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On suitable inlet boundary conditions for fluid-structure interaction problems in a channel

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Abstract

We are interested in the numerical solution of a two-dimensional fluid-structure interaction problem. A special attention is paid to the choice of physically relevant inlet boundary conditions for the case of channel closing. Three types of the inlet boundary conditions are considered. Beside the classical Dirichlet and the do-nothing boundary conditions also a generalized boundary condition motivated by the penalization prescription of the Dirichlet boundary condition is applied. The fluid flow is described by the incompressible Navier-Stokes equations in the arbitrary Lagrangian-Eulerian (ALE) form and the elastic body creating a part of the channel wall is modelled with the aid of linear elasticity. Both models are coupled with the boundary conditions prescribed at the common interface.

The elastic and the fluid flow problems are approximated by the finite element method. The detailed derivation of the weak formulation including the boundary conditions is presented. The pseudo-elastic approach for construction of the ALE mapping is used. Results of numerical simulations for three considered inlet boundary conditions are compared. The flutter velocity is determined for a specific model problem and it is shown that the boundary condition with the penalization approach is suitable for the case of the fluid flow in a channel with vibrating walls.

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Authors and Affiliations

  1. Department of Technical Mathematics, Faculty of Mechanical Engineering, Czech Technical University in Prague, Karlovo nám. 13, Praha 2, Czech Republic

    Jan Valášek & Petr Sváček

  2. Center of Advanced Aerospace Technology, Faculty of Mechanical Engineering, Czech Technical University in Prague, Technická 4, 166 07, Praha 6, Czech Republic

    Jan Valášek & Petr Sváček

  3. Institute of Thermomechanics of the Czech Academy of Sciences, Dolejškova 1402/5, 182 00, Praha 8, Czech Republic

    Jaromír Horáček

Authors
  1. Jan Valášek
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  2. Petr Sváček
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Correspondence to Jan Valášek.

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Authors acknowledge support from the ESIF, EU Operational Programme Research, Development and Education, and from the Center of Advanced Aerospace Technology (CZ.02.1.01/0.0/0.0/16_019/0000826), Faculty of Mechanical Engineering, Czech Technical University in Prague and by Grant No. GA16-01246S of Czech Science Foundation

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Valášek, J., Sváček, P. & Horáček, J. On suitable inlet boundary conditions for fluid-structure interaction problems in a channel. Appl Math 64, 225–251 (2019). https://doi.org/10.21136/AM.2019.0267-18

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