This paper deals with a numerical solution of the interaction of two-dimensional (2-D) incompressible viscous flow and a vibrating profile NACA 0012 with large amplitudes. The laminar flow is described by the Navier-Stokes equations in... more
This paper deals with a numerical solution of the interaction of two-dimensional (2-D) incompressible viscous flow and a vibrating profile NACA 0012 with large amplitudes. The laminar flow is described by the Navier-Stokes equations in the arbitrary Lagrangian-Eulerian form. The profile with two degrees of freedom (2-DOF) can rotate around its elastic axis and oscillate in the vertical direction. Its motion is described by a nonlinear system of two ordinary differential equations. Deformations of the computational domain due to the profile motion are treated by the arbitrary Lagrangian-Eulerianmethod. The finite volume method and the finite element method are applied, and the numerical results are compared.
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summary: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... more
summary: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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In this paper the numerical approximation of turbulent and laminar incompressible turbulent flow is considered. The mathematical model is either based on incompressible Navier-Stokes equations or on Reynolds averaged Navier-Stokes (RANS)... more
In this paper the numerical approximation of turbulent and laminar incompressible turbulent flow is considered. The mathematical model is either based on incompressible Navier-Stokes equations or on Reynolds averaged Navier-Stokes (RANS) equations enclosed by a turbulence model. The problem is discretized in space by the finite element method, the detailed description of the stabilization shall be given and several aspects of approximation of the turbulence/transition model shall be given. The numerical results of the finite element method shall be presented.
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In this paper the numerical method for solution of an aeroelastic model describing the interactions of air flow with vocal folds is described. The flow is modelled by the incompressible Navier-Stokes equations spatially discretized with... more
In this paper the numerical method for solution of an aeroelastic model describing the interactions of air flow with vocal folds is described. The flow is modelled by the incompressible Navier-Stokes equations spatially discretized with the aid of the stabilized finite element method, [1]. The motion of the computational domain is treated with the aid of the Arbitrary Lagrangian Eulerian method. The structure dynamics is replaced by a mechanically equivalent system with the two degrees of freedom governed by a system of ordinary differential equations, see [2]. The structure model discretized in time with the aid of an implicit multistep method and strongly coupled with the flow model. The influence of inlet/outlet boundary conditions is studied and the attention is paid to the application of the physically correct boundary conditions in the case of closing of the channel. The numerical simulations are performed and compared to the related results.
The physical modeling and numerical simulation of the human phonation is very complex topic of ongoing research. Its numerical simulation is of quite importance in medicine today, see, e.g. [5]. In this coupled problem the three different... more
The physical modeling and numerical simulation of the human phonation is very complex topic of ongoing research. Its numerical simulation is of quite importance in medicine today, see, e.g. [5]. In this coupled problem the three different physical fields the deformation of the vocal folds (elastic body), the fluid flow and the acoustics have to be considered with all relevant coupling terms. Thereby, we consider the coupling between the fluid and the structure in a strong sense, whereas the acoustics filed is computed by a forward coupling from the fluid flow. The two-dimensional physical model of fluid-structure interaction problem is described by linear elasticity theory and by incompressible Navier-Stokes equations. In order to enable the change of domain shape in time, the arbitrary Lagrangian-Eulerian method is used. The sound sources are calculated by the Lighthill analogy or evaluated from perturbation equations [4, 2]. The numerical model is based on the finite element metho...
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The present paper is devoted to the numerical solution to flow in time-dependent domains with elastic walls. This problem has several applications in engineering and medicine. The flow is described by the system of Navier-Stokes... more
The present paper is devoted to the numerical solution to flow in time-dependent domains with elastic walls. This problem has several applications in engineering and medicine. The flow is described by the system of Navier-Stokes equations supplemented with suitable initial and boundary conditions. A part of the boundary of the region occupied by the fluid is represented by an elastic wall, whose deformation is driven by a hyperbolic partial differential equation with initial and boundary conditions. Its right-hand side represents the force by which the fluid flow acts on the elastic wall. A numerical method for solving this coupled problem is elaborated, based on the finite element method and the arbitrary Lagrangian-Eulerian (ALE) formulation of the equations describing the flow. The formulation and analysis of the problem together with discretization, algorithmization and programming of modules, which were added to an existing software package, is presented. The developed method ...
