Petr Svacek - Academia.edu (original) (raw)

Papers by Petr Svacek

Research paper thumbnail of Simulation of Free Airfoil Vibrations in Incompressible Viscous Flow — Comparison of FEM and FVM

Acta Polytechnica

This paper deals with a numerical solution of the interaction of two-dimensional (2-D) incompress... 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.

Research paper thumbnail of On mathematical modelling of gust response using the finite element method

summary:In this paper the numerical approximation of aeroelastic response to sudden gust is prese... 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

Research paper thumbnail of On Mathematical Modelling of Flow Induced Vocal Folds Vibrations During Phonation

Springer Proceedings in Mathematics & Statistics

Research paper thumbnail of On finite element approximation of flow induced vibration of elastic structure

Programs and Algorithms of Numerical Mathematics 18, 2017

The classical Hermite-Hermite matrix polynomials for commutative matrices were first studied by M... more The classical Hermite-Hermite matrix polynomials for commutative matrices were first studied by Metwally et al. (2008). Our goal is to derive their basic properties including the orthogonality properties and Rodrigues formula. Furthermore, we define a new polynomial associated with the Hermite-Hermite matrix polynomials and establish the matrix differential equation associated with these polynomials. We give the addition theorems, multiplication theorems and summation formula for the Hermite-Hermite matrix polynomials. Finally, we establish general families and several new results concerning generalized Hermite-Hermite matrix polynomials.

Research paper thumbnail of On Finite Element Approximation of Aeroelastic Problems with Consideration of Laminar-Turbulence Transition

Lecture Notes in Computational Science and Engineering, 2020

Research paper thumbnail of The Flow-Induced Vibrations of Vocal Folds Approximated by the Finite Element Method

Lecture Notes in Mechanical Engineering, 2020

This paper is interested in mathematical model and numerical simulation of the flow-induced vibra... more This paper is interested in mathematical model and numerical simulation of the flow-induced vibrations of human vocal folds model. The elastic tissue of the vocal fold is described by the linear elasticity and the viscous fluid flow in the glottal channel is modelled with the aid of the incompressible Navier-Stokes equations. To incorporate the time change of the fluid domain into the flow description, the arbitrary Lagrangian-Eulerian (ALE) method is used. A special attention is paid to inlet boundary conditions. Besides the classical Dirichlet boundary condition the penalization approach is presented, which allows to relax the exact inlet velocity during the channel closing phase. Such a situation is highly interesting for simulation of human phonation. The developed numerical schemes for the fluid flow and the elastic body are implemented by an in-house solver based on the finite element method. Specially, the fluid flow scheme is approximated with the help of SUPG and PSPG stabilization methods. The implemented numerical partitioned scheme is strongly coupled. Finally, the numerical results of flow induced vibrations are presented and effects of the aforementioned inlet boundary conditions are discussed.

Research paper thumbnail of On Finite Element Approximation of Fluid-Structure Interactions with Consideration of Transition Model

Lecture Notes in Computational Science and Engineering, 2015

In this paper the numerical approximation of turbulent and laminar incompressible turbulent flow ... 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.

Research paper thumbnail of Numerical simulations of flow induced vocal folds vibrations

In this paper the numerical method for solution of an aeroelastic model describing the interactio... 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.

Research paper thumbnail of The comparison of different acoustic approaches in the simulation of human phonation

The physical modeling and numerical simulation of the human phonation is very complex topic of on... 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...

Research paper thumbnail of Numerical Simulation of Interaction Between Incompressible Flow and an Elastic Wall

The present paper is devoted to the numerical solution to flow in time-dependent domains with ela... 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 ...

Research paper thumbnail of Numerical Simulation of Turbulent Transitional Flow Around an Elastically

In this paper the numerical simulation of the interaction of fluid flow with a flexibly supported... 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:

Research paper thumbnail of Numerical simulation of turbulent transitional flow around an elastically supported aerofoil

Journal of Computational and Applied Mechanics, 2016

In this paper the numerical simulation of the interaction of fluid flow with a flexibly supported... 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.

