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

Abstract

Mathematical models and numerical methods are a powerful resource for better understanding phenomena and processes throughout the fluid dynamics field, allowing significant reductions in the costs, which would otherwise be required to perform laboratory experiments, and even allowing to obtain useful data that could not be gathered through measurements.The correct characterization of the interactions that occur between the fluid and the wall that surrounds it is a fundamental aspect in all contexts involving deformable ducts, which requires the utmost attention at every stage of both the development of the computational method and the interpretation of the results and their application to cases of practical interest.In this work, innovative mathematical models able to predict the behavior of the fluid-structure interaction (FSI) mechanism that underlies the dynamics of flows in different compliant ducts is presented. Starting from the purely civil engineering sector, with the study of plastic water pipelines, the final application of the proposed tool is linked to the medical research field, to reproduce the mechanics of blood flow in both arteries and veins. With this aim, various linear viscoelastic models, from the simplest to the more sophisticated, have been applied and extended to obtain augmented FSI systems in which the constitutive equation of the material is directly embedded into the system as partial differential equation [1]. These systems are solved recurring to second-order Finite Volume Methods that take into account the recent evolution in the computational literature of hyperbolic balance laws systems [2]. To avoid the loss of accuracy in the stiff regimes of the proposed systems, asymptotic-preserving IMEX 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 [3]. The models have been extensively validated through different types of test cases, highlighting the advantages of using the augmented formulation of the system of equations. Furthermore, comparisons with experimental data have been considered both for the water pipelines scenario and the blood flow modeling, recurring to in-vivo measurements for the latter.REFERENCES[1] Bertaglia, G., Caleffi, V. and Valiani, A. Modeling blood flow in viscoelastic vessels: the 1D augmented fluid-structure interaction system. Comput. Methods Appl. Mech. Eng., 360(C):112772 (2020).[2] Bertaglia, G., Ioriatti, M., Valiani, A., Dumbser, M. and Caleffi, V. Numerical methods for hydraulic transients in visco-elastic pipes. J. Fluids Struct., 81:230-254 (2018).[3] Pareschi, L. and Russo, G. Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation. J. Sci. Comput., 25:129-155 (2005).