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Existence of a weak solution to a steady 2D fluid-1D elastic structure interaction problem with Tresca slip boundary condition

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  • Ayed, Hela
  • Baffico, Leonardo
  • Sassi, Taoufik

Abstract

We study a steady state fluid–structure interaction problem between an incompressible viscous Newtonian fluid and an elastic structure using a nonlinear boundary condition of friction type on the fluid–structure interface. This condition, also known as Tresca slip boundary condition, allows the fluid to slip on the interface when the tangential component of the fluid shear stress attains a certain threshold function. The governing equations are the 2D Stokes equations for the fluid, written in an unknown domain depending on the structure displacement, and the 1D Euler–Bernoulli model for the structure. We prove that there exists a weak solution of this nonlinear coupled problem by designing a proof based on the Schauder fixed-point theorem. The theoretical result will be illustrated with a numerical example.

Suggested Citation

  • Ayed, Hela & Baffico, Leonardo & Sassi, Taoufik, 2021. "Existence of a weak solution to a steady 2D fluid-1D elastic structure interaction problem with Tresca slip boundary condition," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 189(C), pages 253-275.
    • Handle: RePEc:eee:matcom:v:189:y:2021:i:c:p:253-275
    DOI: 10.1016/j.matcom.2020.12.032
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