Petr Sváček

Application of a Stabilized FEM to Problems of Aeroelasticity

This paper is concerned with modelling of fluid-structure interaction. We consider two-dimensional viscous incompressible flow past a moving airfoil, which is considered as a solid body with two degrees of freedom, allowing vertical and torsional oscillations of the airfoil. The fluid flow is simulated by the Navier-Stokes equations in the Arbitrary Lagrangian-Eulerian formulation, discretized by the finite element method. We describe the SUPG stabilization of the FEM, time discretization, equations describing the motion of the airfoil and the solution of the discrete problem. The solution of a test problem is presented.

Numerical modelling of aeroelastic behaviour of an airfoil in viscous incompressible flow

In this paper, the problem of the numerical approximation of a two-dimensional incompressible viscous fluid flow interacting with a flexible structure is considered. Due to high Reynolds numbers in the range 104-106 the turbulent character of the flow is considered and modelled with the aid of Reynolds equations coupled with the k-ω turbulence model. The structure motion is described by a system of ordinary differential equations for three degrees of freedom: vertical displacement, rotation and rotation of the aileron. The problem is discretized in space by the Galerkin Least-Squares stabilized finite element method and the computational domain is treated with the aid of Arbitrary Lagrangian Eulerian method.

On energy conservation for finite element approximation of flow-induced airfoil vibrations

In this paper the numerical approximation of a two-dimensional fluid-structure interaction problem is addressed. The fully coupled formulation of incompressible viscous fluid flow interacting with a flexibly supported airfoil is considered. The flow is described by the incompressible system of Navier-Stokes equations, where large values of the Reynolds number are considered. The Navier-Stokes equations are spatially discretized by the finite element method and stabilized with a modification of the Galerkin Least Squares (GLS) method; cf. [T. Gelhard, G. Lube, M.A. Olshanskii, J.-H. Starcke, Stabilized finite element schemes with LBB-stable elements for incompressible flows, Journal of Computational and Applied Mathematics 177 (2005) 243-267]. The motion of the computational domain is treated with the aid of Arbitrary Lagrangian Eulerian (ALE) method and the stabilizing terms are modified in a consistent way with the ALE formulation.

Numerical Solution of Fluid‐Structure Interaction Problems by Finite Element Method

In this paper the problem of the numerical approximation of a incompressible viscous fluid flow interacting with a flexible structure is considered. The problem is modelled with the aid of Reynolds equations together with k−ω turbulence model and structure motion is described by a system of ordinary differential equations. The problem is discretized in space by the Galerkin Least Squares stabilized FE method and the computational domain is treated with the aid of Arbitrary Lagrangian Eulerian method.

Numerical Solution of Flow in Backward Facing Step

The work deals with numerical testing of two different numerical methods based on finite volumes (FV) and finite elements (FE) for different Reynolds numbers. The finite volume method is based on upwind scheme (third order) for convective terms and central second order for dissipative terms. Finite element method consists of stabilization of weak formulation for higher Reynolds numbers with the help of streamline-upwind (Petrov-Galerkin) modification.

Numerical Simulation of Fluid–Structure Interaction Problems with Applications to Flow in Vocal Folds

Recently, the numerical solution of FSI problems has become important also in biomechanics, among others in voice modelling. The numerical analysis of this case is very complicated: Human voice is created by passage of air flow between vocal folds, where the constriction formed by the vocal folds induces acceleration of the flow and vocal fold oscillations, which generates the sound. The modelling of such a complex phenomenon encounters many difficulties as it is a result of coupling complex fluid dynamics and structural behavior. We focus on mathematical and numerical modelling of nonlinear coupled problems of fluid–structure interactions (FSI). The main attention is paid to the mathematical description of a relevant problem and to the description of the applied numerical methods. The mathematical description consists of the elasticity equations describing the motion of an elastic structure, and the air flow modelled by the Navier–Stokes equations. Both models are coupled via interface conditions.

Numerical Simulation of Interaction of Human Vocal Folds and Fluid Flow

Our goal is to simulate airflow in human vocal folds and their flow-induced vibrations. We consider two-dimensional viscous incompressible flow in a time-dependent domain. The fluid flow is described by the Navier-Stokes equations in the arbitrary Lagrangian-Eulerian formulation. The flow problem is coupled with the elastic behaviour of the solid bodies. The developed solution of the coupled problem based on the finite element method is demonstrated by numerical experiments.

On Numerical Approximation of Fluid-Structure Interaction Problems

In this paper the problem of mutual interaction fluid flow over an airfoil with control section is addressed. The numerical approximation of turbulent incompressible viscous flow modelled by Reynolds Averaged Navier-Stokes equations is described. The application of the method on an aeroelastic problem is shown.

On mathematical modeling of fluid-structure interactions with nonlinear effects

In this paper the numerical simulation of aeroelastic interactions of flexibly supported two-degrees of freedom (2-DOF) airfoil in two-dimensional (2D) incompressible viscous turbulent flow subjected to a gust (sudden change of flow conditions) is considered. The flow is modeled by Reynolds averaged Navier-Stokes equations (RANS), and by k - ω turbulence model. The considered flow problem is discretized in space using the fully stabilized finite element (FE) method implemented in the developed in-house program, which allows to solve interaction problems. In order to treat the time dependent inlet boundary condition the standard stabilization procedure was modified. Further, the under relaxation procedure was introduced in order to overcome the artificial instability of the coupling algorithm. The aeroelastic response to a sudden gust is numerically analyzed with the aid of the developed FE code.

On numerical simulation of three-dimensional flow problems by finite element and finite volume techniques

Abstract This paper is interested in the numerical approximation of the turbulent 3D incompressible flow. The turbulent flow is mathematically modeled using the Reynolds averaged Navier–Stokes (RANS) equations and two classes of the turbulent models are considered. RANS equations are approximated by two numerical techniques, the finite volume and the finite element methods. The finite element approximation on general 3D domains using general meshes consisting of hexahedrons as well as tetrahedrons, pyramids and prisms is described. The definition of the continuous piecewise trilinear/linear finite element space is given, and the stabilization based on the streamline-upwind/Petrov–Galerkin method together with the pressure stabilizing/Petrov–Galerkin techniques is used. The turbulence k – ω model is approximated on the finite element spaces, and the nonlinear stabilization technique is applied. Furthermore, the finite volume technique is used for the approximation of the RANS equations. The turbulent k – ω or the explicit algebraic Reynolds stress models are used. The numerical solution is carried out by the implicit finite volume method. The artificial compressibility method is used to solve the incompressibility constraint. The numerical results are shown.