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In this paper the numerical simulation of the interaction of fluid flow with a flexibly supported aerofoil is addressed. Particularly, the turbulent flow model with a laminar-turbulence transition is considered. The transitional model is... more
In this paper the numerical simulation of the interaction of fluid flow with a flexibly supported aerofoil is addressed. Particularly, the turbulent flow model with a laminar-turbulence transition is considered. The transitional model is based on the two equation k − ω turbulence model, where the additional two equations for the intermittency and transitional onset Reynolds number are included. The motion of the computational domain is treated with the aid of the arbitrary Lagrangian-Eulerian method. The attention is paid mainly to the numerical approximation of the complex nonlinear coupled problem. The numerical results are shown for aeroelastic response of the aerofoil. Mathematical Subject Classification:
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Research Interests: Cognitive Science, Computer Science, Distributed Computing, Statistics, XML, and 14 moreVocabulary, Terminology, Distributed System, Probability, Discrete Mathematics, Data Structure, Computer Network, Computers Applications, World Wide Web, Adaptive System, Tutoring System, Implementation, Information System, and Test Method
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This paper describes the usage of the finite element library CFEM for solution of boundary value problems for partial differential equations. The application of the finite element method is shown based on the weak formulation of a... more
This paper describes the usage of the finite element library CFEM for solution of boundary value problems for partial differential equations. The application of the finite element method is shown based on the weak formulation of a boundary value problem. A unified approach for solution of linear scalar, linear vector, and nonlinear vector problems is presented. A direct link between the mathematical formulation and the design of the computer code is shown. Several examples and results are shown.
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This paper is interested in solution of two-dimensional aeroelastic problems. Two mathematical models are compared for a benchmark problem. First, the classical approach of linearized aerodynamical forces is described to determine the... more
This paper is interested in solution of two-dimensional aeroelastic problems. Two mathematical models are compared for a benchmark problem. First, the classical approach of linearized aerodynamical forces is described to determine the aeroelastic instability and the aeroelastic response in terms of frequency and damping coefficient. This approach is compared to the coupled fluid-structure model solved with the aid of finite element method used for approximation of the incompressible Navier-Stokes equations. The finite element approximations are coupled to the non-linear motion equations of a flexibly supported airfoil. Both methods are first compared for the case of small displacement, where the linearized approach can be well adopted. The influence of nonlinearities for the case of post-critical regime is discussed.
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This paper focuses on the mathematical modelling and the numerical approximation of the flow of two immiscible incompressible fluids,which is influenced by the surface tension and the contact angle effects. The weak formulation is... more
This paper focuses on the mathematical modelling and the numerical approximation of the flow of two immiscible incompressible fluids,which is influenced by the surface tension and the contact angle effects. The weak formulation is introduced, discretized in time, and the finite element method is applied. The surface tension effects are taken into account using the variational reformulation. The stability of the discrete problem is increased using the implicit formulation of the surface tension. The free surface motion is treated with the aid of the level set method. The numerical results are shown.
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ABSTRACT 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... more
ABSTRACT 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.
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ABSTRACT Problems with nonlinear boundary condition are studied on an elliptic 2nd order problem with nonlinear Newton boundary condition in a bounded two-dimensional domain. The main attention is paid to the analysis of the error... more
ABSTRACT Problems with nonlinear boundary condition are studied on an elliptic 2nd order problem with nonlinear Newton boundary condition in a bounded two-dimensional domain. The main attention is paid to the analysis of the error estimates. The effect of numerical integration is included. The obtained theoretical error estimates are documented on several numerical examples.
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This paper focuses on the mathematical and numerical modelling of interaction of the two-dimensional incompressible fluid flow and a flexibly supported airfoil section with a control section. A simplified problem is considered: The flow... more
This paper focuses on the mathematical and numerical modelling of interaction of the two-dimensional incompressible fluid flow and a flexibly supported airfoil section with a control section. A simplified problem is considered: The flow is modelled by the system of Navier-Stokes equations and 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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ABSTRACT We address the problem of the numerical approximation of the incompressible flow around a vibrating airfoil. The robust higher order finite element method (FEM) for incompressible flow approximation is presented. The method is... more
ABSTRACT We address the problem of the numerical approximation of the incompressible flow around a vibrating airfoil. The robust higher order finite element method (FEM) for incompressible flow approximation is presented. The method is based on the combination of several techniques, e.g., the Arbitrary Lagrangian-Eulerian formulation of the Navier-Stokes equations, the stabilization of the finite element scheme and the linearization of the discrete nonlinear problem.