Research paper thumbnail of Recent Advances in Computing

Applied Mathematics and Computation, 2018

Research paper thumbnail of Interactive Tutoring Model Using Information Cycling on the WWW

International Journal of Computers and Applications, 2003

The goal of this article is to describe a user system framework that provides tutoring and testin... more The goal of this article is to describe a user system framework that provides tutoring and testing. Because this tutoring system helps to introduce definitions and simple relations among concepts, it is suitable for classroom use. For every individual, the mode and amount of information delivered is personalized by the system order to achieve optimal information delivery, each user is characterized by a set of parameters. These parameters are used to minimize the time of the learning process. We consider only the parameters that we believe are the most significant, namely, the number of presentations that allow the user to pass a test without the need for future cycling of the same unit. The system was developed using the PHP and XML programming environment. We present preliminary classroom results along with statistical simulations of the system. Typical application domains were simple procedures from discrete mathematics, probability, computer science terminology, statistics, and elementary vocabulary. The presented implementation via the XML data structure is intended for the future WWW where servers can exchange tutorial materials developed by different authors.

Research paper thumbnail of Mathematical modelling and numerical simulation of flow induced vibrations of vocal folds model with collisions

CENTRAL EUROPEAN SYMPOSIUM ON THERMOPHYSICS 2019 (CEST), 2019

In this paper the problem of mutual interaction of incompressible viscous fluid flow with an elas... more In this paper the problem of mutual interaction of incompressible viscous fluid flow with an elastic structure is considered. A model problem of aiflow induced vibratioon of a simplified human vocal folds model is studied. The main attention is paid to the problem of the periodical collisions of vocal folds. First, these collisions are taken into account in the flow model by the application of a suitable inlet boundary condition. Further, in the structure model the contact is resolved with the aid of application of Hertz forces. Numerical results are shown.

Research paper thumbnail of On implementation aspects of finite element method and its application

Advances in Computational Mathematics, 2019

This paper describes the usage of the finite element library CFEM for solution of boundary value ... 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.

Research paper thumbnail of On the Application of Acoustic Analogies in the Numerical Simulation of Human Phonation Process

Flow, Turbulence and Combustion, 2018

This paper deals with the numerical simulation of the flow induced sound as generated in the huma... more This paper deals with the numerical simulation of the flow induced sound as generated in the human phonation process. The two-dimensional fluid-structure interaction problem is modeled with the aid of linear elastic problem coupled to the incompressible Navier-Stokes equations in the arbitrary Lagrangian-Eulerian form. For calculation of sound sources and its propagation the Lighthill acoustic analogy is used. This approach is compared to the Perturbed Convective Wave Equation method. All partial differential equations, describing the elastic body motion, the fluid flow and the acoustics, are solved by applying the finite element method. In order to overcome numerical instabilities in the Navier-Stokes equations arising due to high Reynolds numbers, the modified streamline-upwind/Petrov-Galerkin stabilization is used. The implemented iterative coupling procedure is described. Numerical results are presented.

Research paper thumbnail of On mathematical modelling of aeroelastic problems with finite element method

EPJ Web of Conferences, 2018

This paper is interested in solution of two-dimensional aeroelastic problems. Two mathematical mo... 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.

Research paper thumbnail of On numerical approximation of incompresible fluid flow with free surface influenced by surface tension

EPJ Web of Conferences, 2017

This paper deals with the numerical approximation of two immiscible incompressible fluids flow. T... more This paper deals with the numerical approximation of two immiscible incompressible fluids flow. The two-dimensional problem is mathematically described with the aid of the incompressible Navier-Stokes equations. The motion of the two phases is treated with the aid of level set method. The surface tension effects are taken into account as well as the contact angle influence. The problem is formulated in a weak sense and discretized with the aid of the finite element method. The details of the numerical methods are given and several possibilities of the realization of the surface tension term are discussed. Numerical results are shown.

Research paper thumbnail of On the Finite Element Method Application for Approximation of Free-Surface Flows with Surface Tension and Contact Angles

Applied Mechanics and Materials, 2016

This paper focuses on the mathematical modelling and the numerical approximation of the flow of t... 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.

