Applications of Mathematics

, Volume 64, Issue 2, pp 225–251

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

• Jan Valášek
• Petr Sváček
• Jaromír Horáček
Article

## 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.

## Keywords

flow-induced vibration 2D incompressible Navier-Stokes equations linear elasticity inlet boundary conditions flutter instability

## MSC 2010

76D05 65N30 65N12

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## Authors and Affiliations

• Jan Valášek
• 1
• 2
Email author
• Petr Sváček
• 1
• 2
• Jaromír Horáček
• 3
1. 1.Department of Technical Mathematics, Faculty of Mechanical EngineeringCzech Technical University in PraguePraha 2Czech Republic
2. 2.Center of Advanced Aerospace Technology, Faculty of Mechanical EngineeringCzech Technical University in PraguePraha 6Czech Republic
3. 3.Institute of Thermomechanics of the Czech Academy of SciencesPraha 8Czech Republic