoustics and hyperbolic heat equations are presented. A complete set of benchmark problems with analytical solution, including transient and steady situations with discontinuities in the medium properties, are presented and used to assess the equilibrium properties of the schemes. It is shown that the proposed schemes satisfy the expected equilibrium and convergence properties

Computational haemodynamics in stenotic internal jugular veins

Stenosis in internal jugular veins (IJVs) are frequently associated to pathological venous circulation and insufficient cerebral blood drainage. In this work, we set up a computational framework to assess the relevance of IJV stenoses through numerical simulation, combining medical imaging, patient-specific data and a mathematical model for venous occlusions. Coupling a three-dimensional (3D) description of blood flow in IJVs with a reduced one-dimesional model (1D) for major intracranial veins, we are able to model different anatomical configurations, an aspect of importance to understand the impact of IJV stenosis in intracranial venous haemodynamics. We investigate several stenotic configurations in a physiologic patient-specific regime, quantifying the effect of the stenosis in terms of venous pressure increase and wall shear stress patterns. Simulation results are in qualitative agreement with reported pressure anomalies in pathological cases. Moreover, they demonstrate the potential of the proposed multiscale framework for individualbased studies and computer-aided diagnosis

Computational haemodynamics in stenotic internal jugular veins

Stenosis in internal jugular veins (IJVs) are frequently associated to pathological venous circulation and insufficient cerebral blood drainage. In this work, we set up a computational framework to assess the relevance of IJV stenoses through numerical simulation, combining medical imaging, patient-specific data and a mathematical model for venous occlusions. Coupling a three-dimensional (3D) description of blood flow in IJVs with a reduced one-dimesional model (1D) for major intracranial veins, we are able to model different anatomical configurations, an aspect of importance to understand the impact of IJV stenosis in intracranial venous haemodynamics. We investigate several stenotic configurations in a physiologic patient-specific regime, quantifying the effect of the stenosis in terms of venous pressure increase and wall shear stress patterns. Simulation results are in qualitative agreement with reported pressure anomalies in pathological cases. Moreover, they demonstrate the potential of the proposed multiscale framework for individual-based studies and computer-aided diagnosis

Numerical modelling of open channel junctions using the Riemann problem approach

The solution of an extended Riemann problem is used to provide the internal boundary conditions at a junction when simulating one-dimensional flow through an open channel network. The proposed approach, compared to classic junction models, does not require the tuning of semi-empirical coefficients and it is theoretically well-founded. The Riemann problem approach is validated using experimental data, two-dimensional model results and analytical solutions. In particular, a set of experimental data is used to test each model under subcritical steady flow conditions, and different channel junctions are considered, with both continuous and discontinuous bottom elevation. Moreover, the numerical results are compared with analytical solutions in a star network to test unsteady conditions. Satisfactory results are obtained for all the simulations, and particularly for Y-shaped networks and for cases involving variations in channels' bottom and width. By contrast, classic models suffer when geometrical channel effects are involved