Research paper thumbnail of Simulation of Free Airfoil Vibrations in Incompressible Viscous Flow — Comparison of FEM and FVM

Acta Polytechnica

This paper deals with a numerical solution of the interaction of two-dimensional (2-D) incompress... 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.

Research paper thumbnail of On mathematical modelling of gust response using the finite element method

summary:In this paper the numerical approximation of aeroelastic response to sudden gust is prese... 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

Research paper thumbnail of On Mathematical Modelling of Flow Induced Vocal Folds Vibrations During Phonation

Springer Proceedings in Mathematics & Statistics

Research paper thumbnail of On finite element approximation of flow induced vibration of elastic structure

Programs and Algorithms of Numerical Mathematics 18, 2017

The classical Hermite-Hermite matrix polynomials for commutative matrices were first studied by M... more The classical Hermite-Hermite matrix polynomials for commutative matrices were first studied by Metwally et al. (2008). Our goal is to derive their basic properties including the orthogonality properties and Rodrigues formula. Furthermore, we define a new polynomial associated with the Hermite-Hermite matrix polynomials and establish the matrix differential equation associated with these polynomials. We give the addition theorems, multiplication theorems and summation formula for the Hermite-Hermite matrix polynomials. Finally, we establish general families and several new results concerning generalized Hermite-Hermite matrix polynomials.

Research paper thumbnail of On Finite Element Approximation of Aeroelastic Problems with Consideration of Laminar-Turbulence Transition

Lecture Notes in Computational Science and Engineering, 2020

Research paper thumbnail of The Flow-Induced Vibrations of Vocal Folds Approximated by the Finite Element Method

Lecture Notes in Mechanical Engineering, 2020

This paper is interested in mathematical model and numerical simulation of the flow-induced vibra... more This paper is interested in mathematical model and numerical simulation of the flow-induced vibrations of human vocal folds model. The elastic tissue of the vocal fold is described by the linear elasticity and the viscous fluid flow in the glottal channel is modelled with the aid of the incompressible Navier-Stokes equations. To incorporate the time change of the fluid domain into the flow description, the arbitrary Lagrangian-Eulerian (ALE) method is used. A special attention is paid to inlet boundary conditions. Besides the classical Dirichlet boundary condition the penalization approach is presented, which allows to relax the exact inlet velocity during the channel closing phase. Such a situation is highly interesting for simulation of human phonation. The developed numerical schemes for the fluid flow and the elastic body are implemented by an in-house solver based on the finite element method. Specially, the fluid flow scheme is approximated with the help of SUPG and PSPG stabilization methods. The implemented numerical partitioned scheme is strongly coupled. Finally, the numerical results of flow induced vibrations are presented and effects of the aforementioned inlet boundary conditions are discussed.

Research paper thumbnail of On Finite Element Approximation of Fluid-Structure Interactions with Consideration of Transition Model

Lecture Notes in Computational Science and Engineering, 2015

In this paper the numerical approximation of turbulent and laminar incompressible turbulent flow ... 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.

Research paper thumbnail of Numerical simulations of flow induced vocal folds vibrations

In this paper the numerical method for solution of an aeroelastic model describing the interactio... 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.

Research paper thumbnail of The comparison of different acoustic approaches in the simulation of human phonation

The physical modeling and numerical simulation of the human phonation is very complex topic of on... 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...

Research paper thumbnail of Numerical Simulation of Interaction Between Incompressible Flow and an Elastic Wall

The present paper is devoted to the numerical solution to flow in time-dependent domains with ela... 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 ...

Research paper thumbnail of Numerical Simulation of Turbulent Transitional Flow Around an Elastically

In this paper the numerical simulation of the interaction of fluid flow with a flexibly supported... 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:

Research paper thumbnail of Numerical simulation of turbulent transitional flow around an elastically supported aerofoil

Journal of Computational and Applied Mechanics, 2016

In this paper the numerical simulation of the interaction of fluid flow with a flexibly supported... 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.

