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Poiseuille-Type Approximations for Axisymmetric Flow in a Thin Tube with Thin Stiff Elastic Wall

Author

Listed:
  • Kristina Kaulakytė

    (Institute of Applied Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko Str., 24, 03225 Vilnius, Lithuania)

  • Nikolajus Kozulinas

    (Institute of Applied Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko Str., 24, 03225 Vilnius, Lithuania)

  • Grigory Panasenko

    (Institute of Applied Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko Str., 24, 03225 Vilnius, Lithuania
    Institute Camille Jordan UMR CNRS 5208, University Jean Monnet, 23, Rue Dr Paul Michelon, 42023 Saint-Etienne, France)

  • Konstantinas Pileckas

    (Institute of Applied Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko Str., 24, 03225 Vilnius, Lithuania)

  • Vytenis Šumskas

    (Institute of Applied Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko Str., 24, 03225 Vilnius, Lithuania)

Abstract

An asymptotic ansatz for the solution of the axisymmetric problem of interaction between a thin cylindrical elastic tube and a viscous fluid filling the thin interior of the elastic tube was recently introduced and justified by G. Panasenko and R. Stavre. The thickness of the elastic medium ( ε ) and that of the fluid domain ( ε 1 ) are small parameters with ε < < ε 1 < < 1 , while the scale of the longitudinal characteristic size is of order one. At the same time, the magnitude of the stiffness and density of the elastic tube may be large or finite parameters with respect to the viscosity and density of the fluid when the characteristic time is of order one. This ansatz can be considered as a Poiseuille-type solution for the fluid–structure interaction problem. Its substitution to the Stokes fluid–elastic wall coupled problem generates a one-dimensional model. We present a numerical experiment comparing this model with the solution of the full-dimensional fluid–structure interaction problem.

Suggested Citation

  • Kristina Kaulakytė & Nikolajus Kozulinas & Grigory Panasenko & Konstantinas Pileckas & Vytenis Šumskas, 2023. "Poiseuille-Type Approximations for Axisymmetric Flow in a Thin Tube with Thin Stiff Elastic Wall," Mathematics, MDPI, vol. 11(9), pages 1-18, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2106-:d:1135985
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    References listed on IDEAS

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    1. David Evans, 2010. "From the Editor," CPI Journal, Competition Policy International, vol. 6.
    2. Gongbo Long & Yingjie Liu & Wanrong Xu & Peng Zhou & Jiaqi Zhou & Guanshui Xu & Boqi Xiao, 2022. "Analysis of Crack Problems in Multilayered Elastic Medium by a Consecutive Stiffness Method," Mathematics, MDPI, vol. 10(23), pages 1-16, November.
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