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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 structure vibration is described by two... more
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 structure vibration is described by two nonlinear ordinary differential equations of motion for large vibration amplitudes. The flow is modeled by Reynolds averaged Navier-Stokes equations (RANS) and by k–ω turbulence model. The numerical simulation consists of the finite element (FE) solution of the RANS equations and the equations for the turbulent viscosity. This is coupled with the equations of motion for the airfoil by a strong coupling procedure. The time dependent computational domain and a moving grid are taken into account with the aid of the arbitrary Lagrangian-Eulerian formulation. In order to avoid spurious numerical oscillations, the SUPG and div-div stabilizations are applied. The solution of the ordinary differential equations is carried out by the Runge-Kutta method. The resulting nonlinear discrete algebraic systems are solved by the Oseen iterative process. The aeroelastic response to a sudden gust is numerically analyzed with the aid of the developed FE code. The gust responses exhibit similar oscillations as those found in literature.Copyright © 2014 by ASME
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The paper presents the comparison of numerical solution of a 2D aeroelastic problem and experimental results. For the numerical approximation the coupled formulation of a turbulent flow over an oscillating solid airfoil is considered. The... more
The paper presents the comparison of numerical solution of a 2D aeroelastic problem and experimental results. For the numerical approximation the coupled formulation of a turbulent flow over an oscillating solid airfoil is considered. The flow is modelled by the incompressible Reynolds averaged Navier–Stokes (RANS) equations rewritten in Arbitrary Lagrangian–Eulerian (ALE) form and discretized by the stabilized finite element method (FEM). The numerical results are compared with the results of optical measurements of flow field around an elastically supported vibrating double circular arc (DCA) 18% profile. The measurements were performed above the critical airflow velocity for loss of the system stability by flutter. The numerical results for the time dependent pressure distribution on the fluttering airfoil are presented.
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Abstract. In this paper we are concerned with numerical methods for fluid-structure interaction (FSI) problems and with their verification and validation. The fluid-structure interaction modelling is very complicated problem, where the... more
Abstract. In this paper we are concerned with numerical methods for fluid-structure interaction (FSI) problems and with their verification and validation. The fluid-structure interaction modelling is very complicated problem, where the most complicated and cruicial part is modelling of the fluid flow. Therefore the main interest of this paper is the numerical approximation of two dimensional incompressible viscous fluid over a flexibly supported profile. In technical problems the relevant Reynolds numbers are usually very high (104 − 106) and the fluid flow is turbulent. The correct numerical approximation requires very fine mesh refining as well as very small time steps involved in the computation. On the other hand in many technical applications the Reynolds Averaged NavierStokes equations are being used together with a suitable turbulence model. Here, both (laminar) Navier-Stokes equations as well as Reynolds Averaged Navier-Stokes equations are considered, numerically approximated by the Finite Element Method (FEM), stabilized by Galerkin-LeastSquares technique, and the obtained solution compared to the experimental data.
The paper focuses on numerical simulations of coupled fluid and structural models of aeroelasticity. The fluid motion is described by the incompressible Reynolds Av-eraged Navier-Stokes equations (RANS) coupled with Spallart-Almaras... more
The paper focuses on numerical simulations of coupled fluid and structural models of aeroelasticity. The fluid motion is described by the incompressible Reynolds Av-eraged Navier-Stokes equations (RANS) coupled with Spallart-Almaras turbulence model. The numerical solution by finite element method (FEM) stabilized with the Galerkin Least Squares (GLS) method is applied onto RANS system of equations. The Spallart-Almaras turbulence model is approximated by the FEM stabilized by the streamline upwind/Petrov-Galerkin (SUPG) method. The airfoil motion is described by a system of ordinary dif-ferential equations. The airfoil vibrations with large amplitudes result in deformations of the computational domain, which are treated with the aid of Arbitrary Lagrangian-Eulerian(ALE) method. Numerical results for several problems are compared to NAS-TRAN computations as well as to available experimental data.