Research paper thumbnail of Recent Advances in Computing

Applied Mathematics and Computation, 2018

Research paper thumbnail of Interactive Tutoring Model Using Information Cycling on the WWW

International Journal of Computers and Applications, 2003

The goal of this article is to describe a user system framework that provides tutoring and testin... more The goal of this article is to describe a user system framework that provides tutoring and testing. Because this tutoring system helps to introduce definitions and simple relations among concepts, it is suitable for classroom use. For every individual, the mode and amount of information delivered is personalized by the system order to achieve optimal information delivery, each user is characterized by a set of parameters. These parameters are used to minimize the time of the learning process. We consider only the parameters that we believe are the most significant, namely, the number of presentations that allow the user to pass a test without the need for future cycling of the same unit. The system was developed using the PHP and XML programming environment. We present preliminary classroom results along with statistical simulations of the system. Typical application domains were simple procedures from discrete mathematics, probability, computer science terminology, statistics, and elementary vocabulary. The presented implementation via the XML data structure is intended for the future WWW where servers can exchange tutorial materials developed by different authors.

Research paper thumbnail of Mathematical modelling and numerical simulation of flow induced vibrations of vocal folds model with collisions

CENTRAL EUROPEAN SYMPOSIUM ON THERMOPHYSICS 2019 (CEST), 2019

In this paper the problem of mutual interaction of incompressible viscous fluid flow with an elas... more In this paper the problem of mutual interaction of incompressible viscous fluid flow with an elastic structure is considered. A model problem of aiflow induced vibratioon of a simplified human vocal folds model is studied. The main attention is paid to the problem of the periodical collisions of vocal folds. First, these collisions are taken into account in the flow model by the application of a suitable inlet boundary condition. Further, in the structure model the contact is resolved with the aid of application of Hertz forces. Numerical results are shown.

Research paper thumbnail of On implementation aspects of finite element method and its application

Advances in Computational Mathematics, 2019

This paper describes the usage of the finite element library CFEM for solution of boundary value ... 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.

Research paper thumbnail of On the Application of Acoustic Analogies in the Numerical Simulation of Human Phonation Process

Flow, Turbulence and Combustion, 2018

This paper deals with the numerical simulation of the flow induced sound as generated in the huma... more This paper deals with the numerical simulation of the flow induced sound as generated in the human phonation process. The two-dimensional fluid-structure interaction problem is modeled with the aid of linear elastic problem coupled to the incompressible Navier-Stokes equations in the arbitrary Lagrangian-Eulerian form. For calculation of sound sources and its propagation the Lighthill acoustic analogy is used. This approach is compared to the Perturbed Convective Wave Equation method. All partial differential equations, describing the elastic body motion, the fluid flow and the acoustics, are solved by applying the finite element method. In order to overcome numerical instabilities in the Navier-Stokes equations arising due to high Reynolds numbers, the modified streamline-upwind/Petrov-Galerkin stabilization is used. The implemented iterative coupling procedure is described. Numerical results are presented.

Research paper thumbnail of On mathematical modelling of aeroelastic problems with finite element method

EPJ Web of Conferences, 2018

This paper is interested in solution of two-dimensional aeroelastic problems. Two mathematical mo... 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.

Research paper thumbnail of On numerical approximation of incompresible fluid flow with free surface influenced by surface tension

EPJ Web of Conferences, 2017

This paper deals with the numerical approximation of two immiscible incompressible fluids flow. T... more This paper deals with the numerical approximation of two immiscible incompressible fluids flow. The two-dimensional problem is mathematically described with the aid of the incompressible Navier-Stokes equations. The motion of the two phases is treated with the aid of level set method. The surface tension effects are taken into account as well as the contact angle influence. The problem is formulated in a weak sense and discretized with the aid of the finite element method. The details of the numerical methods are given and several possibilities of the realization of the surface tension term are discussed. Numerical results are shown.

Research paper thumbnail of On the Finite Element Method Application for Approximation of Free-Surface Flows with Surface Tension and Contact Angles

Applied Mechanics and Materials, 2016

This paper focuses on the mathematical modelling and the numerical approximation of the flow of t... 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.