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

Jan Valášek; Petr Sváček; Jaromír Horáček

Applications of Mathematics (2019)

  • Volume: 64, Issue: 2, page 225-251
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Valášek, Jan, Sváček, Petr, and Horáček, Jaromír. "On suitable inlet boundary conditions for fluid-structure interaction problems in a channel." Applications of Mathematics 64.2 (2019): 225-251. <http://eudml.org/doc/294165>.

@article{Valášek2019,
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.},
author = {Valášek, Jan, Sváček, Petr, Horáček, Jaromír},
journal = {Applications of Mathematics},
keywords = {flow-induced vibration; 2D incompressible Navier-Stokes equations; linear elasticity; inlet boundary conditions; flutter instability},
language = {eng},
number = {2},
pages = {225-251},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On suitable inlet boundary conditions for fluid-structure interaction problems in a channel},
url = {http://eudml.org/doc/294165},
volume = {64},
year = {2019},
}

TY - JOUR
AU - Valášek, Jan
AU - Sváček, Petr
AU - Horáček, Jaromír
TI - On suitable inlet boundary conditions for fluid-structure interaction problems in a channel
JO - Applications of Mathematics
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 2
SP - 225
EP - 251
AB - 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.
LA - eng
KW - flow-induced vibration; 2D incompressible Navier-Stokes equations; linear elasticity; inlet boundary conditions; flutter instability
UR - http://eudml.org/doc/294165
ER -

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