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On numerical approximation of fluid-structure interactions of air flow with a model of vocal folds
Valášek, J. ; Horáček, Jaromír ; Sváček, P.
This paper deals with flow driven vibration of an elastic body. Our goal is to develop and mathematically describe a simplified model of the human vocal fold. The developed numerical schemes for viscous incompressible fluid flow in ALE formulation and the elastic body are implemented by two solvers, specific for each domain. The studied problem is coupled by Dirichlet-Neumann boundary conditions. Both solvers are based on the finite element method. Particularly, for the fluid model the crossgrid elements are used. Numerical results focus on the verification of the developed program.
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On application of finite element method for approximation of 3D flow problems
Sváček, P. ; Horáček, Jaromír
This paper is interested to the interactions of the incompressible flow with a flexibly supported airfoil. The bending and the torsion modes are considered. The problem is mathematically described. The numerical method is based on the finite element method. A combination of the streamline-upwind/Petrov-Galerkin and pressure stabilizing/Petrov-Galerkin method is used for the stabilization of the finite element method. The numerical results for a three-dimensional problem of flow over an airfoil are shown.
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Finite element simulation of aeroelasticity problems
Horáček, Jaromír ; Sváček, P. ; Feistauer, M.
The paper presents results achieved by the authors in development of in-house codes based the finite element (FE) method and applied to solution of fluid-structure problems in aeroelasticity of airfoils. We consider flexibly supported airfoil with two- or three degrees of freedom (2- or3-DOF) in two-dimensional (2D) incompressible viscous flow. The airfoil vibration is described by nonlinear ordinary differential equations of motion for large vibration amplitudes. The flow is medeled by the Navier-Stokes equations for laminar flow or by the Reynolds averaged Navier-Stokes (RANS) equations for turbulent model.
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On mathematical modelling of gust response using the finite element method
Sváček, P. ; Horáček, Jaromír
In this paper the numerical approximation of aeroelastic response to sudden gust is presented. The fully coupled formulation of two dimensional incompressible viscous fluid flow over a flexibly supported structure is used. The flow is modelled with the system of Navier-Stokes equations written in Arbitrary Lagrangian-Eulerian form and coupled with system of ordinary differential equations describing the airfoil vibrations with two degrees of freedom. The Navier-Stokes equations are spatially discretized by the fully stabilized finite element method. The numerical results are shown.
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On higher-order space-time discretization of an nonlinear aeroelastic problem with the consideration of large displacements
Sváček, P. ; Horáček, Jaromír
This paper focuses on the mathematical and numerical modelling of interaction of the two-dimensional incompressible fluid flow and a flexibly supported airfoil section wit control section. A simplified problem is considered: The flow is modelled by the system of Navier-Stokes equations and the structure motion is described with the aid of nonlinear ordinary differential equations. The time-dependent computational domain is taken into account by the Arbitrary Lagrangian-Eulerian method. Higher order time discretization is considered within the stabilized finite element method. The application of the described method is shown.
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On approximation of an aeroelastic problem in post-critical regimes
Sváček, P. ; Horáček, Jaromír
This paper focused on the mathematical modelling and the numerical approximation of interactions of a simplified problem of the two-dimensional flow and flexibly supported airfoil section with control section. The flow is modelled with the aid of the incompressible Navier-Stokes equations and for the approximation the stabilized finite element method is used. The structure motion is described with the aid of nonlinear ordinary differential equations. The time-dependent computational domain is taken into account by the Arbitrary Lagrangian-Eulerian method.
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Numerical solution of flow over 2D backward facing step with different inclination angle
Louda, P. ; Sváček, P. ; Kozel, K. ; Příhoda, Jaromír
The finite-volume and finite-element techniques are used for the numerical simulation of the incompressible turbulent flows in a closed channel with a backward-facing step and with an inclined step under the angle 45 degree. A comparison of the finite-volume method based on the averaged Navier-Stokes equations closed by the explicit algebraic Reynolds stress model and the finite-element method using the Navier-Stokes equations with the two-equation k-eps model is presented. Numerical results are compared with experimental data of Makiola (1992).
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Interakce tekutiny se strukturou
Feistauer, M. ; Horáček, Jaromír ; Kučera, V. ; Prokopova, J. ; Sváček, Petr
Článek se zabývá jednak vibracemi profilu způsobené proudem tekutiny, jednak prouděním v kanálu s pohyblivými stěnami. Tento problém se vyskytuje např. v simulacích proudění lidskými hlasivkami. Vyvinutá nespojitá Galerkinova metoda konečných prvků (DGFEM) je slibná robustní metoda pro řešení stlačitelného proudění tekutin a v kombinaci s ALE metodou dovoluje řešit problémy proudění na časově závislých oblastech.
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